| Abstract: | The paper presents exact analytical solutions for periodic radial heat conduction through an inhomogeneous hollow circular cylinder for a certain class of thermal conductivity profile. The exact analytical solutions for some of these profiles (including linear and quadratic) are compared with those obtained by considering the cylindrical medium to be made up of a number of homogeneous layers with different thermal conductivities, varying from layer to layer, and using the layered-structure (or matrix-multiplication) method. The numerical results arrived at by the layered-structure method converge rapidly (with increasing number of layers considered) to the values obtained from the exact analytical solutions. This gives confidence in the application of the layered-structure method to periodic heat conduction through an inhomogeneous hollow cylinder. Assuming the inhomogeneous hollow cylinder to be made up of a number of cylindrical layers with a linear profile of thermal conductivity has also been shown to be a more effective alternative method of considering any type of inhomogeniety; it saves computation time, as the rate of converegence is much higher than for the homogeneous-layer structure method. Numerical results are presented in the form of elements of a 2 × 2 matrix, relating the sinusoidal steady-state temperature and the heat flux on the two sides of the cylinder. |
