**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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Preview: Heat Conduction through a Wall Calculator

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 (m^{2}) = H x W

L = Thickness (m)

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