Heat Transfer · Heat exchangers and effectiveness methods
A single horizontal condenser tube of outer diameter D = 25 mm and length L = 2.40 m…
Problem
A single horizontal condenser tube of outer diameter D = 25 mm and length L = 2.40 m has an outer wall temperature Ts = 32 °C. Saturated R-134a vapor at Tsat = 40 °C condenses on the outside. Liquid R-134a properties at Tf = 36 °C: ρ_l = 1147 kg/m³, μ_l = 1.85×10⁻⁴ N·s/m², k_l = 0.0790 W/m·K, c_p,l = 1447 J/kg·K; ρ_v = 49.0 kg/m³; h_fg = 163 kJ/kg. For laminar film condensation on a single horizontal cylinder, h_D = 0.729 [ ρ_l (ρ_l − ρ_v) g h_fg' k_l³ / (μ_l (Tsat − Ts) D) ]^{1/4}, h_fg' = h_fg + 0.375 c_p,l (Tsat − Ts). Determine h_D, the heat transfer rate for the tube, and the R-134a condensation rate. The cooling water inside the tube has ṁ_c = 0.22 kg/s, cp,c = 4178 J/kg·K, and inlet temperature T_c,i = 18 °C. Assuming the outer-wall temperature remains 32 °C, find the cooling-water outlet temperature from an energy balance on the coolant. Check energy conservation by verifying that ṁ h_fg' equals ṁ_c cp,c (T_c,o − T_c,i) to within the precision of the calculated h_D.
Hint
Use the horizontal-cylinder coefficient 0.729 (not the vertical-plate 0.943) and \(h_{fg}'\) with 0.375.
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