Shape Optimization of Forced Heat-convection Fields

Abstract

This paper presents a numerical analysis method for solving two shape determination problems of temperature distribution prescribed problem in sub-domains and thermal dissipation maximization problem on sub-boundaries of steady heat convective fields. The square error integral between the actual temperature distributions and the prescribed temperature distributions in the prescribed sub-domains is used as the objective functional for the temperature distribution prescribed problem. Each shape gradient for these shape determination problems was derived theoretically using the adjoint variable method, the Lagrange multiplier method and the formulae of the material derivative.Reshaping was accomplished using a traction method that was proposed as a solution to the domain optimization problems. A new numerical procedure using finite element method for the shape determination problems was proposed. The validity of the proposed method was confirmed by the results of 2D numerical analysis.