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A boundary‐integral formulation for complex three‐dimensional geometries
Author(s) -
Rezayat Mohsen,
Burton Thomas E.
Publication year - 1990
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/nme.1620290204
Subject(s) - boundary (topology) , mathematics , integral equation , mathematical analysis , boundary value problem , geometry
A new boundary‐integral formulation is proposed to analyse the heat transfer in complex three‐dimensional geometries. One example of such geometry is the die sets in the injection moulding process. Networks of cooling conduits within the mould and the closely spaced die surfaces require special attention both in formulation and numerical treatment of the integral equations. The proposed formulation couples the boundary formula, the gradient of the boundary formula and the exterior formula. The derivation of the integral equations is presented here along with an efficient method for integration of some of the kernels in these equations and a semi‐analytical procedure for the integration of the highly singular integrands which result from differentiating the boundary formula. Although the techniques introduced here are applied to a particular problem in heat transfer, their potential application is much broader.