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SENSITIVITY ANALYSIS FORMULATION FOR THREE‐DIMENSIONAL CONDUCTION HEAT TRANSFER WITH COMPLEX GEOMETRIES USING A BOUNDARY ELEMENT METHOD
Author(s) -
PARK S. J.,
KWON T. H.
Publication year - 1996
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19960830)39:16<2837::aid-nme981>3.0.co;2-4
Subject(s) - sensitivity (control systems) , thermal conduction , heat transfer , boundary element method , boundary (topology) , boundary value problem , finite element method , mathematics , mathematical analysis , molding (decorative) , mechanics , geometry , mechanical engineering , physics , engineering , structural engineering , thermodynamics , electronic engineering
A special boundary integral formulation had been proposed to analyse many engineering problems of conduction heat transfer in complex three‐dimensional geometries (closely spaced surface and circular hole in infinite domain or simple modification of it) by Rezayat and Burton. One example of such geometries is the mold sets in the injection molding process. In this paper, an efficient and accurate approach for the design sensitivity analysis (DSA) is presented for these kinds of problems in the similar complex geometries using the direct differentiation approach (DDA) based on the above special boundary integral formulation. The present approach utilizes the implicit differentiation of the boundary integral equations with respect to the design variables (radii and locations of circular holes) to yield the sensitivity equations. A sample problem (heat transfer of injection molding cooling system) is solved to demonstrate the accuracy of the present sensitivity analysis formulation. Although the techniques introduced here are applied to a particular problem in heat transfer of injection molding cooling system, their potential application is quite broad.