Unsteady solid sphere

Solve the one-dimensional, unsteady conductive heat transfer equation for a homogeneous solid sphere. (Hint (1) Let = R T so that... 

The rate of unsteady-state heat conduction into a solid sphere is characterized by the following parameters ... 

Piret et al.(3> attempted to reproduce the conditions in a porous solid using banks of capillary tubes, beds of glass beads and porous spheres, and measured the rate of transfer of a salt as solute through water to the outside of the system. It was shown that the rate of mass transfer is that predicted for an unsteady transfer process and that the shape of the pores could be satisfactorily taken into account. 

Fig. 5.7 Temperature profiles for unsteady-state heat conduction in spheres T(r,0) = 7 q, T(R, t) — / j. [Reprinted by permission from H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed., Oxford University Press, New York, 1973.]...

Maxey MR (1993) The equation of motion for a small rigid sphere in a nonuniform or unsteady flow. ASME, FED-Vol 166, Gas-Solid Flows Middleman S (1998) An Introduction to Mass and Heat Transfer Principles of Analysis and Design. John Wiley Sons, Inc., New York Middleman S (1998) An Introduction to Fluid Dynamics Principles of Analysis and Design. John Wiley Sons, Inc., New York... 

The numerical results of this case are presented graphically in Figs. 5.3-5 and 5.3-6. Figure 5.3-5 by Gurney and Lurie (G2) is a convenient chart for determining the temperatures at any position in the plate and at any time t. The dimensionless parameters used in these and subsequent unsteady-state charts in this section are given in Table 5.3-1 (x is the distance from the center of the flat plate, cylinder, orsphere. x, is one half the thickness of the flat plate radius of cylinder, or radius of sphere, x = distance from the surface for a semiinfinite solid.)... 

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