An aluminium tube carrying a hot liquid at 118°C has 12 integrally machined longitudinal fins on its outer surface. The tube's inner and outer radii are 12 and 20 mm, and its total length is 281 mm, while the fins' height is 18 mm and their thickness is 2.2 mm. Air at 25°C flows over the fin surface, providing an approximately uniform convection heat transfer coefficient of 35 W/m2°C, and the heat transfer coefficient of the hot liquid inside the tube is 51 W/m2°C. The thermal conductivity of aluminium is 204 W/m °C. (a) State the assumptions and draw a clear sketch showing the geometry, boundary conditions and equivalent thermal circuit. Demonstrate how these assumptions could be used in solution of the problem. (b) Calculate the thermal resistance of the entire fin system. (c) Calculate the fin's heat transfer rate.

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