An appliance manufacturer is designing the insulated door of a new chest freezer. For each square meter of door area, the company must ensure that the steady–state heat gain does not exceed 15W when the temperature difference between the kitchen (22∘C) and the freezer interior (−18∘C) is 40∘C. Two candidate insulation materials and their bulk costs are listed below.
• Material A: thermal conductivity 0.040Wm−1K−1, cost $8.00 per cubic meter
• Material B: thermal conductivity 0.050Wm−1K−1, cost $6.00 per cubic meter
Assume the door’s interior and exterior surface areas are equal and that heat transfer occurs only by conduction through the insulation layer.
(a) For each material, calculate the minimum insulation thickness per square meter of door area required to satisfy the heat–gain specification.
(b) Using your results from part (a), determine the cost of insulation per square meter for each material.
(c) Identify which material is more cost-effective for this application and justify your choice quantitatively.