For each of the following cases, determine an appropriate characteristic length Lc 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. (a) A toroidal shape of diameter D _ 50 mm and cross-sectional area Ac _ 5mm2 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.