A sphere 30 mm in diameter initially at 800 K isquenched

Chapter 5, Problem 5.75

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A sphere 30 mm in diameter initially at 800 K isquenched in a large bath having a constant temperatureof 320 K with a convection heat transfer coefficient of75 W/m2?K. The thermophysical properties of thesphere material are: ??400 kg/m3, c?1600 J/kg?K,and k?1.7 W/m?K.(a) Show, in a qualitative manner on T tcoordinates,the temperatures at the center and at the surface of thesphere as a function of time.(b) Calculate the time required for the surface of thesphere to reach 415 K.(c) Determine the heat flux (W/m2) at the outer surfaceof the sphere at the time determined in part (b).(d) Determine the energy (J) that has been lost by thesphere during the process of cooling to the surfacetemperature of 415 K.(e) At the time determined by part (b), the sphere isquickly removed from the bath and covered withperfect insulation, such that there is no heat lossfrom the surface of the sphere. What will be thetemperature of the sphere after a long period oftime has elapsed?(f ) Compute and plot the center and surface tempera-ture histories over the period 0?t?150 s. Whateffect does an increase in the convection coefficientto h?200 W/m2?K have on the foregoing temper-ature histories? For h?75 and 200 W/m2?K, com-pute and plot the surface heat flux as a function oftime for 0?t?150 s