Chapter 2, Problem 2.46P

The wall of a liquid-to-gas heat exchanger has a surface area on the liquid side of $\text{1}{\text{.8 m}}^{\text{2}}\left(\text{0}\text{.6 m }\times \text{ 3}\text{.0 m}\right)$ with a heat transfer coefficient of ${\text{255 W/m}}^{\text{2}}\text{K}$. 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 $(k=3\text{ W/m K)}$ as shown in the accompanying sketch. The fins are 3 m long and the heat transfer coefficient on the gas side is ${\text{57 W/m}}^{\text{2}}\text{K}$. Assuming that the thermal resistance of the wall is negligible, determine the rate of heat transfer if the overall temperature difference is $\text{38°C}$.