Shape Optimization of Steady-State Heat-Conduction Fields Considering Temperature Dependency of Thermal Conductivity Coefficient(Thermal Engineering)

Abstract

This paper presents a numerical analysis method for solving shape optimization problems of domains in which steady-state heat conduction fields considering temperature dependency of thermal conductivity coefficient are defined. In this paper, we formulated two shape optimization problems, namely, maximization of thermal dissipation on heat transfer boundaries and minimization of the heat conduction fields. The shape gradient functions for these shape optimization problems were derived theoretically using the Lagrange multiplier method and the formulae of material derivative. Reshaping was accomplished using the traction method that was proposed as a solution to the shape optimization problems. The validity of the proposed method was confirmed by the results of 2D numerical analysis.