For each of the following cases, determine an appropri-ate

Chapter 5, Problem 5.5

(choose chapter or problem)

For each of the following cases, determine an appropri-ate characteristic length Lcand the corresponding Biotnumber Bithat is associated with the transient thermalresponse of the solid object. State whether the lumpedcapacitance approximation is valid. If temperature infor-mation is not provided, evaluate properties at T?300 K.(a) A toroidal shape of diameter D?50 mm andcross-sectional area Ac?5mm2is of thermalconductivity k?2.3 W/m?K. The surface of thetorus is exposed to a coolant corresponding to aconvection coefficient of h?50 W/m2?K.(b) A long, hot AISI 304 stainless steel bar of rectan-gular cross section has dimensions w?3 mm,W?5 mm, and L?100 mm. The bar is subjectedto a coolant that provides a heat transfer coefficientof h?15 W/m2?K at all exposed surfaces.(c) A long extruded aluminum (Alloy 2024) tube of innerand outer dimensions w?20 mm and W?24 mm,respectively, is suddenly submerged in water, result-ing in a convection coefficient of h?37 W/m2?K atthe four exterior tube surfaces. The tube is plugged atboth ends, trapping stagnant air inside the tube. (d) An L?300-mm-long solid stainless steel rod of diam-eter D?13 mm and mass M?0.328 kg is exposedto a convection coefficient of h?30 W/m2?K.(e) A solid sphere of diameter D?12 mm andthermal conductivity k?120 W/m?K is sus-pended in a large vacuum oven with internal walltemperatures of Tsur?20C. The initial spheretemperature is Ti?100C, and its emissivity is??0.73.(f) A long cylindrical rod of diameter D?20 mm, den-sity ??2300 kg/m3, specific heat cp?1750 J/kg?K,and thermal conductivity k?16 W/m?K is suddenlyexposed to convective conditions with T??20C.The rod is initially at a uniform temperature ofTi?200C and reaches a spatially averaged tempera-ture of T?100C at t?225 s.(g) Repeat part (f) but now consider a rod diameter ofD?200 mm.Case (e)DTi, ?, kTsurCase (c)wAluminumalloyAirDT, hCase (d)LCases (f,g)