Sensitivity Analysis Formulation for Three-Dimensional Conduction Heat Transfer With Complex Geometries Using a Boundary Element Method

Abstract

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.KEY WORDS: special boundary integral formulation; design sensitivity analysis (DSA); direct differentiation approach (DDA); three-dimensional conduction heat transfer

Optimization method for steady conduction in special geometry using a boundary element method

“…Before the discussion of optimization results, it might be noted that the accuracy of the analysis formulation and that of the sensitivity analysis formulation were demonstrated by Rezayat and Burton 7 and by Park and Kwon,9 respectively. The optimization method proposed in this paper has been applied to three representative examples.…”

“…This formulation avoids discretization of the circular channels along the circumference and thus saves a large amount of computer memory and time. See the references by Rezayat and Burton, 7 Himasekhar and co-workers 13 and Park and Kwon 9 for further details of this modiÿed approach for part surfaces, circular holes, and exterior surface.…”

“…It may be noted that in equation (9) 9 for details of evaluating these integrals. Next, sensitivities of boundary conditions can be introduced into equation (9) to obtain a system of linear algebraic equations as follows:…”

An interface integral formulation of heat energy calculation of steady state heat conduction in heterogeneous media

“…Steady state heat conduction in inhomogeneous medium has widely been studied using analytical methods or boundary element methods [4,8,15,5,16]. Further research about steady state heat conduction inhomogeneous problems is to carry out the analysis of shape optimization of inhomogeneities based on the minimization of objective function, i.e.…”

Optimization of the Powder Injection Molding Process Parameters Using the Sequential Simplex Algorithm and Sensitivity Analysis

“…Significant progress has been made in the last few years in the computer modeling of most aspects of the PIM process, from the tool design [9,10], feedstock preparation [1,11-14], heat transfer [15], injection molding stage [1,4,7,10,14, [16][17][18][19][20][21][22], and powderbinder separation [2,8,23], to debinding [24][25][26][27][28], and sintering [29][30][31][32][33][34]. However, most of these are still in the research and development phase, and have not been applied on actual production cases.…”