The models in this section are useful approximations for heat transfer by conduction and convection. The heat conduction equation is the closest model to a true law of physics because it accurately describes most situations.
Models of convection, however, are far more complex and empirical in nature.
The simple form of the equation P = hAΔt buries enormous complexity in the heat transfer coefficient h. The value of h can vary by more than a million depending on the shape of a surface, the flow rate, the specific fluid, and other factors. Realistic calculations of convection must come directly from experimental data and a model that is 10% accurate for one situation often gives unrealistic predictions for a different geometry or flow speed. Models of heat transfer should always be assumed to be approximations subject to test by experiment for anything other than the simplest geometry.

The heat conduction equation

The heat conduction equation

The heat conduction equation (24.1) describes the thermal energy that flows through a material because of a difference in temperature between one part of the material and another. Since the flow of energy is power, the equation gives the power P in watts (W) for a temperature difference ΔT. The material may be a solid, liquid, or a gas. In equation (24.1) the following geometry is assumed:

Heat flows across area A through length L.

The temperature difference ΔT = (T_{2} − T_{1}) occurs across the same distance L.

The material has a uniform thermal conductivity κ.

(24.1)

$$P=\frac{\kappa A}{L}\text{\Delta}T$$

P

=

power (W)

κ

=

thermal conductivity (W m^{−1} °C^{−1})

A

=

cross-sectional area (m^{2})

L

=

length (m)

ΔT

=

temperature difference (°C)

Heat conduction

How do I use the conduction equation?

Equation (24.1) is most useful when applied to solids because in most realistic situations, convection moves heat more rapidly than conduction in liquids and gases. To use the equation, you need to know something about the shape of the object the heat flows through. Two geometric factors are important:

Heat flow is directly proportional to the area the heat flows through. Double the area, and the heat flow also doubles for the same temperature difference.

Heat flow is inversely proportional to length. If you double the length the heat has to flow through, the power of heat flow is reduced by half.

Test your knowledge

A solid wall separates the cold air outside a house from the warmth inside a house. If the wall was made twice as thick, but of the same material, the heat conducted through the wall would

double.

be reduced by half.

increase by a factor of 4.

remain approximately the same.

Choice b is correct since the heat flow is inversely proportional to the length through which the heat travels, which is the thickness of the wall in this case.