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Question: a a toroidal shape of diameter d50 mm and crosssectional...

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(a A toroidal shape of diameter D-50 mm and cross-sectional area Ac-5 mm2 is of thermal conductivity k-23 w m K. The surtaceo e torus is exposed to a coo a 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-5mm, and L-100 mm. The bar is subjected to a coolant that provides a heat transfer coefficient of h -15W/m2 Kat 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-K is 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-o.75 f) A long cylindrical rod of diameter D-20 mm density ρ-2300 kg/m3 specific heat C -1750 J/kg K, and thermal conductivity k-16 w/m K s suddenly exposed to convective conditions with T -20°C. The rodis 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 () but now consider a rod diameter of D- 200 mm5.6 For each of the following cases, determine an appropriate characteristic length Le and the corresponding Biot number Bi that is associated with the transient thermal response of the solid object. State whether the lumped capacitance approximation is valid. If temperature information is not provided, evaluate properties at T-300 K T, h Ac Case (a) Case (b) Th Aluminumm alloy Air Case (c) Case (d) rep, k, cp Case (e) Cases (f.g

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