The wall of a refrigerator is constructed of fiberglass insulation (k = 0.035 W/m·K) sandwiched between two layers of 1-mm-thick sheet metal (k = 15.1 W/m·K). The refrigerated space is maintained at 3°C, and the average heat transfer coefficients at the inner and outer surfaces of the wall are 4 W/m²·K and 9 W/m²·K, respectively. The kitchen temperature averages 25°C. It is observed that condensation occurs on the outer surfaces of the refrigerator when the temperature of the outer surface drops to 20°C. Determine the minimum thickness of fiberglass insulation that needs to be used in the wall in order to avoid condensation on the outer surfaces.

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Sheet metal Refrigerated Kitchen alr 25°C space 3°C Insulation 1 mm mm