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

Park, Seong Jin; Kwon, Tai Hun

doi:10.1002/(sici)1097-0207(19981130)43:6<1109::aid-nme465>3.0.co;2-r

Cited by 11 publications

(1 citation statement)

References 12 publications

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“…This paper presents a numerical method for solving the transient heat conduction problem of a two-dimensional medium containing multiple circular inhomogeneities, cavities and point sources. This problem has applications in the areas of heat conduction in composite materials [1][2][3][4][5][6], die casting and molding [7][8][9], heat exchange between blood tissue and embedded blood vessels [10] and heat exchange between the earth and buried pipes [11]. Additionally, due to the mathematical equivalence of transient heat conduction [12] and transient groundwater flow [13], the method can be applied to transient groundwater flow problems [14,15].…”

Section: Introductionmentioning

confidence: 99%

Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Gordeliy¹,

Mogilevskaya²,

Crouch³

2009

Numerical Meth Engineering

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SUMMARYA two-dimensional transient heat conduction problem of multiple interacting circular inhomogeneities, cavities and point sources is considered. In general, a non-perfect contact at the matrix/inhomogeneity interfaces is assumed, with the heat flux through the interface proportional to the temperature jump. The approach is based on the use of the general solutions to the problems of a single cavity and an inhomogeneity and superposition. Application of the Laplace transform and the so-called addition theorem results in an analytical transformed solution. The solution in the time domain is obtained by performing a numerical inversion of the Laplace transform. Several numerical examples are given to demonstrate the accuracy and the efficiency of the method. The approximation error decreases exponentially with the number of the degrees of freedom in the problem. A comparison of the companion two-and threedimensional problems demonstrates the effect of the dimensionality.

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Section: Introductionmentioning

confidence: 99%

Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Gordeliy¹,

Mogilevskaya²,

Crouch³

2009

Numerical Meth Engineering

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Cooling Simulation

and

Zhou

2013

Computer Modeling for Injection Molding

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Optimization of 3D cooling channels in injection molding using DRBEM and model reduction

et al. 2009

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Today, around 30% of manufactured plastic goods rely on injection moulding. The cooling time can represent more than 70% of the injection cycle. In this process, heat transfer during the cooling step has a great influence both on the quality of the final parts that are produced, and on the moulding cycle time. In the numerical solution of three-dimensional boundary value problems, the matrix size can be so large that it is beyond a computer capacity to solve it. To overcome this difficulty, we develop an iterative dual reciprocity boundary element method (DRBEM) to solve Poisson's equation without the need of assembling a matrix. This yields a reduction of the computational space dimension from 3D to 2D, avoiding full 3D remeshing. Only the surface of the cooling channels needs to be remeshed at each evaluation required by the optimisation algorithm. For more efficiency, DRBEM computing results are extracted stored and exploited in order to construct a model with very few degrees of freedom. This approach is based on a model reduction technique known as proper orthogonal (POD) or Karhunen-Loève decompositions. We introduce in this paper a practical methodology to optimise both the position and the shape of the cooling channels in 3D injection moulding processes. First, we propose an implementation of the model reduction in the 3D transient BEM solver. This reduction permits to reduce considerably the computing time required by each direct computation. Secondly, we present an optimisation methodology applied to different injection cooling problems. For example, we can minimize the maximal temperature on the cavity surface subject to a temperature uniformity constraint. Thirdly, we compare our results obtained by our approach with experimental results to show that our optimisation methodology is viable.

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

Cited by 11 publications

References 12 publications

Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Cooling Simulation

Optimization of 3D cooling channels in injection molding using DRBEM and model reduction

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