Sizing Design Sensitivity Analysis of Linear Steady Heat Transfer Systems Using Established Finite Element Codes

Abstract

Abstract A method for design sensitivity analysis of linear steady-state heat transfer systems is presented. To carry out computation of the sensitivity expressions derived in this paper, only postprocessing data from established finite element heat transfer codes are required. It is shown that design sensitivity computations can be performed efficiently without having to embed design sensitivity software into the finite element heat transfer code. Heat conduction is considered with convection boundary conditions. For heat transfer systems made up of one or more component types, sizing design variables such as thickness and cross-sectional areas of components of individual members, heat conductivities of materials, and surface convection coefficients are considered. A distributed parameter approach to design sensitivity analysis is used to retain the continuum formulation throughout the derivation of design sensitivity results. Expressions for design sensitivity of a general functional are thus derived in the continuum setting, using both direct differentiation and adjoint variable methods, which can be evaluated numerically using analysis results from established finite element heat transfer analyzers. The methods do not require differentiation of element thermal conductivity matrices in conventional finite element models. For numerical implementation, only the adjoint variable method is considered. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy and high cost associated with selection of finite difference perturbations.