A thermal barrier (a wall) consists of N layers, each with their own thickness (

Question

A thermal barrier (a wall) consists of N layers, each with their own thickness (d) and thermal conductivity (k). For each layer you can define a thermal resistance as R_th = d/kA.

Show that the heat flow through the wall is given by:

Q = dT/R_th,eff Where R_th,eff = SR_th dT is the temperature difference across the wall. A thermal barrier (a wall) consists of N layers, each with their own thickness (d) and thermal conductivity (k). For each layer you can define a thermal resistance as R_th = d/kA.

Show that the heat flow through the wall is given by:

Q = dT/R_th,eff Where R_th,eff = SR_th dT is the temperature difference across the wall.

Explanation / Answer

The thickness of the layer is d The thermal conductivity of the material is k the area of thelayer is A The thermal resistance of each layer is Rth = d/kA The heat transfered per unit area of the layer which is maintained ata temperature differance of dT is given by the Fourier's formula, Q/A = k dT/d Q = kA dT/d Q = dT/(d/kA) Q = dT/Rth This is for a single layer As we have n such layers Q = dT/Rth_eff Where Rth_eff = nRth

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