Subtopic: Steady state heat transfer in conduction, convection and radiation
Question Statement:
In a falling film evaporator, the inside and outside diameters of the tube wall are 25 mm and 27 mm, respectively. The tube is made of SS304 (thermal conductivity = 15 W m⁻¹ K⁻¹) and the inside convective film coefficient is 750 W m⁻² K⁻¹. Outside the tube wall, film coefficient of condensing steam is 7175 W m⁻² K⁻¹. Based on the inside area of the tube, the overall heat transfer coefficient is __________ W m⁻² K⁻¹.
Official Answer Key:
650 to 670
Step-by-Step Solution & Explanation
Overall coefficient referred to the inside area:
1/U_i = 1/h_i + d_i ln(d_o/d_i)/(2k) + d_i/(d_o h_o)
Term 1: 1/750 = 1.3333×10⁻³
Term 2: 0.025 × ln(27/25)/(2 × 15) = 0.025 × 0.07696/30 = 6.413×10⁻⁵
Term 3: 0.025/(0.027 × 7175) = 0.025/193.73 = 1.2905×10⁻⁴
Σ = 1.5265×10⁻³ ⇒ U_i = 655 W m⁻² K⁻¹ — within the official range 650–670.
Note the inside film (87 % of the resistance) dominates; the wall contributes only ~4 %.
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