International Scientific Journal

Authors of this Paper

External Links


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.
PAPER REVISED: 2017-05-01
PAPER ACCEPTED: 2017-05-10
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Supplement 1, PAGES [S25 - S31]
  1. Tester, J. W., et al., The Future of Geothermal Energy, Impact of Enhanced Geothermal Systems (EGS) on the United States in the 21st Century, Massachusetts Institute of Technology, Cambridge, Mass., USA, 2006
  2. Osmani, A., et al., Electricity Generation from Renewables in the United States: Resource Potential, Current Usage, Technical Status, Challenges, Strategies, Policies, and Future Directions, Renewable and Sustainable Energy Reviews, 24 (2013), Aug., pp. 454-472
  3. Lewis, R. W., et al., Finite Element Modelling of Two-Phase Heat and Fluid Flow in Deforming Porous Media, Transport in Porous Media, 4 (1989), 4, pp. 319-334
  4. Jiang, F. M., et al., A Three-Dimensional Transient Model for EGS Subsurface Thermo-Hydraulic Process, Energy, 72 (2014), 1, pp. 300-310
  5. Kohl, T., et al., Coupled Hydraulic, Thermal and Mechanical Considerations for the Simulation of Hot Dry Rock Reservoirs, Geothermics, 24 (1995), 24, pp. 345-359
  6. Taron, J., et al., Thermal - Hydrologic - Mechanical - Chemical Processes in the Evolution of Engineered Geothermal Reservoirs, Inter Journal of Rock Mechanics and Mining Sciences, 46 (2009), 5, pp. 855-864
  7. Noorishad, J., et al., Coupled Thermal - Hydraulic - Mechanical Phenomena in Saturated Fractured Porous Rocks: Numerical Approach, Journal of Geophysical Research: Solid Earth, 89 (1984), B12, pp. 10365-10373
  8. Kang, J. H., et al., Numerical Modeling and Experimental Validation of Anomalous Time and Space Subdiffusion for Gas Transport in Porous Coal Matrix, International Journal of Heat and Mass Transfer, 100 (2016), Sept., pp. 747-757
  9. Lomize, G. M., Flow in Fractured Rocks, Gosenergoizdat, Moscow, 1951, pp.127-197
  10. Qi, H., Jin H., Unsteady Helical Flows of a Generalized Oldroyd-B Fluid with Fractional Derivative, Nonlinear Anal. RWA, 10 (2009), 5, pp. 2700-2708
  11. Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, USA, 2015
  12. Yang, X. J., et al., Systems of Navier-Stokes Equations on Cantor Sets, Mathematical Problems in Engineering, 2013 (2013), ID 769724
  13. Liu, H. Y., et al., Fractional Calculus for Nanoscale Flow and Heat Transfer, International Journal of Numerical Methods for Heat & Fluid Flow, 24 (2014), 6, pp. 1227-1250
  14. Yang, X. J., et al., A New Family of the Local Fractional PDEs, Fundamenta Informaticae, 151 (2017), 1-4, pp. 63-75
  15. Gao, F., Yang, X. J., Local Fractional Euler's Method for the Steady Heat-Conduction Problem, Thermal Science, 20 (2016), Suppl. 3, S735-S738
  16. Yang, X. J., et al., New Rheological Models within Local Fractional Derivative, Romanian Reports in Physics, 69 (2017), 3, ID 113
  17. Yang, X. J., et al., On a Fractal LC-Electric Circuit Modeled by Local Fractional Calculus, Communications in Nonlinear Science and Numerical Simulation, 47 (2017), June, pp. 200-206
  18. Yang, X. J., et al., Exact Travelling Wave Solutions for the Local Fractional Two-Dimensional Burgers- Type Equations, Computers & Mathematics with Applications, 73 (2017), 2, pp. 203-210
  19. Yang, X. J., et al., On Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain, Fractals, 25 (2017), 4, pp. 1740006-1-7
  20. Yang, X. J., et al., On Exact Traveling-Wave Solutions for Local Fractional Korteweg-de Vries Equation, Chaos: An Interdisciplinary Journal of Nonlinear Science, 26 (2016), 8, 084312
  21. Yang, X. J., Baleanu, D., Fractal Heat Conduction Problem Solved by Local Fractional Variation Method, Thermal Science, 17 (2013), 2, pp. 625-628
  22. Abdallah, G., et al., Thermal Convection of Fluid in Fractured Media, Inter Journal of Rock Mechanics and Mining Sciences, 32 (1995), 5, pp. 481-490
  23. Xu, J., et al., Fractal Complex Transform Technology for Fractal Korteweg-de Vries Equation within a Local Fractional Derivative, Thermal Science, 20 (2016), Suppl. 3, pp. S841-S845

© 2022 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, 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