Heat Transfer and Diffusion Processes in Fractal Domains

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 2068

Special Issue Editor


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Guest Editor
School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, China
Interests: fractals; heat transfer and diffusion; computational fluid dynamics; porous media

Special Issue Information

Dear Colleagues,

The aim of studying heat transfer and diffusion processes in fractal domains is to explore the intricate and complex phenomena that arise when heat and mass are exchanged within objects with non-integer (fractal) dimension. Fractals are geometrical patterns characterized by self-affinity at different scales, and they appear abundantly in nature, from irregular coastlines to the flow of fluid. Understanding heat and mass transfer in such domains holds significant importance for various scientific and engineering applications. By investigating these processes, researchers aim to unravel the underlying principles governing the behavior of heat transfer and diffusion in fractal systems, enabling the design of more efficient heat exchangers, materials, and industrial processes. Additionally, exploring these phenomena may provide valuable insights into natural phenomena, such as heat diffusion in porous media or nutrient diffusion in biological tissues.

The scope of this field encompasses theoretical analyses, numerical simulations, and experimental studies, all aimed at elucidating the fundamental mechanisms and practical implications of heat transfer and diffusion processes in fractal domains. Topics that are invited for submission include (but are not limited to):

  • Fractal dimension and heat transfer behavior;
  • Heat transfer and diffusion of porous media with fractal characteristics
  • Multi-scale heat transfer modeling of fractal structures;
  • Multi-dimensional diffusion in fractal media
  • Fractal heat exchangers: design and optimization
  • Heat and mass transfer in biology with fractal characteristics
  • Numerical modeling of heat transfer in fractal systems

Prof. Dr. Qingyong Zhu
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (2 papers)

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25 pages, 3799 KiB  
Article
Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source
by Yasir Nawaz, Muhammad Shoaib Arif, Muavia Mansoor, Kamaleldin Abodayeh and Amani S. Baazeem
Fractal Fract. 2024, 8(5), 276; https://doi.org/10.3390/fractalfract8050276 - 6 May 2024
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Abstract
An explicit computational scheme is proposed for solving fractal time-dependent partial differential equations (PDEs). The scheme is a three-stage scheme constructed using the fractal Taylor series. The fractal time order of the scheme is three. The scheme also ensures stability. The approach is [...] Read more.
An explicit computational scheme is proposed for solving fractal time-dependent partial differential equations (PDEs). The scheme is a three-stage scheme constructed using the fractal Taylor series. The fractal time order of the scheme is three. The scheme also ensures stability. The approach is utilized to model the time-varying boundary layer flow of a non-Newtonian fluid over both stationary and oscillating surfaces, taking into account the influence of heat generation that depends on both space and temperature. The continuity equation of the considered incompressible fluid is discretized by first-order backward difference formulas, whereas the dimensionless Navier–Stokes equation, energy, and equation for nanoparticle volume fraction are discretized by the proposed scheme in fractal time. The effect of different parameters involved in the velocity, temperature, and nanoparticle volume fraction are displayed graphically. The velocity profile rises as the parameter I grows. We primarily apply this computational approach to analyze a non-Newtonian fluid’s fractal time-dependent boundary layer flow over flat and oscillatory sheets. Considering spatial and temperature-dependent heat generation is a crucial factor that introduces additional complexity to the analysis. The continuity equation for the incompressible fluid is discretized using first-order backward difference formulas. On the other hand, the dimensionless Navier–Stokes equation, energy equation, and the equation governing nanoparticle volume fraction are discretized using the proposed fractal time-dependent scheme. Full article
(This article belongs to the Special Issue Heat Transfer and Diffusion Processes in Fractal Domains)
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15 pages, 1732 KiB  
Article
Research on Effective Thermal Conductivity in Porous Media Embedded with Randomly Distributed Damaged Tree-like Bifurcation Networks
by Yihao Shao, Xiuya Guo, Huili Wang, Limei Zhu and Qian Zheng
Fractal Fract. 2023, 7(12), 853; https://doi.org/10.3390/fractalfract7120853 - 30 Nov 2023
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Abstract
Due to the complexity of the microstructure of porous media, it is of great significance to explore the heat transport mechanism in porous media in many engineering applications. In this study, an expression for effective thermal conductivity (ETC) of porous media embedded with [...] Read more.
Due to the complexity of the microstructure of porous media, it is of great significance to explore the heat transport mechanism in porous media in many engineering applications. In this study, an expression for effective thermal conductivity (ETC) of porous media embedded with randomly distributed damaged tree-like bifurcation networks is derived based on the theory of thermodynamics and fractal features of tree-like bifurcation networks. We investigate the effect of heat conduction and heat convection in porous media embedded with randomly distributed damaged tree-like bifurcation networks on the ETC of the porous media. It is found that our fractal model has good consistency with the existing available experimental data. In addition, the influence of the microstructural parameters of the model on heat transfer in the porous media is analyzed in detail. The research results can provide significant theoretical guidance for the development and design of heat transfer systems. Full article
(This article belongs to the Special Issue Heat Transfer and Diffusion Processes in Fractal Domains)
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