A cooling system is to be designed for a food storage warehouse for keeping perishable foods cool prior to transportation to grocery stores. The warehouse has an effective surface area of 1860 m2 exposed to an ambient air temperature of 320C. The warehouse wall insulation (k = 0.17 W/(m K)) is 7.5 cm thick. Determine the rate at which heat must be removed (W) from the warehouse to maintain the food at 4°C.
GIVEN
• Cooled warehouse
• Effective area (A) = 1860 m2
• Temperatures
? Outside air = 32°C
? food inside = 4°C
• Thickness of wall insulation (L) = 7.5 cm = 0.075 m
• Thermal conductivity of insulation (k) = 0.17 W/(m K)
FIND
• Rate at which heat must be removed (q)
ASSUMPTIONS
• One dimensional, steady state heat flow
• The food and the air inside the warehouse are at the same temperature
• The thermal resistance of the wall is approximately equal to the thermal resistance of the wall insulation alone
SKETCH
The rate at which heat must be removed is equal to the rate at which heat flows into the warehouse. There will be convective resistance to heat flow on the inside and outside of the wall. To estimate the upper limit of the rate at which heat must be removed these convective resistances will be neglected. Therefore the inside and outside wall surfaces are assumed to be at the same temperature as the air inside and outside of the wall. Then the heat flow,
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