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Exhaust combustion products flow through a concentric square composite (k = 0.85 W/m·K) channel of unit...

Exhaust combustion products flow through a concentric square composite (k = 0.85 W/m·K) channel of unit length. The edge of the outer square is b = 6 cm and the inner edge is a = 2 cm. The duct is placed in a corridor such that the air temperature is 300 K with a convection coefficient of 75 W/m2·K. The exhaust gases maintain a uniform inner channel surface temperature of 500 K.

a) Using numerical methods, find the temperature distribution in the wall and the heat loss per unit length from the channel for a grid spacing of ?x = ?y = 1 cm. (Note that symmetry will reduce the numerical calculation to 9 nodes).

b) Compare the heat loss of part (a) to the result found from a shape factor calculation.

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