11.7 The following heat sink consists of a 1 m tall central tube and 12 radial fins that are uniformly distributed every 30°C around the central tube. The central tube has an outer diameter of 0.4 m and an inner diameter of 0.36 m. Each fin is 0.048 m wide, 0.4 m long, and 1 m tall. The vapor temperature inside the tube is 315°C with a heat transfer coefficient of 2.94 x 105 W/(m2°C). The surrounding air temperature is 0°C with a heat transfer coefficient of 40.88 W/(m2°C). The heat sink is made of aluminum alloy with a thermal conductivity of 175 W/ (m K), a density of 2770 kg/m³, and a specific heat of 870 J/(kg K). Optimize the fin width W and the fin length L to minimize the use of material while achieving a minimum heat dissipation of 75 kW per unit length. The design variables W and L have the following range of variations: 0.03 m < W<0.052 m, and 0.2 m

11.7 The following heat sink consists of a 1 m tall central tube and 12 radial fins that are uniformly distributed every 30°C around the central tube. The central tube has an outer diameter of 0.4 m and an inner diameter of 0.36 m. Each fin is 0.048 m wide, 0.4 m long, and 1 m tall. The vapor temperature inside the tube is 315°C with a heat transfer coefficient of 2.94 x 105 W/(m2°C). The surrounding air temperature is 0°C with a heat transfer coefficient of 40.88 W/(m2°C). The heat sink is made of aluminum alloy with a thermal conductivity of 175 W/ (m K), a density of 2770 kg/m³, and a specific heat of 870 J/(kg K). Optimize the fin width W and the fin length L to minimize the use of material while achieving a minimum heat dissipation of 75 kW per unit length. The design variables W and L have the following range of variations: 0.03 m < W<0.052 m, and 0.2 m

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter10: Heat Exchangers

Section: Chapter Questions

Problem 10.51P

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