Boundary Shape Determination on Steady-State Heat Conduction Field.

Abstract

This paper presents a practical method of numerical analysis for boundary shape design of steady-state heat conduction fields to control temperature distribution to a prescribed distribution. Reshaping was accomplished by the traction method that was proposed by one of the authors as a solution to domain optimization problems in which elliptic boundary value problems were defined. In this paper, we formulated a temperature square error norm minimization problem between prescribed distribution and actual distribution on prescribed boundaries and theoretically derived shape gradient function for this problem. We developed a convenient numerical method using a general-purpose FEM program for the temperature prescribed problem. The successful results for two-dimensional problems of a erosion surface on blast furnace hearth and a coolant flow passage in turbin blade show the validity of the presented method.