Question 4 The wall of a refrigerator is constructed of fiberglass insulation (k

Question

Question 4 The wall of a refrigerator is constructed of fiberglass insulation (k = 0.07 W/mK) sandwiched between two layers of 1-mm-thick sheet metal (k = 16 W/mK). The refrigerated space is maintained at 4°C, and the average heat transfer coefficients at the inner and outer surfaces of the wall are 12 W/m2-K and 10 W/m2-K, respectively. The kitchen temperature averages 27 C. It is observed that condensation occurs on the outer surfaces of the refrigerator when the temperature of the outer surface drops to 20°O. Determine the minimum thickness of fiberglass insulation that needs to be used in the wall in order to avoid condensation on the outer surfaces.

Explanation / Answer

Let X be the thickness required.

The convective heat transfer from the refrigerator surface will be:

Q = k A (Th - Tc)

Q/A = 10 (27 - 20) = 70 W/m^2

Q/A = (Th - Tc')/1/k1 + 2L/k2 + X/k3 + 1/k4

70 = (27 - 4)/[(1/10 + 2 x 0.001/16 + X/0.07 + 1/12)]

[(1/10 + 2 x 0.001/16 + X/0.07 + 1/12)] = 0.33

0.1 + 0.000125 + 14.29 X + 0.083 = 0.33

14.29 X = 0.33 - 0.183125 = 0.146875

X = 0.0102 m = 1.02 cm

Hence, X = 1.02 cm

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