Compare the rate of heat flow from the bottom to the top in the aluminum structure shown in the sketch below with the rate of heat flow through a solid slab. The top is at –10°C, the bottom at 0°C. The holes are filled with insulation which does not conduct heat appreciably.

GIVEN

The aluminum structure shown in the sketch below

Temperature of the top (TT) = – 10°C

Temperature of the bottom (TB) = 0°C

The holes are filled with insulation which does not conduct heat appreciably

FIND

Compare the rate of heat flow from the bottom to the top with the rate of heat flow through a solid slab

ASSUMPTIONS

Compare the rate of heat flow from the bottom to the top with the rate of heat flow through a solid slab

ASSUMPTIONS

The structure is in steady state

Heat transfer through the insulation is negligible

The thermal conductivity of the aluminum is uniform

The edges of the structure are insulated

Two dimensional conduction through the structure

SKETCH


Because of the symmetry of the structure, we can draw the flux plot for just one of the twenty-four equivalent sections



(a) The total number of flow lanes in the structure, (M) = (12) (4) = (48). Each flow lane consists of 12

curvilinear squares (6 on top as shown, and 6 on bottom. Therefore, the shape factor is



The heat flow per meter, is



The total rate of heat flow is



(b) For a solid aluminum plate, the total heat flow from is

Physics & Space Science

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