Solid Sphere Key Problem

Reconsider the flat plate (key problem) now for solid sphere of diameter 2jR. The exact analytical solution of this problem (see, for example, Ex. 5.10 of Reference 1) is parametrically identical to Eq. (3.128). In Fig. 3.24 the unsteady temperature of the sphere is plotted against Fo for the center (p — 0) and surface (p = 1) of the sphere, with Bi as parameter, where Fo = at JR1 and Bi = hR/k. 

The hottest spot of this cylinder is at location ( = 0, p = 0). Then, for this spot, 

The heat transfer Q from the sphere over a time interval (0, t), relative to the initial internal energy of the sphere, 

Compare these temperatures with the hottest and coldest temperatures of the cube of Ex. 3.12 and the finite cylinder of Ex. 3.13, Justify the results with physical reasoning.  

The foregoing considerations for finite geometry are now extended to semi-infinite geometry. 

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