Hybrid perturbation/Bubnov-Galerkin technique for nonlinear thermal analysis

Abstract

A two step hybrid analysis technique to predict the nonlinear steady state temperature distribution in structures and solids is presented. The technique is based on the regular perturbation expansion and the classical Bubnov-Galerkin approximation. The functions are obtained by using the regular perturbation method. These functions are selected as coordinate functions and the classical Bubnov-Galerkin technique is used to compute their amplitudes. The potential of the proposed hybrid technique for the solution of nonlinear thermal problems is discussed. The effectiveness of this technique is demonstrated by the effects of conduction, convection, and radiation modes of heat transfer. It is indicated that the hybrid technique overcomes the two major drawbacks of the classical techniques: (1) the requirement of using a small parameter in the regular perturbation method; and (2) the arbitrariness in the choice of the coordinate functions in the Bubnov-Galerkin technique. The proposed technique extends the range of applicability of the regular perturbation method and enhances the effectiveness of the Bubnov-Galerkin technique