Heat Transfer · Thermal radiation and enclosure exchange
Refrigerant vapor is condensed on the outside of a 19 mm o.d
Problem
Refrigerant vapor is condensed on the outside of a 19 mm o.d. copper tube (k_w = 400 W/m·K, wall thickness 1.2 mm), imposing a nearly uniform outer-surface temperature of 8 °C. Liquid water flows inside at ṁ = 0.12 kg/s. Water properties at 15 °C are μ = 1.14 × 10⁻³ kg/m·s, k = 0.591 W/m·K, Pr = 8.06, cp = 4186 J/kg·K. The inner flow is turbulent; use Gnielinski’s correlation Nu_D = ((f/8)(Re_D − 1000) Pr)/(1 + 12.7 (f/8)^{1/2} (Pr^{2/3} − 1)) with f = (0.790 ln Re_D − 1.64)^{−2} based on the inner diameter. Assemble the series resistance per unit length from internal convection and wall conduction, compute the overall coefficient based on the inner surface, U_i, and find the water bulk temperature at a station where the inner-surface heat flux is 2.5 × 10⁴ W/m².
Hint
Recover \(D_i=D_o-2t\) before computing \(Re_D\) and Gnielinski \(Nu_D\).
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