Shape optimization of steady‐state heat‐conduction fields considering temperature dependency of thermal conductivity coefficient. Issue 4 (15th September 2011) - Katamine, Eiji; Mikada, Shingo; Azegami, Hideyuki
Abstract This paper presents a numerical analysis method for shape optimization of domains with steady‐state heat‐conduction fields considering the temperature dependence of the thermal conductivity coefficient. In this paper, we formulate two shape optimization problems, namely, maximization of thermal dissipation on heat transfer boundaries and minimization of heat‐conduction fields. The shape gradient functions for these shape optimization problems are derived theoretically using the Lagrange multiplier method and formulae of the material derivative. Reshaping is accomplished using the traction method proposed as a solution to the shape optimization problems. The proposed method is validated from the results of two‐dimensional numerical analysis. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20374