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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 Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another pol ...
of thermal conductance. * (Absolute) thermal resistance ''R'' in kelvins per watt (K/W) is a property of a particular component. For example, a characteristic of a
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, ...
. * Specific thermal resistance or thermal resistivity ''Rλ'' in kelvin–metres per watt (K⋅m/W), is a
material constant A materials property is an intensive property of a material, i.e., a physical property that does not depend on the amount of the material. These quantitative properties may be used as a metric by which the benefits of one material versus another ca ...
. * Thermal insulance has the units square metre kelvin per watt (m2⋅K/W) in
SI 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. ...
or
square foot The square foot (plural square feet; abbreviated sq. ft, sf, or ft2; also denoted by '2) is an imperial unit and U.S. customary unit (non- SI, non- metric) of area, used mainly in the United States and partially in Canada, the United Kingdom, B ...
degree Fahrenheit The Fahrenheit scale () is a temperature scale based on one proposed in 1724 by the physicist Daniel Gabriel Fahrenheit (1686–1736). It uses the degree Fahrenheit (symbol: °F) as the unit. Several accounts of how he originally defined his ...
hour An hour (symbol: h; also abbreviated hr) is a unit of time conventionally reckoned as of a day and scientifically reckoned between 3,599 and 3,601 seconds, depending on the speed of Earth's rotation. There are 60 minutes in an hour, and 24 ...
s per
British thermal unit 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 ...
(ft2⋅°F⋅h/Btu) 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 th ...
. It is the thermal resistance of unit area of a material. In terms of insulation, it is measured by the R-value.


Absolute thermal resistance

Absolute thermal resistance is the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
difference across a structure when a unit of
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
energy flows through it in unit
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
. It is the reciprocal of thermal conductance. The SI unit of absolute thermal resistance is
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 ...
s per
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 ...
(K/W) or the equivalent
degrees Celsius The degree Celsius is the unit of temperature on the Celsius scale (originally known as the centigrade scale outside Sweden), one of two temperature scales used in the International System of Units (SI), the other being the Kelvin scale. The d ...
per watt (°C/W) – the two are the same since the intervals are equal: Δ''T'' = 1 K = 1 °C. The thermal resistance of materials is of great interest to electronic engineers because most electrical components generate heat and need to be cooled. Electronic components malfunction or fail if they overheat, and some parts routinely need measures taken in the design stage to prevent this.


Analogies and nomenclature

Electrical engineers are familiar with
Ohm's law Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equa ...
and so often use it as an analogy when doing calculations involving thermal resistance. Mechanical and structural engineers are more familiar with
Hooke's law In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring by some distance () scales linearly with respect to that distance—that is, where is a constant factor characteristic of t ...
and so often use it as an analogy when doing calculations involving thermal resistance.


Explanation from an electronics point of view


Equivalent thermal circuits

The heat flow can be modelled by analogy to an electrical circuit where heat flow is represented by current, temperatures are represented by voltages, heat sources are represented by constant current sources, absolute thermal resistances are represented by resistors and thermal capacitances by capacitors. The diagram shows an equivalent thermal circuit for a semiconductor device with a
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, ...
.


Example calculation


Derived from Fourier's law for heat conduction

From
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 t ...
for
heat conduction 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 te ...
, the following equation can be derived, and is valid as long as all of the parameters (x and k) are constant throughout the sample. : R_ = \frac = \frac where: * R_ is the absolute thermal resistance (K/W) across the thickness of the sample * \Delta x is the thickness (m) of the sample (measured on a path parallel to the heat flow) * k is the thermal conductivity (W/(K·m)) of the sample * r is the thermal resistivity (K·m/W) of the sample * A is the cross-sectional area (m2) perpendicular to the path of heat flow. In terms of the temperature gradient across the sample and
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 ...
through the sample, the relationship is: : R_ = \frac\frac = \frac where: * R_\theta is the absolute thermal resistance (K/W) across the thickness of the sample, * \Delta x is the thickness (m) of the sample (measured on a path parallel to the heat flow), * \phi_q 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 ...
through the sample ( W·m−2), * \frac is the temperature gradient ( K·m−1) across the sample, * A is the cross-sectional area (m2) perpendicular to the path of heat flow through the sample, * \Delta T is the temperature difference ( K) across the sample, * q is the
rate of heat flow The rate of heat flow is the amount of heat that is transferred per unit of time in some material, usually measured in watt ( joules per second). Heat is the flow of thermal energy driven by thermal non-equilibrium, so that 'heat flow' ...
( W) through the sample.


Problems with electrical resistance analogy

A 2008 review paper written by Philips researcher Clemens J. M. Lasance notes that: "Although there is an analogy between heat flow by conduction (Fourier's law) and the flow of an electric current (Ohm’s law), the corresponding physical properties of thermal conductivity and electrical conductivity conspire to make the behavior of heat flow quite unlike the flow of electricity in normal situations. ..Unfortunately, although the electrical and thermal differential equations are analogous, it is erroneous to conclude that there is any practical analogy between electrical and thermal resistance. This is because a material that is considered an insulator in electrical terms is about 20 orders of magnitude less conductive than a material that is considered a conductor, while, in thermal terms, the difference between an "insulator" and a "conductor" is only about three orders of magnitude. The entire range of thermal conductivity is then equivalent to the difference in electrical conductivity of high-doped and low-doped silicon."


Measurement standards

The junction-to-air thermal resistance can vary greatly depending on the ambient conditions. (A more sophisticated way of expressing the same fact is saying that junction-to-ambient thermal resistance is not Boundary-Condition Independent (BCI).)
JEDEC The JEDEC Solid State Technology Association is an independent semiconductor engineering trade organization and standardization body headquartered in Arlington County, Virginia, United States. JEDEC has over 300 members, including some of the w ...
has a standard (number JESD51-2) for measuring the junction-to-air thermal resistance of electronics packages under
natural 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 another standard (number JESD51-6) for measurement under forced convection. A JEDEC standard for measuring the junction-to-board thermal resistance (relevant for
surface-mount technology Surface-mount technology (SMT), originally called planar mounting, is a method in which the electrical components are mounted directly onto the surface of a printed circuit board (PCB). An electrical component mounted in this manner is referred ...
) has been published as JESD51-8. A JEDEC standard for measuring the junction-to-case thermal resistance (JESD51-14) is relatively newcomer, having been published in late 2010; it concerns only packages having a single heat flow and an exposed cooling surface.


Resistance in composite wall


Parallel thermal resistance

Similarly to electrical circuits, the total thermal resistance for steady state conditions can be calculated as follows. The total thermal resistance (1) Simplifying the equation, we get (2) With terms for the thermal resistance for conduction, we get (3)


Resistance in series and parallel

It is often suitable to assume one-dimensional conditions, although the heat flow is multidimensional. Now, two different circuits may be used for this case. For case (a) (shown in picture), we presume
isothermal In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature ''T'' of a system remains constant: Δ''T'' = 0. This typically occurs when a system is in contact with an outside thermal reservoir, an ...
surfaces for those normal to the x- direction, whereas for case (b) we presume adiabatic surfaces parallel to the x- direction. We may obtain different results for the total resistance and the actual corresponding values of the heat transfer are bracketed by . When the multidimensional effects becomes more significant, these differences are increased with increasing .


Radial systems

Spherical and cylindrical systems may be treated as one-dimensional, due to 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 degre ...
s in the radial direction. The standard method can be used for analyzing radial systems under steady state conditions, starting with the appropriate form of the heat equation, or the alternative method, starting with the appropriate form of
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 t ...
. For a hollow cylinder in steady state conditions with no heat generation, the appropriate form of heat equation is (4) Where is treated as a variable. Considering the appropriate form of Fourier's law, the physical significance of treating as a variable becomes evident when the rate at which energy is conducted across a cylindrical surface, this is represented as (5) Where is the area that is normal to the direction of where the heat transfer occurs. Equation 1 implies that the quantity is not dependent of the radius , it follows from equation 5 that the heat transfer rate, is a constant in the radial direction. In order to determine the temperature distribution in the cylinder, equation 4 can be solved applying the appropriate boundary conditions. With the assumption that is constant (6) Using the following boundary conditions, the constants and can be computed and The general solution gives us and Solving for and and substituting into the general solution, we obtain (7) The logarithmic distribution of the temperature is sketched in the inset of the thumbnail figure. Assuming that the temperature distribution, equation 7, is used with Fourier's law in equation 5, the heat transfer rate can be expressed in the following form Finally, for radial conduction in a cylindrical wall, the thermal resistance is of the form such that


See also

* Thermal engineering * Thermal design power * Safe operating area


References

10. K Einalipour, S. Sadeghzadeh'', F. Molaei. “Interfacial thermal resistance engineering for polyaniline (C3N)-graphene heterostructure”,'' ''The Journal of Physical Chemistry,'' 2020. DOI: 10.1021/acs.jpcc.0c02051 *Michael Lenz, Günther Striedl, Ulrich Fröhler (January 2000
Thermal Resistance, Theory and Practice
Infineon Technologies AG Infineon Technologies AG is a German semiconductor manufacturer founded in 1999, when the semiconductor operations of the former parent company Siemens AG were spun off. Infineon has about 50,280 employees and is one of the ten largest semicond ...
,
Munich Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the third-largest city in Germany, after Berlin and ...
,
Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwee ...
. *Directed Energy, Inc./IXYSRF (March 31, 2003
R Theta And Power Dissipation Technical NoteIxys RF
Fort Collins, Colorado. Example thermal resistance and power dissipation calculation in semiconductors.


Further reading

There is a large amount of literature on this topic. In general, works using the term "thermal resistance" are more engineering-oriented, whereas works using the term
thermal conductivity 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 ...
are more ure-hysics-oriented. The following books are representative, but may be easily substituted. * * * {{cite book, author=Xingcun Colin Tong, title=Advanced Materials for Thermal Management of Electronic Packaging, year=2011, publisher=Springer Science & Business Media, isbn=978-1-4419-7759-5


External links

* Guoping Xu (2006)
Thermal Management for Electronic Packaging
Sun Microsystems * http://www.electronics-cooling.com/2012/09/update-on-jedec-thermal-standards/ *The importance o
Soil Thermal Resistivity
for power companies Heat conduction Electronic engineering