State whether the lumped capacitance approximation is valid. If temperature information is not provided, evaluate properties at T= 300 K. (a) A toroidal shape of diameter D = 50 mm and cross-sectional area Ac = 5 mm² is of thermal conductivity k = 2.3 W/m K. The surface of the torus is exposed to a coolant corresponding to a convection coefficient of h = 50 W/m2 K. (b) A long, hot AISI 304 stainless steel bar of rectangular cross section has dimensions w = 3 mm, W = 5 mm, and L = 100 mm.The bar is subjected to a coolant that provides a heat transfer coefficient of h = 15 W/m2 . K at all exposed surfaces. (c) A long extruded aluminum (Alloy 2024) tube of inner and outer dimensions w = 20 mm and W = 24 mm, respectively, is suddenly submerged in water, resulting in a convection coefficient of h = 37 W/m2 . K at the four exterior tube surfaces.The tube is plugged at both ends, trapping stagnant air inside the tube. (d) An L = 300-mm-long solid stainless steel rod of diameter D= 13 mm and mass m = 0.328 kg is exposed to a convection coefficient of h = 30 W/m2 . K. (e) A solid sphere of diameter D = 13 mm and thermal conductivity k = 130 W/m · Kis suspended in a large vacuum oven with internal wall temperatures of Tsur = 18°C. The initial sphere temperature is T; = 100°C, and its emissivity is e = 0.75. (f) A long cylindrical rod of diameter D = 20 mm, density p =2300 kg/m3, specific heat c, = 1750 J/kg · K, and thermal Cp conductivity k = 16 W/m · K is suddenly exposed to convective conditions with T = 20°C. The rod is initially at a uniform temperature of T; = 200°C and reaches a spatially averaged temperature of T = 100°C at t = 225 s. (g) Repeat part (f) but now consider a rod diameter of D = 200mm.
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