Abstract
AbstractThis paper presents a numerical analysis method for solving two shape optimization problems, namely, determining temperature distributions in subdomains and maximizing the thermal dissipation on sub‐boundaries of steady‐state thermal convective fields. The square‐error integral between the actual temperature distributions and the prescribed temperature distributions in the prescribed subdomains is employed as the objective function for determining the temperature distribution. The shape gradients for these shape determination problems were 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 is proposed that applies the finite element method to the shape determination problems. The validity of this method was confirmed by 2D numerical analysis. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(5): 313–328, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20202
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