Related Resources: heat transfer

Heat Conduction Wall Equations and Calculator

Heat Transfer Engineering
Thermodynamics
Engineering Physics

Heat Conduction through a wall equations and calculator.

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Variation in thermal conductivity of a material with temperature in the temperature range of interest can often be approximated as a linear function and expressed as:

Where:

k(T) = Variation in thermal conductivity (W/m • K)
β = Temperature Coefficient of Thermal Conductivity (K^-1)
k_o = Thermal Conductivity (W/m • K)
T = Temperature (K)

Average Thermal Conductivity

Example Heat Conduction through a Wall with k(T )

2-m-high and 0.7-m-wide bronze plate whose thickness is 0.1 m. One side of the plate is maintained at a constant temperature of 600 K while the other side is maintained at 400 K. The thermal conductivity of the bronze plate can be assumed to vary linearly in that temperature range as k (T) = k_o(1  βT ,) where k_o = 38 W/m · K and β 9.21  10^-4 K^-1. Disregarding the edge effects and assuming steady one-dimensional heat transfer, determine the rate of heat conduction through the plate.

Assumptions:

1 Heat transfer is given to be steady and one-dimensional.
2 Thermal conductivity varies linearly.
3 There is no heat generation.

therefore

Then the rate of heat conduction:

Where:
A = Area (m²) = H x W
L = Thickness (m)