A New Exact Analysis for Anisotropic Conductive Heat Transfer in Truncated Composite Spherical Shells

Abstract

ABSTRACTIn the present paper, a general analytical solution is proposed for anisotropic heat conduction through truncated composite spherical shells. The solution is so important in designing the spherical vessels which are usually used to store the CNG, LNG, LPG and other petroleum condensates. Herein, it is supposed that the fiber angle of composite laminate is in range of zero to 90 degrees. Heat convection with ambient flow, an external heat radiation, and a possible internal heat generation are modeled within the heat transfer equation. The exact solution is derived using the complex finite Fourier transform method. The particular solution of transferred equation is found based on the Green’s function and Sturm-Liouville theories. Finally, an inverse integral transformation is applied to form the final analytical solution in physical space. Defining four materials differing in the value of conductivity coefficient in fiber direction, the effects of used composite material and fiber angle on temperature distribution of the spherical shell are investigated in detail.