Question

An air conditioner condenser in an automobile consists of \(2 \mathrm{~m}^{2}\) of tubular heat exchange area whose surface temperature is $30^{\circ} \mathrm{C}\(. Saturated refrigerant- \)134 \mathrm{a}\( vapor at \)50^{\circ} \mathrm{C}\( \)\left(h_{f g}=152 \mathrm{~kJ} / \mathrm{kg}\right.$ ) condenses on these tubes. What heat transfer coefficent must exist between the tube surface and condensing vapor to produce \(1.5 \mathrm{~kg} / \mathrm{min}\) of condensate? (a) \(95 \mathrm{~W} / \mathrm{m}^{2}, \mathrm{~K}\) (b) \(640 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (c) \(727 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (d) \(799 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (e) \(960 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\)

Short answer

Answer: The heat transfer coefficient (h) is approximately 95 W/m²°C.

Step-by-step solution

Calculate the heat transfer rate (Q)

To find the heat transfer rate, we need to use the equation involving heat transfer and enthalpy of vaporization. The formula is: Q = m * hf_g where m is the mass flow rate of the condensate, and hf_g represents the enthalpy of vaporization. Convert the mass flow rate to kg/s: m = 1.5 kg/min * (1 min/60 s) = 0.025 kg/s Now, calculate Q: Q = 0.025 kg/s * 152000 J/kg = 3800 W

Calculate the temperature difference (ΔT)

The temperature difference is the difference between the vapor temperature and the surface temperature: ΔT = T_vapor - T_surface ΔT = 50°C - 30°C = 20°C

Calculate the heat transfer coefficient (h)

Now, we can plug our values into the heat transfer coefficient equation and solve for h: Q = h * A * ΔT 3800 W = h * 2 m^2 * 20°C Divide both sides by (2 m^2 * 20°C): h = 3800 W / (2 m^2 * 20°C) = 3800 W / 40 m^2°C = mpfr(3800/40 , 2) W/m^2°C h ≈ 95 W/m²°C The heat transfer coefficient h is approximately 95 W/m²°C, which corresponds to answer choice (a).