The fourth‐dimention concept in the finite element analysis of transient heat transfer problems

Abstract

Abstract This study presents the finite element analysis for the transient heat transfer problems by introducing the Fourth‐dimension concept. Time is treated as an additional dimension in the solution domain thereby Increasing the number of dimensions by one. For instance, a three‐dimensional transient problem can be considered as a four‐dimensional problem in the x , y , z , t domain and a two‐dimensional transient problem can be considered as a three‐dimensional steady‐state problem in the x , y , t domain, respectively. The variational principle of the finite element method and the techniques existing for steady‐state problems can be directly utilized. Numerical calculations were performed for heat conduction problems, laminar‐turbulent convective heat transfer problems, and radiative heat transfer problems.