The rate of heat flow is the amount of heat that is transferred per unit of time in some material, usually 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 ...
(
joules
The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied. ...
per second). Heat is the flow of thermal energy driven by thermal non-equilibrium, so that 'heat flow' is a redundancy (i.e. a
pleonasm
Pleonasm (; , ) is redundancy in linguistic expression, such as "black darkness" or "burning fire". It is a manifestation of tautology by traditional rhetorical criteria and might be considered a fault of style. Pleonasm may also be used for em ...
, and the same for ‘work flow’). Heat must not be confused with stored thermal energy, and moving a hot object from one place to another must not be called heat transfer. But, in spite of all these remarks, it is common in normal parlance to say ‘heat flow’, to talk of ‘heat content’, etc.
The equation of heat flow is given by Fourier's Law of Heat Conduction.
Rate of heat flow = - (heat transfer coefficient) * (area of the body) * (variation of the temperature) / (length of the material)
The formula for the rate of heat flow is:
:
where
*
is the net heat (energy) transfer,
*
is the time taken,
*
is the difference in temperature between the cold and hot sides,
*
is the thickness of the material conducting heat (distance between hot and cold sides),
*
is the
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 ...
, and
*
is the surface area of the surface emitting heat.
If a piece of material whose cross-sectional area is
and thickness is
with a temperature difference
between its faces is observed, heat flows between the two faces in a direction perpendicular to the faces. The time rate of heat flow,
, for small
and small
, is proportional to
. In the limit of infinitesimal thickness
, with temperature difference
, this becomes
, where
is the time rate of heat flow through the area
,
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 ...
'' across the material, and
, the proportionality constant, is the ''
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 ...
'' of the material. People often use
,
, or the Greek letter
to represent this constant. The minus sign is there because the rate of heat flow is always negative—heat flows from the side at higher temperature to the one at lower temperature, not the other way around.
See also
*
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, ). ...
*
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, ...
*
Thermal 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 tem ...
*
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 ...
*
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 ...
*
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 ...
*
Flux
Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...
References
Thermodynamic properties
Heat flow
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, ...
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