Generalization of the integral transform method to nonlinear heat-conduction problems in multilayered spherical media

A method of solving heat conduction problems in multilayered spherical media is presented; it is based on producing an alternative formulation in which the inner layer of the composite sphere is lumped and the transient temperature distribution in the outer layer is obtained, in this, the nonlinear boundary conditions are treated as a source. The temperature distribution of the alternative formulation is then solved analytically. Different parametric studies are worked out and plotted to compare the two formulations for different values of Biot number and different thermal characteristic ratio with those obtained from a numerical solution developed using an explicit finite difference method, and to find the limiting criterion where breakdown of the approximation occurs.