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
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