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FRACTAL ANALYSIS FOR HEAT EXTRACTION IN GEOTHERMAL SYSTEM

ABSTRACT
Heat conduction and convection play a key role in geothermal development. These two processes are coupled and influenced by fluid seepage in hot porous rock. A number of integer dimension thermal fluid models have been proposed to describe this coupling mechanism. However, fluid flow, heat conduction and convection in porous rock are usually non-linear, tortuous and fractal, thus the integer dimension thermal fluid flow models can not well describe these phenomena. In this study, a fractal thermal fluid coupling model is proposed to describe the heat conduction and flow behaviors in fractal hot porous rock in terms of local fractional time and space derivatives. This coupling equation is analytically solved through the fractal travelling wave transformation method. Analytical solutions of Darcy's velocity, fluid temperature with fractal time and space are obtained. The solutions show that the introduction of fractional parameters is essential to describe the mechanism of heat conduction and convection.
KEYWORDS
PAPER SUBMITTED: 2017-03-10
PAPER REVISED: 2017-05-01
PAPER ACCEPTED: 2017-05-10
PUBLISHED ONLINE: 2017-12-02
DOI REFERENCE: https://doi.org/10.2298/TSCI17S1025S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Supplement 1, PAGES [S25 - S31]
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© 2017 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence