A Coupled B-Spline Based Multi-Step Method and Differential Quadrature for 2D Transient Heat Transfer Analysis of FG Truncated Cone

A new multi-step method based on the B-spline curves is developed for the solution of system of differential equations. Efficiency of the presented method in terms of convergence and accuracy is demonstrated through the two-dimensional transient heat transfer analysis of functionally graded truncated cone subjected to to thermal load. The differential quadrature method (DQM), as an efficient and accurate numerical tool is employed to discretize obtained governing equations with the related boundary conditions in the spatial domain. For this purpose, a mapping technique is used to transform the cross section of the shell into the computational domain of DQM. This transforms the partial differential equations into a system of ordinary differential equations in the temporal domain which is then solved using the presented technique. The material properties are assumed to be graded in radius direction, which it can vary according to a simple power law distribution. Finally, the effects of different parameters on the transient temperature of the truncated cone are studied. It is expected that the presented multi-step method to be applied on various practical engineering problems in future studies.