Non-Fourier Heat Transfer Analysis of Functionally Graded Spherical Shells under Convection-Radiation Conditions

Abstract

Non-Fourier heat transfer analysis of functionally graded (FG) spherical shells subjected to the radiative-convective boundary conditions at their inner and outer surfaces are presented. It is assumed that the material properties have continuous variations along the thickness direction. The incremental differential quadrature method (IDQM) as an accurate and computationally efficient numerical tool is adopted to discretize the governing differential equations in both the spatial and temporal domain. The fast rate of convergence behavior and accuracy of the method is investigated through different examples and also, the results are compared with those available in the open literature wherever possible. Comparison studies between the results of IDQM and Runge-Kutta method (RKM) are also performed to establish the superior computational efficiency of the IDQM with respect to RKM. After validating the present formulation and method of solution, the influences of different parameters on the temperature time history and temperature distribution of the FG spherical shells are investigated. It is shown that the radiation boundary conditions decrease the period of oscillation of temperature time history. Also, it is observed that by increasing the non-Fourier time constant, the non-dimensional temperature oscillatory behavior increases. On the other hand, the present study reveals that the IDQM, as an accurate and practically efficient method, can be used for the analysis of different problems in the fields of the oil and petrochemical engineering in the future.