Study on Heat Transfer of Fluid in a Porous Media by VOF Method with Fractal Reconstruction

Shuai Liu (), Qingyong Zhu and Wenjun Xu
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Shuai Liu: School of Humanities and Basic Sciences, Shenzhen University of Information Technology, Shenzhen 518107, China
Qingyong Zhu: School of Aeronautics and Astronautics, Sun Yat-Sen University, Shenzhen 518107, China
Wenjun Xu: School of Humanities and Basic Sciences, Shenzhen University of Information Technology, Shenzhen 518107, China

Energies, 2025, vol. 18, issue 15, 1-22

Abstract: This paper addresses the critical gap in the existing literature regarding the combined buoyancy–Marangoni convection of power-law fluids in three-dimensional porous media with complex evaporation surfaces. Previous studies have rarely investigated the convective heat transfer mechanisms in such systems, and there is a lack of effective methods to accurately track fractal evaporation surfaces, which are ubiquitous in natural and engineering porous media (e.g., geological formations, industrial heat exchangers). This research is significant because understanding heat transfer in these complex porous media is essential for optimizing energy systems, enhancing thermal management in industrial processes, and improving the efficiency of phase-change-based technologies. For this scientific issue, a general model is designed. There is a significant temperature difference on the left and right sides of the model, which drives the internal fluid movement through the temperature difference. The upper end of the model is designed as a complex evaporation surface, and there is flowing steam above it, thus forming a coupled flow field. The VOF fractal reconstruction method is adopted to approximate the shape of the complex evaporation surface, which is a major highlight of this study. Different from previous research, this method can more accurately reflect the flow and phase change on the upper surface of the porous medium. Through numerical simulation, the influence of the evaporation coefficient on the flow and heat transfer rate can be determined. Key findings from numerical simulations reveal the following: (1) Heat transfer rates decrease with increasing fractal dimension (surface complexity) and evaporation coefficient; (2) As the thermal Rayleigh number increases, the influence of the Marangoni number on heat transfer diminishes; (3) The coupling of buoyancy and Marangoni effects in porous media with complex evaporation surfaces significantly alters flow and heat transfer patterns compared to smooth-surfaced porous media. This study provides a robust numerical framework for analyzing non-Newtonian fluid convection in complex porous media, offering insights into optimizing thermal systems involving phase changes and irregular surfaces. The findings contribute to advancing heat transfer theory and have practical implications for industries such as energy storage, chemical engineering, and environmental remediation.

Keywords: porous media; buoyancy–Marangoni convection; fractal reconstruction; VOF method; Weierstrass–Mandelbrot function (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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