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This page calculates the temperature on one side of an isothermal (constant temperature) multilayered plate or wall. You must define the heat load (Q) conducted through the layers as well as the temperature on one side of the plate (T₁) .The temperature on the opposite side of the plate is calculated. For each layer you must define the layer thickness (t_i) as well as the layer conductivity k_i.

The temperature (T_n) is calculated as:

T_n =

Where T₁ is the known surface temperature, Q is the heat flow (positive heat flow is from T_n to T₁), t_i is the thickness of the layer i,, k_i is the thermal conductivity of layer i, H is the height of the plate, and D is the depth of the plate. The end surfaces of the plate are assumed adiabatic.

Positive values of heat (Q) result in T_n being hotter than T₁. Negative values of heat (Q) result in T_n being cooler than T₁.

References

Holman, J.P., Heat Transfer, 7th ed., McGraw Hill Book Company, New York, 1990, p 27-29.