Heat transfer

That is to say two objects has and B indeformable in a system perfectly isolated thermically and mechanically having the following characteristics:

In accordance with the first principle of thermodynamics we can write:

$dU=\; \backslash \; delta\; \backslash \; Q\; \backslash \; +\; \backslash \; delta\; \backslash \; W\; \backslash ,$

• the objects are indeformable thus

• the system is thus insulated

If δQ_A and δQ_B are respectively the elementary thermal energies exchanged between the object has and the object B, belonging to the isolated system.

$\backslash \; delta\; \backslash \; Q\; \backslash \; =\; \backslash \; delta\; \backslash \; Q\_A\; \backslash \; +\; \backslash \; delta\; \backslash \; Q\_B\; \backslash \; =\; 0$

From where: $\backslash \; delta\; \backslash \; Q\_A\; \backslash \; =\; -\; \backslash \; delta\; \backslash \; Q\_B\; \backslash ,$

The second principle of thermodynamics makes it possible to write the following relation binding the Entropie S of the objects has and b:

$dS\; (syst)\; =\; dS\_A\; +dS\_B\; \backslash \; >\; 0$, since the system is isolated.

by definition.

$dS=\; \backslash \; frac\; \{\backslash \; delta\; \backslash \; Q\}\; \{T\}\; \backslash ,$

$\backslash \; Rightarrow\; dS\; (syst)\; =\; \backslash \; frac\; \{\backslash \; delta\; \backslash \; Q\_A\}\; \{T\_A\}\; +\; \backslash \; frac\; \{\backslash \; delta\; \backslash \; Q\_B\}\; \{T\_B\}\; \backslash ,$

We can write:

$\backslash \; delta\; \backslash \; Q\_A\; \backslash \; \backslash \; left\; (\backslash \; frac\; \{1\}\; \{T\_A\}\; -\; \backslash \; frac\; \{1\}\; \{T\_B\}\; \backslash \; right)\; >\; 0\; \backslash ,$

If: $T\_A>\; T\_B\; \backslash ,$

That means that:

and thus that: $\backslash \; delta\; \backslash \; Q\_B\; >\; 0\; \backslash ,$

According to the rule of the signs, one concludes that the object has yields heat to the object B. the hottest object thus yields heat to the coldest object.

Modes of heat transfers

There are three modes of transfer:

*Conduction: heat passes from a body to another, by contact.

*Convection: a body which moves takes along the heat which it contains. The quantity of heat thus transported can be important, in particular in the case of a phase shift.

*Radiation (Radiation): all the bodies emit light, according to their temperature, and are done themselves to heat by the light that they receive.

Conduction

The transfer by conduction is an energy exchange with contact when there exists a Gradient of temperature within a system.

In a gas or a liquid, energy is propagated by direct contact between Molécule S without notable displacement of molecules. In a solid , the vibration of the atoms around their position is transmitted gradually.

In the case of the crystals, the vibrations of the network have heterogeneities which form “particle S”, the Phonon S. These phonons interact with the free electron S, which explains why the Conductivité thermal and electric are dependant (for example, the metals are good conductive of electricity and heat).

Examples of transfer by conduction: transfer through a wall, congelation of the ground in winter.

See also: thermal Conduction

Convection

Definition: transfer of energy which is accompanied by movement of molecules in a Fluide (Liquide or Gaz).

natural *Convection (or free): the heat transfer is responsible for the movement. The transfer of heat causes the movement.

forced *Convection: there is projection by a mechanical device of the molecules on the heating device. The movement causes the transfer of heat.

It will be noted that the laws are extremely different in the 2 cases.

Example of transfer by convection: exchange between heat and cold in exchangers (forced convection), cooling of a cup of hot liquid in blowing top (forced convection), diffusion above an electric radiator (natural convection if there is no blower in the radiator).

See the developed article: Convection

Radiation

Definition: transfer of energy without Matter. The transfer is done by electromagnetic radiation (for example: Infra-red). The transfer can be indeed carried out in the vacuum. The example characteristic of this type of transfer is the radiation of the sun in space.

Example of transfer per radiation: System of heating called by radiant, Sun.

It is the Loi of Stefan-Boltzmann (or law of Stefan) who allows to quantify these exchanges. The energy radiated by a body is written:

$E\; =\; \backslash \; epsilon\; S\; \backslash \; sigma\; T^4\; \backslash ,$

with

• $\backslash \; sigma\; \backslash ,$: constant of Stefan-Boltzmann = 5,6703. 10^-8 W.m^-2.K^-4
• $\backslash \; epsilon\; \backslash ,$: coefficient which is worth 1 for a black Corps and which lies between 0 and 1 depending on the surface quality of material.
• $S\; \backslash ,$: surface body
• $T\; \backslash ,$: temperature of the body in Kelvin

If the receiving body reflects certain wavelengths or is transparent with others, only the absorptive wavelengths contribute to its thermal balance. So on the other hand the receiving body is a black Corps, i.e. it absorbs all the electromagnetic radiations, then all the radiations contribute to its thermal balance.

Combination of the modes of transfer

The transfer by heat is generally carried out by a combination of several modes.

For example, the system Central heating, combines the convection (in general forced) to heat the fluid in the Chaudière, conduction to heat the walls of the radiator and the convection (in general natural) to heat the air around the radiator. In the case of a heating of a solid (not transparency in a strict sense of the term) per radiation, the transfer heat will be a combination of radiation and conduction. It is the case of the Verre heated by the solar radiation. In this case, the transfer could be also combined with a natural convection behind the pane of a part.

It will be noted that sometimes the heat transfer is accompanied by a transfer of matter. For example, it is the case of the boiling part of the liquid undergoes a Transformation of phase and the gas thus created moves.

Physical sizes

Heat flux

The heat flux is the thermal quantity of energy which crosses a surface Isotherme per unit of Temps. It is called “thermal power” for the thermal equipment such as the Radiateur S.

$\backslash \; Phi=\; \backslash \; frac\; \{dQ\}\; \{dt\}\; \backslash ,$

Flow is expressed in:

• Watt: W (IF);
• calorie by second: kcal.s^-1 (unit used by the heat engineers).

Density flux thermal

The density flux thermal (or surface heat flux) it is the heat flux per unit of Surface. The density flux thermal is expressed in Watt by square meter (W.m^-2).

$\backslash \; varphi=\; \backslash \; frac\; \{D\; \backslash \; Phi\}\; \{dS\}\; =\; \backslash \; frac\; \{1\}\; \{S\}\; \backslash \; frac\; \{dQ\}\; \{dt\}\; \backslash ,$

If the density flux is uniform on surface considered:

$\backslash \; varphi=\; \backslash \; frac\; \{\backslash \; Phi\}\; \{S\}\; \backslash ,$

Total coefficient of thermal transmission

In permanent mode, the relation which binds flow with the temperatures of two objects in contact can be written by using the following relation:

$\backslash \; Phi=\; KS\; (T\_A-T\_B)\; \backslash ,$

*S in $m^2$

*T in Kelvin (K)

*K out of W. $m^\; \{-\; 2\}$.$K^\; \{-\; 1\}$

The coefficient K characterizing the medium in which the transfer will be carried out.

One can make an analogy with the electric relation: $(U\_A-U\_B)\; =\; IH\; \backslash ,$

$(T\_A-T\_B)\; =\; \backslash \; frac\; \{1\}\; \{KS\}\; \backslash \; cdot\; \backslash \; \backslash \; Phi\; \backslash ,$

Where 1/KS represents the thermal resistance which one can note R_th (K.W^-1).

By analogy with the electric laws, we can make the following diagram:

See also

• Gradient

• Temperature
• Insulator
• Heat transfers in the building