Steady State Conduction Multilayer Isothermal Walls Calculation

Heat Transfer Engineering | Thermodynamics

The following equation will calculate the temperature on one side of an isothermal constant temperature multilayered plate or wall. The heat load (q) conducted through the layers as well as the temperature on one side of the plate (T1) are required as well . For each layer  the layer thickness (ti) as well as the layer conductivity ki must be defined. 

The temperature Tn is calculated as:

 

or

Where:

Tn   = Temperature oC
T1  = Known surface temperature oC
q   = Heat flow (positive heat flow is from T1 to Tn
ti    = Thickness of each layer i (M)
ki    = Thermal conductivity of layer i (W/m-oC) 
HD = Surface area (H x D) the plate being considered M2

End surfaces of the plate are assumed adiabatic.

Positive values of heat (q) result in Tn being hotter than T1. Negative values of heat (q) result in Tn being cooler than T1.

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