AN ASYMPTOTIC INTEGRAL EQUATION METHOD FOR THE STUDY OF HEAT TRANSFER IN LONG, THIN DOMAINS

Abstract

A numerical method is presented for the computationally efficient and accurate solution of heat transfer boundary-value problems (BVPs) within long, slender bodies (e.g., fin assemblies). The method is based on the well-known boundary integral equation (BIE) technique for the solution of steady-state two-dimensional Laplacian BVPs. Whereas the classical BIE is satisfactory for BVPs in which the solution domain has a low length-to-width aspect ratio, it is established that the accuracy and efficiency of the classical BIE deteriorate rapidly for aspect ratios of order greater than O(10). In the present paper the BIE is modified to cope with BVPs in which aspect ratios of O(1000) are encountered. This enables accurate treatment of more physically viable fin assembly geometries that were hitherto beyond the scope of the BIE. The modification essentially incorporates the asymptotic (analytically derived) solution in the majority of the fin, leaving the BIE to solve the BVP numerically in only a minor part of t...