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 (SACVM) 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 SACVM is superior to the other methods considered in terms of computation time and sensitivity to perturbation size.
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Application of the Semi-Analytic Complex Variable Method to Computing Sensitivities in Heat Conduction
James Grisham,
James Grisham
Department of Mechanical and Aerospace
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
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Ashkan Akbariyeh,
Ashkan Akbariyeh
Department of Mechanical and Aerospace
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Search for other works by this author on:
Weiya Jin,
Weiya Jin
Professor
College of Mechanical Engineering,
Zhejiang University of Technology,
Hangzhou 310032, Zhejiang, China
College of Mechanical Engineering,
Zhejiang University of Technology,
Hangzhou 310032, Zhejiang, China
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Brian H. Dennis,
Brian H. Dennis
Professor
Department of Mechanical and Aerospace
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Department of Mechanical and Aerospace
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Search for other works by this author on:
Bo P. Wang
Bo P. Wang
Professor
Department of Mechanical and Aerospace
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Department of Mechanical and Aerospace
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Search for other works by this author on:
James Grisham
Department of Mechanical and Aerospace
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Ashkan Akbariyeh
Department of Mechanical and Aerospace
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Weiya Jin
Professor
College of Mechanical Engineering,
Zhejiang University of Technology,
Hangzhou 310032, Zhejiang, China
College of Mechanical Engineering,
Zhejiang University of Technology,
Hangzhou 310032, Zhejiang, China
Brian H. Dennis
Professor
Department of Mechanical and Aerospace
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Department of Mechanical and Aerospace
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Bo P. Wang
Professor
Department of Mechanical and Aerospace
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Department of Mechanical and Aerospace
Engineering,
University of Texas at Arlington,
Arlington, TX 76019
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 27, 2017; final manuscript received February 17, 2018; published online June 29, 2018. Assoc. Editor: Alan McGaughey.
J. Heat Transfer. Aug 2018, 140(8): 082006 (9 pages)
Published Online: June 29, 2018
Article history
Received:
February 27, 2017
Revised:
February 17, 2018
Citation
Grisham, J., Akbariyeh, A., Jin, W., Dennis, B. H., and Wang, B. P. (June 29, 2018). "Application of the Semi-Analytic Complex Variable Method to Computing Sensitivities in Heat Conduction." ASME. J. Heat Transfer. August 2018; 140(8): 082006. https://doi.org/10.1115/1.4039541
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