PERIODIC HEAT-TRANSFER THROUGH INHOMOGENEOUS-MEDIA .1. SLAB

The paper presents exact analytical solutions of one-dimensional perio dic heat conduction through an inhomogeneous slab for a certain class of thermal conductivity profiles (including linear and exponential). T he exact analytical solutions for some of these profiles have been com pared with those obtained by considering the slab to be made up of a n umber of homogeneous layers with different thermal conductivities vary ing from layer to layer and using the layered structure (or matrix mul tiplication) method. The numerical results arrived at by the layered-s tructure method converge rapidly (with increasing number of layers con sidered) to the values obtained from the exact analytical solutions. T his gives confidence in the application of the layered-structure metho d to periodic heat conduction through inhomogeneous slabs. The numeric al results have been presented in the form of elements of a 2 x 2 matr ix, relating the sinusoidal steady-state temperature and heat flux on the two sides of the slab.