Chapter 11, Problem 11.48P

A plate-tin heat exchanger is used to condense a saturated refrigerant vapor in an air-conditioning system.The vapor has a saturation temperature of $45°C$ , and a condensation rate of $0.015\text{ kg/s}$ is dictated by systemperformance requirements. The frontal area of thecondenser is fixed at $A_{fr}=0.25{\text{m}}^2$ by installationrequirements, and a value of $h_{fg}=135\text{ KJ/kg}$ may beassumed for the refrigerant.

(a) The condenser design is to be based on a nominal air inlet temperature of $T_{c,i}=30°C$ and nominal airinlet velocity of $V=2\text{ m/s}$ for which the manufacturer of the heat exchanger core indicates an overall coefficientof $U=50{\text{ W/m}}^2\cdot \text{K}$ . What is thecorresponding value of the heat transfer surfacearea required to achieve the prescribed condensation rate? What is the air outlet temperature?

(b) From the manufacturer of the heat exchangercore, it is also known that $U\infty V^{0.7}$ . Duringdaily operation the air inlet temperature is notcontrollable and may vary from $27$ to $38°C$ . Ifthe heat exchanger area is fixed by the result ofpart (a), what is the range of air velocities neededto maintain the prescribed condensation rate? Plot the velocity as a function of the air inlettemperature.