The wall of a liquid-to-gas heat exchanger has a surface area on the liquid side of 1.8 m2 (0.6m x 3m) with a heat transfer coefficient of 255 W/(m2 K). On the other side of the heat exchanger wall flows a gas, and the wall has 96 thin rectangular steel fins 0.5-cm-thick and 1.25-cm- high [k = 3 W/(m K)]. The fins are 3-m-long and the heat transfer coefficient on the gas side is 57 W/(m2 K). Assuming that the thermal resistance of the wall is negligible, determine the rate of heat transfer if the overall temperature difference is 38°C.
GIVEN
FIND
The rate of heat transfer (q)
ASSUMPTIONS
The thermal resistance of the wall is negligible
The heat transfer through the wall is steady state
The thermal conductivity of the steel is constant
SKETCH
The heat transfer from a single fin can be calculated from for a fin with convection from the tip
The rate of heat transfer on the gas side is the sum of the convection from the fins and the convection from the bare wall between the fins. The bare area is
The total rate of heat transfer to the gas is
The thermal resistance on the gas side is
The thermal resistance on the liquid side is
The rate of heat transfer is
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