On high-continuity transfinite-element formulations for linear/nonlinear transient thermal problems

This paper describes recent developments in the applicability of a hybrid transfinite-element methodology with emphasis on high-continuity formulations for linear/nonlinear transient thermal problems. The proposed concepts furnish accurate temperature distributions and temperature gradients making use of a relatively smaller number of degrees of freedom; and the methodology is applicable to linear /nonlinear thermal problems. Characteristic features of the formulations are described in technical detail, as the proposed hybrid approach combines the major advantages and modeling features of high-continuity thermal finite elements in conjunction with transform methods and classical Galerkin schemes. Several numerical test problems are evaluated, and the results obtained validate the proposed concepts for linear /nonlinear thermal problems.