Consider the sphere of Example 5.6, which is initiallyat a
Chapter 5, Problem 5.82(choose chapter or problem)
Consider the sphere of Example 5.6, which is initiallyat a uniform temperature when it is suddenly removedfrom the furnace and subjected to a two-step coolingprocess. Use the Transient Conduction, Spheremodelof IHTto obtain the following solutions.(a) For step 1, calculate the time required for the centertemperature to reach T(0, t)?335C, while cool-ing in air at 20C with a convection coefficient of10 W/m2?K. What is the Biot number for this cool-ing process? Do you expect radial temperature gra- dients to be appreciable? Compare your results tothose of the example.(b) For step 2, calculate the time required for the centertemperature to reach T(0, t)?50C, while coolingin a water bath at 20C with a convection coeffi-cient of 6000 W/m2?K.(c) For the step 2 cooling process, calculate and plotthe temperature histories, T(r, t), for the center andsurface of the sphere. Identify and explain key fea- tures of the histories. When do you expect the tem-perature gradients in the sphere to be the largest?
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