A 50-mm-thick air gap separates two horizontal metalplates

Chapter 9, Problem 9.93

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A 50-mm-thick air gap separates two horizontal metalplates that form the top surface of an industrial furnace.The bottom plate is at Th?200?C and the top plate is atTc?50?C. The plant operator wishes to provide insula-tion between the plates to minimize heat loss. The rela-tively hot temperatures preclude use of foamed or feltinsulation materials. Evacuated insulation materials cannot be used due to the harsh industrial environmentand their expense. A young engineer suggests that equallyspaced, thin horizontal sheets of aluminum foil may beinserted in the gap to eliminate natural convection andminimize heat loss through the air gap.(a) Determine the convective heat flux across the gapwhen no insulation is in place.(b) Determine the minimum number of foil sheetsthat must be inserted in the gap to eliminate freeconvection.(c) Determine the conduction heat flux across the airgap with the foil sheets in place.