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research-article

Semi-Analytic Complex Variable Method for Computing Sensitivities in Heat Transfer Problems

[+] Author and Article Information
James Grisham

Graduate Research Assistant, Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, Texas 76019
james.grisham@mavs.uta.edu

Ashkan Akbariyeh

Graduate Research Assistant, Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, Texas 76019
ashkan.akbariyeh@mavs.uta.edu

Weiya Jin

Professor, College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, Zhejiang, China
jinweiya@zjut.edu.cn

Dr. Brian H. Dennis

Professor, Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, Texas 76019
dennisb@uta.edu

Bo P. Wang

Professor, Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, Texas 76019
bpwang@mae.uta.edu

1Corresponding author.

ASME doi:10.1115/1.4039541 History: Received February 27, 2017; Revised February 17, 2018

Abstract

Sensitivity information is often of interest in engineering applications (e.g., gradient-based optimization). Heat transfer problems frequently involve complicated geometries for which exact solutions cannot be easily derived. As such, it is common to resort to numerical solution methods such as the finite element method. The semi-analytic complex variable method is an accurate and efficient approach to computing sensitivities within a finite element framework. The method is introduced and a derivation is provided along with a detailed description of the algorithm which requires very minor changes to the analysis code. Three benchmark problems in steady-state heat transfer are studied including a nonlinear problem, an inverse shape determination problem and a reliability analysis problem. It is shown that the semi-analytic complex variable method is superior to the other methods considered in terms of computation time and sensitivity to perturbation size.

Copyright (c) 2018 by ASME
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