Abstract
This paper presents a numerical analysis method for solving the shape optimization problems of domains in which unsteady heat conduction fields problems are defined. Reshaping was accomplished by the traction method that was proposed as a solution to domain optimization problems in which boundary value problems were defined. In this paper, we formulated a maximaization problem of thermal dissipation on heat transfer boundaries in the steady and unsteady heat conduction fields and theoretically derived shape gradient function for these problems using the Lagrange multiplier method and the formulation of material derivative. The time-histories of temperature distributions are evaluated using the finite element method for space integral and the Crank-Nicolson method for time integral. The successful results to 2D problems of thermal dissipation model show the validity of the presented method.
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