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The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. For instance, metals typically have high thermal conductivity and are very efficient at conducting heat, while the opposite is true for
insulating materials This is a list of insulation materials used around the world. Typical R-values are given for various materials and structures as approximations based on the average of available figures and are sorted by lowest value.'' R-value at 1 n'' giv ...
like
Rockwool Mineral wool is any fibrous material formed by spinning or drawing molten mineral or rock materials such as slag and ceramics. Applications of mineral wool include thermal insulation (as both structural insulation and pipe insulation), f ...
or
Styrofoam Styrofoam is a trademarked brand of closed-cell extruded polystyrene foam (XPS), commonly called "Blue Board", manufactured as foam continuous building insulation board used in walls, roofs, and foundations as thermal insulation and water barrie ...
. Correspondingly, materials of high thermal conductivity are widely used in
heat sink A heat sink (also commonly spelled heatsink) is a passive heat exchanger that transfers the heat generated by an electronic or a mechanical device to a fluid medium, often air or a liquid coolant, where it is dissipated away from the device, th ...
applications, and materials of low thermal conductivity are used as
thermal insulation Thermal insulation is the reduction of heat transfer (i.e., the transfer of thermal energy between objects of differing temperature) between objects in thermal contact or in range of radiative influence. Thermal insulation can be achieved with s ...
. The reciprocal of thermal conductivity is called thermal resistivity. The defining equation for thermal conductivity is \mathbf = - k \nabla T, where \mathbf is the
heat flux Heat flux or thermal flux, sometimes also referred to as ''heat flux density'', heat-flow density or ''heat flow rate intensity'' is a flow of energy per unit area per unit time. In SI its units are watts per square metre (W/m2). It has both a ...
, k is the thermal conductivity, and \nabla T is the
temperature gradient A temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature gradient is a dimensional quantity expressed in units of degree ...
. This is known as
Fourier's Law Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its ''thermal conductivity'', and is denoted . Heat spontaneously flows along a tem ...
for heat conduction. Although commonly expressed as a
scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers * Scalar (physics), a physical quantity that can be described by a single element of a number field such ...
, the most general form of thermal conductivity is a second-rank
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...
. However, the tensorial description only becomes necessary in materials which are
anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
.


Definition


Simple definition

Consider a solid material placed between two environments of different temperatures. Let T_1 be the temperature at x=0 and T_2 be the temperature at x=L, and suppose T_2 > T_1. A possible realization of this scenario is a building on a cold winter day: the solid material in this case would be the building wall, separating the cold outdoor environment from the warm indoor environment. According to the
second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...
, heat will flow from the hot environment to the cold one as the temperature difference is equalized by diffusion. This is quantified in terms of a
heat flux Heat flux or thermal flux, sometimes also referred to as ''heat flux density'', heat-flow density or ''heat flow rate intensity'' is a flow of energy per unit area per unit time. In SI its units are watts per square metre (W/m2). It has both a ...
q, which gives the rate, per unit area, at which heat flows in a given direction (in this case minus x-direction). In many materials, q is observed to be directly proportional to the temperature difference and inversely proportional to the separation distance L: : q = -k \cdot \frac. The constant of proportionality k is the thermal conductivity; it is a physical property of the material. In the present scenario, since T_2 > T_1 heat flows in the minus x-direction and q is negative, which in turn means that k>0. In general, k is always defined to be positive. The same definition of k can also be extended to gases and liquids, provided other modes of energy transport, such as
convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...
and
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visi ...
, are eliminated or accounted for. The preceding derivation assumes that the k does not change significantly as temperature is varied from T_1 to T_2. Cases in which the temperature variation of k is non-negligible must be addressed using the more general definition of k discussed below.


General definition

Thermal conduction is defined as the transport of energy due to random molecular motion across a temperature gradient. It is distinguished from energy transport by convection and molecular work in that it does not involve macroscopic flows or work-performing internal stresses. Energy flow due to thermal conduction is classified as heat and is quantified by the vector \mathbf(\mathbf, t), which gives the heat flux at position \mathbf and time t. According to the second law of thermodynamics, heat flows from high to low temperature. Hence, it is reasonable to postulate that \mathbf(\mathbf, t) is proportional to the gradient of the temperature field T(\mathbf, t), i.e. : \mathbf(\mathbf, t) = -k \nabla T(\mathbf, t), where the constant of proportionality, k > 0, is the thermal conductivity. This is called Fourier's law of heat conduction. Despite its name, it is not a law but a definition of thermal conductivity in terms of the independent physical quantities \mathbf(\mathbf, t) and T(\mathbf, t). As such, its usefulness depends on the ability to determine k for a given material under given conditions. The constant k itself usually depends on T(\mathbf, t) and thereby implicitly on space and time. An explicit space and time dependence could also occur if the material is inhomogeneous or changing with time. In some solids, thermal conduction is
anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
, i.e. the heat flux is not always parallel to the temperature gradient. To account for such behavior, a tensorial form of Fourier's law must be used: : \mathbf(\mathbf, t) = -\boldsymbol \cdot \nabla T(\mathbf, t) where \boldsymbol is symmetric, second-rank
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...
called the thermal conductivity tensor. An implicit assumption in the above description is the presence of
local thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermod ...
, which allows one to define a temperature field T(\mathbf, t). This assumption could be violated in systems that are unable to attain local equilibrium, as might happen in the presence of strong nonequilibrium driving or long-ranged interactions.


Other quantities

In engineering practice, it is common to work in terms of quantities which are derivative to thermal conductivity and implicitly take into account design-specific features such as component dimensions. For instance, thermal conductance is defined as the quantity of heat that passes in unit time through a plate of ''particular area and thickness'' when its opposite faces differ in temperature by one kelvin. For a plate of thermal conductivity k, area A and thickness L, the conductance is kA/L, measured in W⋅K−1.Bejan, p. 34 The relationship between thermal conductivity and conductance is analogous to the relationship between
electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allow ...
and
electrical conductance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual paralle ...
. Thermal resistance is the inverse of thermal conductance. It is a convenient measure to use in multicomponent design since thermal resistances are additive when occurring in
series Series may refer to: People with the name * Caroline Series (born 1951), English mathematician, daughter of George Series * George Series (1920–1995), English physicist Arts, entertainment, and media Music * Series, the ordered sets used in ...
. There is also a measure known as the
heat transfer coefficient In thermodynamics, the heat transfer coefficient or film coefficient, or film effectiveness, is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat (i.e., the temperature difference, ). ...
: the quantity of heat that passes per unit time through a unit area of a plate of particular thickness when its opposite faces differ in temperature by one kelvin. In
ASTM ASTM International, formerly known as American Society for Testing and Materials, is an international standards organization that develops and publishes voluntary consensus technical standards for a wide range of materials, products, systems, an ...
C168-15, this area-independent quantity is referred to as the "thermal conductance".ASTM C168 − 15a Standard Terminology Relating to Thermal Insulation. The reciprocal of the heat transfer coefficient is thermal insulance. In summary, for a plate of thermal conductivity k, area A and thickness L, *thermal conductance = kA/L, measured in W⋅K−1. **thermal resistance = L/(kA), measured in K⋅W−1. *heat transfer coefficient = k/L, measured in W⋅K−1⋅m−2. **thermal insulance = L/k, measured in K⋅m2⋅W−1. The heat transfer coefficient is also known as thermal admittance in the sense that the material may be seen as admitting heat to flow. An additional term,
thermal transmittance Thermal transmittance is the rate of transfer of heat through matter. The thermal transmittance of a material (such as insulation or concrete) or an assembly (such as a wall or window) is expressed as a U-value. The thermal insulance of a structu ...
, quantifies the thermal conductance of a structure along with heat transfer due to
convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...
and
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visi ...
. It is measured in the same units as thermal conductance and is sometimes known as the ''composite thermal conductance''. The term ''
U-value In the context of construction, the R-value is a measure of how well a two-dimensional barrier, such as a layer of insulation, a window or a complete wall or ceiling, resists the conductive flow of heat. R-value is the temperature difference per ...
'' is also used. Finally,
thermal diffusivity In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It measures the rate of transfer of heat of a material from the hot end to the cold end. It has the SI ...
\alpha combines thermal conductivity with
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
and
specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
: :\alpha = \frac. As such, it quantifies the ''thermal inertia'' of a material, i.e. the relative difficulty in heating a material to a given temperature using heat sources applied at the boundary.


Units

In the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI), thermal conductivity is measured in
watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
s per metre-kelvin ( W/( mK)). Some papers report in watts per centimetre-kelvin (W/(cm⋅K)). In
imperial units The imperial system of units, imperial system or imperial units (also known as British Imperial or Exchequer Standards of 1826) is the system of units first defined in the British Weights and Measures Act 1824 and continued to be developed thro ...
, thermal conductivity is measured in
BTU The British thermal unit (BTU or Btu) is a unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is also part of the United States customary units. The modern SI u ...
/( hft°F).1 Btu/(h⋅ft⋅°F) = 1.730735 W/(m⋅K) The
dimension In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...
of thermal conductivity is M1L1T−3Θ−1, expressed in terms of the dimensions mass (M), length (L), time (T), and temperature (Θ). Other units which are closely related to the thermal conductivity are in common use in the construction and textile industries. The construction industry makes use of measures such as the R-value (resistance) and the
U-value In the context of construction, the R-value is a measure of how well a two-dimensional barrier, such as a layer of insulation, a window or a complete wall or ceiling, resists the conductive flow of heat. R-value is the temperature difference per ...
(transmittance or conductance). Although related to the thermal conductivity of a material used in an insulation product or assembly, R- and U-values are measured per unit area, and depend on the specified thickness of the product or assembly.R-values and U-values quoted in the US (based on the inch-pound units of measurement) do not correspond with and are not compatible with those used outside the US (based on the SI units of measurement). Likewise the textile industry has several units including the tog and the clo which express thermal resistance of a material in a way analogous to the R-values used in the construction industry.


Measurement

There are several ways to measure thermal conductivity; each is suitable for a limited range of materials. Broadly speaking, there are two categories of measurement techniques: ''steady-state'' and ''transient''. Steady-state techniques infer the thermal conductivity from measurements on the state of a material once a steady-state temperature profile has been reached, whereas transient techniques operate on the instantaneous state of a system during the approach to steady state. Lacking an explicit time component, steady-state techniques do not require complicated
signal analysis Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, di ...
(steady state implies constant signals). The disadvantage is that a well-engineered experimental setup is usually needed, and the time required to reach steady state precludes rapid measurement. In comparison with solid materials, the thermal properties of fluids are more difficult to study experimentally. This is because in addition to thermal conduction, convective and radiative energy transport are usually present unless measures are taken to limit these processes. The formation of an insulating boundary layer can also result in an apparent reduction in the thermal conductivity.


Experimental values

The thermal conductivities of common substances span at least four orders of magnitude. Gases generally have low thermal conductivity, and pure metals have high thermal conductivity. For example, under
standard conditions Standard temperature and pressure (STP) are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union ...
the thermal conductivity of
copper Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkis ...
is over times that of air. Of all materials,
allotropes Allotropy or allotropism () is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of the elements. Allotropes are different structural modifications of an element: th ...
of carbon, such as
graphite Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on large ...
and
diamond Diamond is a Allotropes of carbon, solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the Chemical stability, chemically stable form of car ...
, are usually credited with having the highest thermal conductivities at room temperature. The thermal conductivity of natural diamond at room temperature is several times higher than that of a highly conductive metal such as copper (although the precise value varies depending on the
diamond type Diamond type is a method of scientifically classifying diamonds by the level and type of their chemical impurities. Diamonds are separated into five types: Type Ia, Type Ib, Type 1aB, Type IIa, and Type IIb. The impurities measu ...
)."Thermal Conductivity in W cm−1 K−1 of Metals and Semiconductors as a Function of Temperature", in CRC Handbook of Chemistry and Physics, 99th Edition (Internet Version 2018), John R. Rumble, ed., CRC Press/Taylor & Francis, Boca Raton, FL. Thermal conductivities of selected substances are tabulated below; an expanded list can be found in the
list of thermal conductivities In heat transfer, the thermal conductivity of a substance, ''k'', is an intensive property that indicates its ability to conduct heat. For most materials, the amount of heat conducted varies (usually non-linearly) with temperature. Thermal con ...
. These values are illustrative estimates only, as they do not account for measurement uncertainties or variability in material definitions.


Influencing factors


Temperature

The effect of temperature on thermal conductivity is different for metals and nonmetals. In metals, heat conductivity is primarily due to free electrons. Following the
Wiedemann–Franz law In physics, the Wiedemann–Franz law states that the ratio of the electronic contribution of the thermal conductivity (''κ'') to the electrical conductivity (''σ'') of a metal is proportional to the temperature (''T''). : \frac \kapp ...
, thermal conductivity of metals is approximately proportional to the absolute temperature (in
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phys ...
s) times electrical conductivity. In pure metals the electrical conductivity decreases with increasing temperature and thus the product of the two, the thermal conductivity, stays approximately constant. However, as temperatures approach absolute zero, the thermal conductivity decreases sharply. In alloys the change in electrical conductivity is usually smaller and thus thermal conductivity increases with temperature, often proportionally to temperature. Many pure metals have a peak thermal conductivity between 2 K and 10 K. On the other hand, heat conductivity in nonmetals is mainly due to lattice vibrations (
phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...
s). Except for high-quality crystals at low temperatures, the phonon mean free path is not reduced significantly at higher temperatures. Thus, the thermal conductivity of nonmetals is approximately constant at high temperatures. At low temperatures well below the
Debye temperature In thermodynamics and solid-state physics, the Debye model is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat (Heat capacity) in a solid. It treats the vibrations of the atomic lattice (hea ...
, thermal conductivity decreases, as does the heat capacity, due to carrier scattering from defects.


Chemical phase

When a material undergoes a phase change (e.g. from solid to liquid), the thermal conductivity may change abruptly. For instance, when ice melts to form liquid water at 0 °C, the thermal conductivity changes from 2.18 W/(m⋅K) to 0.56 W/(m⋅K). Even more dramatically, the thermal conductivity of a fluid diverges in the vicinity of the vapor-liquid critical point.


Thermal anisotropy

Some substances, such as non- cubic
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
s, can exhibit different thermal conductivities along different crystal axes.
Sapphire Sapphire is a precious gemstone, a variety of the mineral corundum, consisting of aluminium oxide () with trace amounts of elements such as iron, titanium, chromium, vanadium, or magnesium. The name sapphire is derived via the Latin "sapphir ...
is a notable example of variable thermal conductivity based on orientation and temperature, with 35 W/(m⋅K) along the c axis and 32 W/(m⋅K) along the a axis.
Wood Wood is a porous and fibrous structural tissue found in the stems and roots of trees and other woody plants. It is an organic materiala natural composite of cellulose fibers that are strong in tension and embedded in a matrix of lignin th ...
generally conducts better along the grain than across it. Other examples of materials where the thermal conductivity varies with direction are metals that have undergone heavy cold pressing,
laminated Lamination is the technique/process of manufacturing a material in multiple layers, so that the composite material achieves improved strength, stability, sound insulation, appearance, or other properties from the use of the differing materia ...
materials, cables, the materials used for the
Space Shuttle thermal protection system The Space Shuttle thermal protection system (TPS) is the barrier that protected the Space Shuttle Orbiter during the searing heat of atmospheric reentry. A secondary goal was to protect from the heat and cold of space while in orbit. Material ...
, and
fiber-reinforced composite __NOTOC__ A fiber-reinforced composite (FRC) is a composite building material that consists of three components:Serope Kalpakjian, Steven R Schmid. "Manufacturing Engineering and Technology". International edition. 4th Ed. Prentice Hall, Inc. 2001 ...
structures. When anisotropy is present, the direction of heat flow may differ from the direction of the thermal gradient.


Electrical conductivity

In metals, thermal conductivity is approximately correlated with electrical conductivity according to the
Wiedemann–Franz law In physics, the Wiedemann–Franz law states that the ratio of the electronic contribution of the thermal conductivity (''κ'') to the electrical conductivity (''σ'') of a metal is proportional to the temperature (''T''). : \frac \kapp ...
, as freely moving
valence electron In chemistry and physics, a valence electron is an electron in the outer shell associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed. In a single covalent bond, a shared pair forms ...
s transfer not only electric current but also heat energy. However, the general correlation between electrical and thermal conductance does not hold for other materials, due to the increased importance of
phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...
carriers for heat in non-metals. Highly electrically conductive
silver Silver is a chemical element with the Symbol (chemistry), symbol Ag (from the Latin ', derived from the Proto-Indo-European wikt:Reconstruction:Proto-Indo-European/h₂erǵ-, ''h₂erǵ'': "shiny" or "white") and atomic number 47. A soft, whi ...
is less thermally conductive than
diamond Diamond is a Allotropes of carbon, solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the Chemical stability, chemically stable form of car ...
, which is an
electrical insulator An electrical insulator is a material in which electric current does not flow freely. The atoms of the insulator have tightly bound electrons which cannot readily move. Other materials—semiconductors and conductors—conduct electric current ...
but conducts heat via phonons due to its orderly array of atoms.


Magnetic field

The influence of magnetic fields on thermal conductivity is known as the
thermal Hall effect In solid-state physics, the thermal Hall effect, also known as the Righi–Leduc effect, named after independent co-discoverers Augusto Righi and Sylvestre Anatole Leduc, is the thermal analog of the Hall effect. Given a thermal gradient across a so ...
or Righi–Leduc effect.


Gaseous phases

In the absence of convection, air and other gases are good insulators. Therefore, many insulating materials function simply by having a large number of gas-filled pockets which obstruct heat conduction pathways. Examples of these include expanded and extruded
polystyrene Polystyrene (PS) is a synthetic polymer made from monomers of the aromatic hydrocarbon styrene. Polystyrene can be solid or foamed. General-purpose polystyrene is clear, hard, and brittle. It is an inexpensive resin per unit weight. It is a ...
(popularly referred to as "styrofoam") and silica
aerogel Aerogels are a class of synthetic porous ultralight material derived from a gel, in which the liquid component for the gel has been replaced with a gas, without significant collapse of the gel structure. The result is a solid with extremely low ...
, as well as warm clothes. Natural, biological insulators such as fur and
feathers Feathers are epidermal growths that form a distinctive outer covering, or plumage, on both avian (bird) and some non-avian dinosaurs and other archosaurs. They are the most complex integumentary structures found in vertebrates and a premier e ...
achieve similar effects by trapping air in pores, pockets, or voids. Low density gases, such as
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
and
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
typically have high thermal conductivity. Dense gases such as
xenon Xenon is a chemical element with the symbol Xe and atomic number 54. It is a dense, colorless, odorless noble gas found in Earth's atmosphere in trace amounts. Although generally unreactive, it can undergo a few chemical reactions such as the ...
and dichlorodifluoromethane have low thermal conductivity. An exception,
sulfur hexafluoride Sulfur hexafluoride or sulphur hexafluoride (British spelling) is an inorganic compound with the formula SF6. It is a colorless, odorless, non- flammable, and non-toxic gas. has an octahedral geometry, consisting of six fluorine atoms attached ...
, a dense gas, has a relatively high thermal conductivity due to its high
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity i ...
.
Argon Argon is a chemical element with the symbol Ar and atomic number 18. It is in group 18 of the periodic table and is a noble gas. Argon is the third-most abundant gas in Earth's atmosphere, at 0.934% (9340 ppmv). It is more than twice as abu ...
and
krypton Krypton (from grc, κρυπτός, translit=kryptos 'the hidden one') is a chemical element with the symbol Kr and atomic number 36. It is a colorless, odorless, tasteless noble gas that occurs in trace amounts in the atmosphere and is often ...
, gases denser than air, are often used in
insulated glazing Insulating glass (IG) consists of two or more glass window panes separated by a space to reduce heat transfer across a part of the building envelope. A window with insulating glass is commonly known as double glazing or a double-paned window, ...
(double paned windows) to improve their insulation characteristics. The thermal conductivity through bulk materials in porous or granular form is governed by the type of gas in the gaseous phase, and its pressure. At low pressures, the thermal conductivity of a gaseous phase is reduced, with this behaviour governed by the
Knudsen number The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. This length scale could be, for example, the radius of a body in a fluid. The number is named ...
, defined as K_n=l/d, where l is the
mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...
of gas molecules and d is the typical gap size of the space filled by the gas. In a granular material d corresponds to the characteristic size of the gaseous phase in the pores or intergranular spaces.


Isotopic purity

The thermal conductivity of a crystal can depend strongly on isotopic purity, assuming other lattice defects are negligible. A notable example is diamond: at a temperature of around 100 K the thermal conductivity increases from 10,000 W· m−1· K−1 for natural type IIa diamond (98.9% 12C), to 41,000 for 99.9% enriched synthetic diamond. A value of 200,000 is predicted for 99.999% 12C at 80 K, assuming an otherwise pure crystal. The thermal conductivity of 99% isotopically enriched cubic boron nitride is ~ 1400 W· m−1· K−1, which is 90% higher than that of natural boron nitride.


Molecular origins

The molecular mechanisms of thermal conduction vary among different materials, and in general depend on details of the microscopic structure and molecular interactions. As such, thermal conductivity is difficult to predict from first-principles. Any expressions for thermal conductivity which are exact and general, e.g. the Green-Kubo relations, are difficult to apply in practice, typically consisting of averages over multiparticle correlation functions. A notable exception is a monatomic dilute gas, for which a well-developed theory exists expressing thermal conductivity accurately and explicitly in terms of molecular parameters. In a gas, thermal conduction is mediated by discrete molecular collisions. In a simplified picture of a solid, thermal conduction occurs by two mechanisms: 1) the migration of free electrons and 2) lattice vibrations (
phonons In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phonon is an excited state in the quantum mechanic ...
). The first mechanism dominates in pure metals and the second in non-metallic solids. In liquids, by contrast, the precise microscopic mechanisms of thermal conduction are poorly understood.


Gases

In a simplified model of a dilute
monatomic In physics and chemistry, "monatomic" is a combination of the words "mono" and "atomic", and means "single atom". It is usually applied to gases: a monatomic gas is a gas in which atoms are not bound to each other. Examples at standard conditions ...
gas, molecules are modeled as rigid spheres which are in constant motion, colliding elastically with each other and with the walls of their container. Consider such a gas at temperature T and with density \rho,
specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
c_v and
molecular mass The molecular mass (''m'') is the mass of a given molecule: it is measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quanti ...
m. Under these assumptions, an elementary calculation yields for the thermal conductivity : k = \beta \rho \lambda c_v \sqrt, where \beta is a numerical constant of order 1, k_\text is the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
, and \lambda is the
mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...
, which measures the average distance a molecule travels between collisions. Since \lambda is inversely proportional to density, this equation predicts that thermal conductivity is independent of density for fixed temperature. The explanation is that increasing density increases the number of molecules which carry energy but decreases the average distance \lambda a molecule can travel before transferring its energy to a different molecule: these two effects cancel out. For most gases, this prediction agrees well with experiments at pressures up to about 10
atmospheres The standard atmosphere (symbol: atm) is a unit of pressure defined as Pa. It is sometimes used as a ''reference pressure'' or ''standard pressure''. It is approximately equal to Earth's average atmospheric pressure at sea level. History The s ...
. On the other hand, experiments show a more rapid increase with temperature than k \propto \sqrt (here, \lambda is independent of T). This failure of the elementary theory can be traced to the oversimplified "elastic sphere" model, and in particular to the fact that the interparticle attractions, present in all real-world gases, are ignored. To incorporate more complex interparticle interactions, a systematic approach is necessary. One such approach is provided by
Chapman–Enskog theory Chapman–Enskog theory provides a framework in which equations of hydrodynamics for a gas can be derived from the Boltzmann equation. The technique justifies the otherwise phenomenological constitutive relations appearing in hydrodynamical descri ...
, which derives explicit expressions for thermal conductivity starting from the
Boltzmann equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerne ...
. The Boltzmann equation, in turn, provides a statistical description of a dilute gas for ''generic'' interparticle interactions. For a monatomic gas, expressions for k derived in this way take the form : k = \frac \frac c_v, where \sigma is an effective particle diameter and \Omega(T) is a function of temperature whose explicit form depends on the interparticle interaction law. For rigid elastic spheres, \Omega(T) is independent of T and very close to 1. More complex interaction laws introduce a weak temperature dependence. The precise nature of the dependence is not always easy to discern, however, as \Omega(T) is defined as a multi-dimensional integral which may not be expressible in terms of elementary functions. An alternate, equivalent way to present the result is in terms of the gas
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
\mu, which can also be calculated in the Chapman–Enskog approach: : k = f \mu c_v, where f is a numerical factor which in general depends on the molecular model. For smooth spherically symmetric molecules, however, f is very close to 2.5, not deviating by more than 1% for a variety of interparticle force laws.Chapman & Cowling, p. 247 Since k, \mu, and c_v are each well-defined physical quantities which can be measured independent of each other, this expression provides a convenient test of the theory. For monatomic gases, such as the
noble gases The noble gases (historically also the inert gases; sometimes referred to as aerogens) make up a class of chemical elements with similar properties; under standard conditions, they are all odorless, colorless, monatomic gases with very low chemi ...
, the agreement with experiment is fairly good. For gases whose molecules are not spherically symmetric, the expression k = f \mu c_v still holds. In contrast with spherically symmetric molecules, however, f varies significantly depending on the particular form of the interparticle interactions: this is a result of the energy exchanges between the internal and translational
degrees of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...
of the molecules. An explicit treatment of this effect is difficult in the Chapman–Enskog approach. Alternately, the approximate expression f = (1/4) was suggested by Eucken, where \gamma is the
heat capacity ratio In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volu ...
of the gas. The entirety of this section assumes the mean free path \lambda is small compared with macroscopic (system) dimensions. In extremely dilute gases this assumption fails, and thermal conduction is described instead by an apparent thermal conductivity which decreases with density. Ultimately, as the density goes to 0 the system approaches a
vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
, and thermal conduction ceases entirely.


Liquids

The exact mechanisms of thermal conduction are poorly understood in liquids: there is no molecular picture which is both simple and accurate. An example of a simple but very rough theory is that of Bridgman, in which a liquid is ascribed a local molecular structure similar to that of a solid, i.e. with molecules located approximately on a lattice. Elementary calculations then lead to the expression : k = 3(N_\text / V)^ k_\text v_\text, where N_\text is the
Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining con ...
, V is the volume of a
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
of liquid, and v_\text is the
speed of sound The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as w ...
in the liquid. This is commonly called ''Bridgman's equation''.


Metals

For metals at low temperatures the heat is carried mainly by the free electrons. In this case the mean velocity is the Fermi velocity which is temperature independent. The mean free path is determined by the impurities and the crystal imperfections which are temperature independent as well. So the only temperature-dependent quantity is the heat capacity ''c'', which, in this case, is proportional to ''T''. So :k=k_0\,T \text with ''k''0 a constant. For pure metals, ''k''0 is large, so the thermal conductivity is high. At higher temperatures the mean free path is limited by the phonons, so the thermal conductivity tends to decrease with temperature. In alloys the density of the impurities is very high, so ''l'' and, consequently ''k'', are small. Therefore, alloys, such as stainless steel, can be used for thermal insulation.


Lattice waves

Heat transport in both amorphous and crystalline
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
solids is by way of elastic vibrations of the lattice (i.e.,
phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...
s). This transport mechanism is theorized to be limited by the elastic scattering of acoustic phonons at lattice defects. This has been confirmed by the experiments of Chang and Jones on commercial glasses and glass ceramics, where the mean free paths were found to be limited by "internal boundary scattering" to length scales of 10−2 cm to 10−3 cm. The phonon mean free path has been associated directly with the effective relaxation length for processes without directional correlation. If Vg is the group velocity of a phonon wave packet, then the relaxation length l\; is defined as: :l\;=V_\text t where ''t'' is the characteristic relaxation time. Since longitudinal waves have a much greater phase velocity than transverse waves, ''V''long is much greater than ''V''trans, and the relaxation length or mean free path of longitudinal phonons will be much greater. Thus, thermal conductivity will be largely determined by the speed of longitudinal phonons. Regarding the dependence of wave velocity on wavelength or frequency (
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
), low-frequency phonons of long wavelength will be limited in relaxation length by elastic
Rayleigh scattering Rayleigh scattering ( ), named after the 19th-century British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the ...
. This type of light scattering from small particles is proportional to the fourth power of the frequency. For higher frequencies, the power of the frequency will decrease until at highest frequencies scattering is almost frequency independent. Similar arguments were subsequently generalized to many glass forming substances using
Brillouin scattering Brillouin scattering (also known as Brillouin light scattering or BLS), named after Léon Brillouin, refers to the interaction of light with the material waves in a medium (e.g. electrostriction and magnetostriction). It is mediated by the refractiv ...
. Phonons in the acoustical branch dominate the phonon heat conduction as they have greater energy dispersion and therefore a greater distribution of phonon velocities. Additional optical modes could also be caused by the presence of internal structure (i.e., charge or mass) at a lattice point; it is implied that the group velocity of these modes is low and therefore their contribution to the lattice thermal conductivity ''λ''L (\kappa L) is small. Each phonon mode can be split into one longitudinal and two transverse polarization branches. By extrapolating the phenomenology of lattice points to the unit cells it is seen that the total number of degrees of freedom is 3''pq'' when ''p'' is the number of primitive cells with ''q'' atoms/unit cell. From these only 3p are associated with the acoustic modes, the remaining 3''p''(''q'' − 1) are accommodated through the optical branches. This implies that structures with larger ''p'' and ''q'' contain a greater number of optical modes and a reduced ''λ''L. From these ideas, it can be concluded that increasing crystal complexity, which is described by a complexity factor CF (defined as the number of atoms/primitive unit cell), decreases λL. This was done by assuming that the relaxation time ''τ'' decreases with increasing number of atoms in the unit cell and then scaling the parameters of the expression for thermal conductivity in high temperatures accordingly. Describing anharmonic effects is complicated because an exact treatment as in the harmonic case is not possible, and phonons are no longer exact eigensolutions to the equations of motion. Even if the state of motion of the crystal could be described with a plane wave at a particular time, its accuracy would deteriorate progressively with time. Time development would have to be described by introducing a spectrum of other phonons, which is known as the phonon decay. The two most important anharmonic effects are the thermal expansion and the phonon thermal conductivity. Only when the phonon number ‹n› deviates from the equilibrium value ‹n›0, can a thermal current arise as stated in the following expression :Q_x=\frac \sum_ \text where ''v'' is the energy transport velocity of phonons. Only two mechanisms exist that can cause time variation of ‹''n''› in a particular region. The number of phonons that diffuse into the region from neighboring regions differs from those that diffuse out, or phonons decay inside the same region into other phonons. A special form of the
Boltzmann equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerne ...
:\frac=_+_\text states this. When steady state conditions are assumed the total time derivate of phonon number is zero, because the temperature is constant in time and therefore the phonon number stays also constant. Time variation due to phonon decay is described with a relaxation time (''τ'') approximation :_\text=-\text\frac, which states that the more the phonon number deviates from its equilibrium value, the more its time variation increases. At steady state conditions and local thermal equilibrium are assumed we get the following equation :_\text=-_\frac\frac\text Using the relaxation time approximation for the Boltzmann equation and assuming steady-state conditions, the phonon thermal conductivity ''λ''L can be determined. The temperature dependence for ''λ''L originates from the variety of processes, whose significance for ''λ''L depends on the temperature range of interest. Mean free path is one factor that determines the temperature dependence for ''λ''L, as stated in the following equation :_=\frac\sum _v\left(q,j\right)\Lambda \left(q,j\right)\frac\epsilon \left(\omega \left(q,j\right),T\right), where Λ is the mean free path for phonon and \frac\epsilon denotes the
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity i ...
. This equation is a result of combining the four previous equations with each other and knowing that \left \langle v_x^2\right \rangle=\fracv^2 for cubic or isotropic systems and \Lambda =v\tau . At low temperatures (< 10 K) the anharmonic interaction does not influence the mean free path and therefore, the thermal resistivity is determined only from processes for which q-conservation does not hold. These processes include the scattering of phonons by crystal defects, or the scattering from the surface of the crystal in case of high quality single crystal. Therefore, thermal conductance depends on the external dimensions of the crystal and the quality of the surface. Thus, temperature dependence of λL is determined by the specific heat and is therefore proportional to T3. Phonon quasimomentum is defined as ℏq and differs from normal momentum because it is only defined within an arbitrary reciprocal lattice vector. At higher temperatures (10 K < ''T'' < ''Θ''), the conservation of energy \hslash _=\hslash _+\hslash _ and quasimomentum \mathbf_=\mathbf_+\mathbf_+\mathbf, where q1 is wave vector of the incident phonon and q2, q3 are wave vectors of the resultant phonons, may also involve a reciprocal lattice vector G complicating the energy transport process. These processes can also reverse the direction of energy transport. Therefore, these processes are also known as Umklapp (U) processes and can only occur when phonons with sufficiently large ''q''-vectors are excited, because unless the sum of q2 and q3 points outside of the Brillouin zone the momentum is conserved and the process is normal scattering (N-process). The probability of a phonon to have energy ''E'' is given by the Boltzmann distribution P\propto ^. To U-process to occur the decaying phonon to have a wave vector q1 that is roughly half of the diameter of the Brillouin zone, because otherwise quasimomentum would not be conserved. Therefore, these phonons have to possess energy of \sim k\Theta /2, which is a significant fraction of Debye energy that is needed to generate new phonons. The probability for this is proportional to ^, with b=2. Temperature dependence of the mean free path has an exponential form ^. The presence of the reciprocal lattice wave vector implies a net phonon backscattering and a resistance to phonon and thermal transport resulting finite ''λ''L, as it means that momentum is not conserved. Only momentum non-conserving processes can cause thermal resistance. At high temperatures (''T'' > Θ), the mean free path and therefore ''λ''L has a temperature dependence ''T''−1, to which one arrives from formula ^ by making the following approximation ^\propto x\text,\text\left(x\right) < 1 and writing x=\Theta /bT. This dependency is known as Eucken's law and originates from the temperature dependency of the probability for the U-process to occur. Thermal conductivity is usually described by the Boltzmann equation with the relaxation time approximation in which phonon scattering is a limiting factor. Another approach is to use analytic models or molecular dynamics or Monte Carlo based methods to describe thermal conductivity in solids. Short wavelength phonons are strongly scattered by impurity atoms if an alloyed phase is present, but mid and long wavelength phonons are less affected. Mid and long wavelength phonons carry significant fraction of heat, so to further reduce lattice thermal conductivity one has to introduce structures to scatter these phonons. This is achieved by introducing interface scattering mechanism, which requires structures whose characteristic length is longer than that of impurity atom. Some possible ways to realize these interfaces are nanocomposites and embedded nanoparticles or structures.


Prediction

Because thermal conductivity depends continuously on quantities like temperature and material composition, it cannot be fully characterized by a finite number of experimental measurements. Predictive formulas become necessary if experimental values are not available under the physical conditions of interest. This capability is important in thermophysical simulations, where quantities like temperature and pressure vary continuously with space and time, and may encompass extreme conditions inaccessible to direct measurement.


In fluids

For the simplest fluids, such as dilute monatomic gases and their mixtures, ''
ab initio ''Ab initio'' ( ) is a Latin term meaning "from the beginning" and is derived from the Latin ''ab'' ("from") + ''initio'', ablative singular of ''initium'' ("beginning"). Etymology Circa 1600, from Latin, literally "from the beginning", from ab ...
'' quantum mechanical computations can accurately predict thermal conductivity in terms of fundamental atomic properties—that is, without reference to existing measurements of thermal conductivity or other transport properties. This method uses Chapman-Enskog theory to evaluate a low-density expansion of thermal conductivity. Chapman-Enskog theory, in turn, takes fundamental intermolecular potentials as input, which are computed ''ab initio'' from a quantum mechanical description. For most fluids, such high-accuracy, first-principles computations are not feasible. Rather, theoretical or empirical expressions must be fit to existing thermal conductivity measurements. If such an expression is fit to high-fidelity data over a large range of temperatures and pressures, then it is called a "reference correlation" for that material. Reference correlations have been published for many pure materials; examples are
carbon dioxide Carbon dioxide (chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is transpar ...
,
ammonia Ammonia is an inorganic compound of nitrogen and hydrogen with the formula . A stable binary hydride, and the simplest pnictogen hydride, ammonia is a colourless gas with a distinct pungent smell. Biologically, it is a common nitrogenous was ...
, and
benzene Benzene is an organic chemical compound with the molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar ring with one hydrogen atom attached to each. Because it contains only carbon and hydrogen atoms, ...
. Many of these cover temperature and pressure ranges that encompass gas, liquid, and supercritical phases. Thermophysical modeling software often relies on reference correlations for predicting thermal conductivity at user-specified temperature and pressure. These correlations may be proprietary. Examples are REFPROP (proprietary) and CoolProp (open-source). Thermal conductivity can also be computed using the Green-Kubo relations, which express transport coefficients in terms of the statistics of molecular trajectories. The advantage of these expressions is that they are formally exact and valid for general systems. The disadvantage is that they require detailed knowledge of particle trajectories, available only in computationally expensive simulations such as
molecular dynamics Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the ...
. An accurate model for interparticle interactions is also required, which may be difficult to obtain for complex molecules.


In solids


See also

*
Copper in heat exchangers Heat exchangers are devices that transfer heat to achieve desired heating or cooling. An important design aspect of heat exchanger technology is the selection of appropriate materials to conduct and transfer heat fast and efficiently. Copper has m ...
*
Heat pump A heat pump is a device that can heat a building (or part of a building) by transferring thermal energy from the outside using a refrigeration cycle. Many heat pumps can also operate in the opposite direction, cooling the building by removing h ...
*
Heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...
* Heat transfer mechanisms * Insulated pipes *
Interfacial thermal resistance Interfacial thermal resistance, also known as thermal boundary resistance, or Kapitza resistance, is a measure of resistance to thermal flow at the interface between two materials. While these terms may be used interchangeably, Kapitza resistance ...
*
Laser flash analysis The laser flash analysis or laser flash method is used to measure thermal diffusivity of a variety of different materials. An energy pulse heats one side of a plane-parallel sample and the resulting time dependent temperature rise on the backsid ...
*
List of thermal conductivities In heat transfer, the thermal conductivity of a substance, ''k'', is an intensive property that indicates its ability to conduct heat. For most materials, the amount of heat conducted varies (usually non-linearly) with temperature. Thermal con ...
*
Phase-change material A phase change material (PCM) is a substance which releases/absorbs sufficient energy at phase transition to provide useful heat or cooling. Generally the transition will be from one of the first two fundamental states of matter - solid and liq ...
*
R-value (insulation) In the context of construction, the R-value is a measure of how well a two-dimensional barrier, such as a layer of insulation, a window or a complete wall or ceiling, resists the conductive flow of heat. R-value is the temperature difference per ...
*
Specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
*
Thermal bridge A thermal bridge, also called a cold bridge, heat bridge, or thermal bypass, is an area or component of an object which has higher thermal conductivity than the surrounding materials, creating a path of least resistance for heat transfer.Gorse, Chr ...
*
Thermal conductance quantum In physics, the thermal conductance quantum g_0 describes the rate at which heat is transported through a single ballistic phonon channel with temperature T. It is given by :g_ = \frac \approx (9.464\times10^ ^)\;T. The thermal conductance of ...
*
Thermal contact conductance In physics, thermal contact conductance is the study of heat conduction between solid or liquid bodies in thermal contact. The thermal contact conductance coefficient, h_c, is a property indicating the thermal conductivity, or ability to conduct he ...
*
Thermal diffusivity In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It measures the rate of transfer of heat of a material from the hot end to the cold end. It has the SI ...
*
Thermal effusivity In thermodynamics, a material's thermal effusivity, thermal inertia or thermal responsivity is a measure of its ability to exchange thermal energy with its surroundings. It is defined as the square root of the product of the material's thermal co ...
*
Thermal entrance length In fluid dynamics, the entrance length is the distance a flow travels after entering a pipe before the flow becomes fully developed.''ES162_08_Notes02a_Flow_In_Pipes_Changtamu.Pdf''. 1st ed. Cambridge: J. R. Rice, 2017. Print. Entrance length refer ...
*
Thermal interface material A thermal interface material (shortened to TIM) is any material that is inserted between two components in order to enhance the thermal coupling between them. A common use is heat dissipation, in which the TIM is inserted between a heat-producing de ...
*
Thermal rectifier The term "thermal diode" is sometimes used for a (possibly non-electrical) device which allows heat to flow preferentially in one direction. Or, the term may be used to describe an electrical (semiconductor) diode in reference to a thermal effect o ...
*
Thermal resistance in electronics Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. Thermal resistance is the reciprocal of thermal conductance. * (Absolute) thermal resistance ''R'' in kelvi ...
*
Thermistor A thermistor is a type of resistor whose resistance is strongly dependent on temperature, more so than in standard resistors. The word thermistor is a portmanteau of ''thermal'' and ''resistor''. Thermistors are divided based on their conduction ...
*
Thermocouple A thermocouple, also known as a "thermoelectrical thermometer", is an electrical device consisting of two dissimilar electrical conductors forming an electrical junction. A thermocouple produces a temperature-dependent voltage as a result of the ...
*
Thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
*
Thermal conductivity measurement There are a number of possible ways to measure thermal conductivity, each of them suitable for a limited range of materials, depending on the thermal properties and the medium temperature. Three classes of methods exist to measure the thermal conduc ...
*
Refractory metals Refractory metals are a class of metals that are extraordinarily resistant to heat and wear. The expression is mostly used in the context of materials science, metallurgy and engineering. The definition of which elements belong to this group diff ...


References


Notes


Citations


Sources

*


Further reading


Undergraduate-level texts (engineering)

*. A standard, modern reference. * * * *


Undergraduate-level texts (physics)

*Halliday, David; Resnick, Robert; & Walker, Jearl (1997). ''Fundamentals of Physics'' (5th ed.). John Wiley and Sons, New York . An elementary treatment. *. A brief, intermediate-level treatment. *. An advanced treatment.


Graduate-level texts

* *. A very advanced but classic text on the theory of transport processes in gases. *Reid, C. R., Prausnitz, J. M., Poling B. E., ''Properties of gases and liquids'', IV edition, Mc Graw-Hill, 1987 *Srivastava G. P (1990), ''The Physics of Phonons''. Adam Hilger, IOP Publishing Ltd, Bristol


External links


Thermopedia THERMAL CONDUCTIVITYContribution of Interionic Forces to the Thermal Conductivity of Dilute Electrolyte Solutions The Journal of Chemical Physics 41, 3924 (1964)
*The importance o
Soil Thermal Conductivity
for power companies
Thermal Conductivity of Gas Mixtures in Chemical Equilibrium. II The Journal of Chemical Physics 32, 1005 (1960)
{{Authority control Heat conduction Heat transfer Physical quantities Thermodynamic properties