Semi‐analytical finite element procedure for conduction in anisotropic axisymmetric solids

Abstract

SUMMARYThrough the use of complex series representations and the properties of adjoint differential operators, a semi-analytical finite element procedure is developed which can analyse the steady state and transient temperature fields of thermally anisotropic axisymmetric bodies with complete circumferential properties. Due to its generality, the procedure can handle arbitrary laminate construction with possible meridional and radial variations in locally or globally thermally anisotropic materials. In this respect, the procedure developed herein supercedes the classical semi-analytical treatment which is limited to specially orthotropic materials. Furthermore, in contrast with the classical procedure, the present treatment reveals several important effects of material anisotropy which are entirely missed by the specially orthotropic assumption.

A Multipoint Flux Approximation of the Steady-State Heat Conduction Equation in Anisotropic Media

“…The energy transport goveming equation is then solved through the threedimensional structures using a high-efficiency lattice Boltzmann scheme. In terms of finite element, one of the earliest works on the subject is that of Padovan [18], who investigated steady heat conduction in linear and nonlinear fully anisotropic media.…”