Consider a 10-m-high, 80-m-long, and four-layers wall whose representative cross

Question

Consider a 10-m-high, 80-m-long, and four-layers wall whose representative cross section is as given in the following. The thickness of each layer is 5.0cm. Also, the thermal conductivities of various materials used, in W/m middot degree C, are k_A = k_D = 0.1, k_B = 0.2, and k_C = 0.02. The left and right surfaces of the wall are maintained at uniform temperatures of 30 degree C and 300 degree C, respectively. Assuming heat transfer through the wall to be one-dimensional, (a) determine the rate of heat transfer through the wall., and (b) What is the temperature at the surface where Layer B are in contact with Layer C? Disregard any contact resistances at the interfaces.

Explanation / Answer

a) dq/dt ( rate of heat transfer through the wall) =80 (270) / ( 0.05/0.1 + 0.05/0.1 +0.05/0.2 + 0.05/ 0.02) = 21600 / (1+0.25 +2.5) = 5760 J

b) Temperature at the point where A and B are in contact

5760 = 0.1 (80) ( T -30)/0.05

T = 66

temp at point where B and C are in touch,

5760 = 0.2 ( 80 ) (T-66)/ 0.05

T = 84

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