In an experiment to measure convection heat transfer coefficients, a very thin metal foil of very low emissivity (e.g., highly polished copper) is attached on the surface of a slab of material with very low thermal conductivity. The other surface of the metal foil is exposed to convection heat transfer by flowing fluid over the foil surface. This setup diminishes heat conduction through the slab and radiation on the metal foil surface, while heat convection plays the prominent role. The slab on which the metal foil is attached to has a thickness of 25 mm and a thermal conductivity of 0.023 W/m·K. In a condition where the surrounding room temperature is 20°C, the metal foil is heated electrically with a uniform heat flux of 5000 W/m². If the bottom surface of the slab is 20°C and the metal foil has an emissivity of 0.02, determine

(a) The convection heat transfer coefficient if air is flowing over the metal foil and the surface temperature of the foil is 150°C;

(b) The convection heat transfer coefficient if water is flowing over the metal foil and the surface temperature of the foil is 30°C.

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Metal foll e = 0.02 Tsurr = 20°C Fluld, T = 20°C - aelac = 5000 W/m? Slab L= 25 mm k= 0.023 W/m-K T2= 20°C