TY - JOUR
TI - Fractal analysis for heat extraction in geothermal system
AU - Shang Xiaoji
AU - Wang Jianguo
AU - Yang Xiaojun
JN - Thermal Science
PY - 2017
VL - 21
IS - 11
SP - 25
EP - 31
PT - Article
AB - 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.