Analysis/Finite-Element Combined Methodology on Temperature Distribution of a Finite Domain With Various Heat Sources

Abstract

A new method, involving the combined use of analysis and the finite-element method, is applicable to the heal conduction problem with isoltlled heat sources. Unlike the finite-element method, the analysis/ finite-element combined metlwd is able to discretiie the distributed sources with discontinuities into course elements, and the solution is stiU calcuJated accurately. The resuJJs are compared in tables with exaa solutions and other numerical data, and the agreement is found to be good.

Analysis/finite-difference combined solution of boundary value problems of heat conduction in finite domains with planar-discrete sources

“…where u(x) is the unit step function and K = 1 W=cm 2 C. As shown in Table I, reÿning the mesh would make the ÿnite-element solutions approach the present solutions, and the number of grids (72 grids) required for the present method is less than that required for the ÿnite element when using the ÿnest mesh methods (929 nodes), as shown in Table I. Moreover, the present solutions agree well with the analysis=ÿnite element solutions [8] when the same mesh is used. This indicates that the combined method presented by the authors is available whichever numerical method is used to combine with the analytical method.…”

“…An analysis=ÿnite element method developed by the authors [8], combining the analysis and ÿnite element method, takes advantage of the exact solution of the analytical method and of the ability of the ÿnite element method to ÿt complex geometries. Hence, it can remove the restriction of mesh reÿnement at the large temperature gradients.…”