Heat conduction across irregular and fractal-like surfaces

Blyth, M. G. and Pozrikidis, C. (2003) Heat conduction across irregular and fractal-like surfaces. International Journal of Heat and Mass Transfer, 46 (8). pp. 1329-1339. ISSN 0017-9310

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Abstract

The effect of irregularities on the rate of heat conduction from a two-dimensional isothermal surface into a semi infinite medium is considered. The effect of protrusions, depressions, and surface roughness is quantified in terms of the displacement of the linear temperature profile prevailing far from the surface. This shift, coined the displacement length, is designated as an appropriate global measure of the effect of the surface indentations incorporating the particular details of the possibly intricate geometry. To compute the displacement length, Laplace's equation describing the temperature distribution in the semi-infinite space above the surface is solved numerically by a modified Schwarz-Christoffel transformation whose computation requires solving a system of highly non-linear algebraic equations by iterative methods, and an integral equation method originating from the single-layer integral representation of a harmonic function involving the periodic Green's function. The conformal mapping method is superior in that it is capable of handling with high accuracy a large number of vertices and intricate wall geometries. On the other hand, the boundary integral method yields the displacement length as part of the solution. Families of polygonal wall shapes composed of segments in regular, irregular, and random arrangement are considered, and pre-fractal geometries consisting of large numbers of vertices are analyzed. The results illustrate the effect of wall geometry on the flux distribution and on the overall enhancement in the rate of transport for regular and complex wall shapes.

Item Type: Article
Additional Information: Funding Information: This research was supported by a grant provided by the National Science Foundation.
Uncontrolled Keywords: condensed matter physics,mechanical engineering,fluid flow and transfer processes ,/dk/atira/pure/subjectarea/asjc/3100/3104
Faculty \ School: Faculty of Science > School of Mathematics
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Depositing User: LivePure Connector
Date Deposited: 19 Jul 2022 15:30
Last Modified: 12 Aug 2022 05:44
URI: https://ueaeprints.uea.ac.uk/id/eprint/86625
DOI: 10.1016/S0017-9310(02)00419-2

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