A wall constructed of three layers is to be considered. The inner surface of the

Question

A wall constructed of three layers is to be considered.  The inner surface of the wall is maintained at 23 C and the outer surface is 8 C.  The combined convection and radiation heat transfer coefficients are 17 W/m^2*K.  The inner layer is plaster with 1cm thickness and k=0.36 W/m*K.  The middle layer is brick 20 cm thickness and k=0.72 W/m*K and the outer layer is cement 2 cm thickness and k=1.4 W/m*k.  The wall system is 6m wide by 2.8m high.   

What is the rate of heat transfer through the wall and temperature drops accross each layer, and surface-ambient air?

Explanation / Answer

Net thermal resistance R = R1 + R2 + R3 + R_conv

R = [t1 / (k1*A1)] + [t2 / (k2*A2)] + [t3 / (k3*A3)] + [1/(h*A)]

R = [0.01/(0.36*6*2.8) + 0.2/(0.72*6*2.8) + (0.02/(1.4*6*2.8) + 1/(17*6*2.8)]

R = 0.0209 K/W

Rate of heat transfer through the wall Q = Temp difference / R

Q = (23 - 8) / 0.0209

Q = 717.6 W

Temp difference across inner layer = Q*R1 = 717.6*0.01/(0.36*6*2.8) = 1.19 deg C

Temp difference across middle layer = Q*R2 = 717.6*0.2/(0.72*6*2.8) = 11.86 deg C

Temp difference across outer layer = Q*R3 = 717.6*0.02/(1.4*6*2.8) = 0.61 deg C

Tep difference between surface-air = Q*R4 = 717.6/(17*6*2.8) = 2.51 deg C

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