PERIODIC HEAT-TRANSFER THROUGH INHOMOGENEOUS-MEDIA .3. HOLLOW SPHERE

The paper presents the exact analytical solutions for periodic radial heat conduction through an inhomogeneous hollow sphere for a certain c lass of thermal-conductivity profile. The exact analytical solutions f or some of these profiles, (including linear and quadratic) have been compared with those obtained by considering the spherical medium to be made up of a number of homogeneous layers with different thermal cond uctivities, varying from layer to layer, and using the layered-structu re (or matrix-multiplication) method. The numerical results arrived at by the layered-structure method converge rapidly (with increasing num ber of layers considered) to the values obtained from the exact analyt ical solutions. It strengthens the confidence in applying the layered- structure method to the case of periodic heat conduction through an in homogeneous hollow cylinder. Considering the inhomogeneous conducting medium to be made up of a number of spherical layers with a linear pro file of thermal conductivity has been shown to be a more effective alt ernative method of accounting for any type of inhomogeniety; and it sa ves computation time, as the rate of convergence is much higher than f or the homogeneous-layered structure method. The numerical results hav e been presented in the form of elements of a 2 x 2 matrix, relating t he sinusoidal steady-state temperature and heat flux on the two surfac es of the hollow sphere.