#39 Calculate the rate of heat transfer through the composite

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Question

#39 Calculate the rate of heat transfer through the composite wall in Problem 1.34 if the temperature difference is 25°C and the contact resistance between the sheets of wood is 0.005 m² K/W.

Answer

Step 1 - Sketch the heat transfer through the composite wall:

Step 2 - Sketch the thermal circuit of the composite wall,

Step 3 - Calculate the combined resistance of the wood and the contact resistance in series:

Here, is the contact resistance.

Substitute for and for 

Step 4 - Calculate the total thermal resistance of the combined resistance of the wood and the contact resistance with the resistance of the nails,

Since, they are in parallel,

Substitute for, and for 

Calculate total heat transfer rate through the composite wall,

Here, is the temperature difference.

Substitute for and  for 

Therefore, the rate of heat transfer through the composite wall is.