Heat Transfer Capability Analysis of Hybrid Brinkman-Type Fluid on Horizontal Solar Collector Plate Through Fractal Fractional Operator

Nanoscience Energy Engineering Mechanical Engineering Chemistry Engineering Physics Fluid Physics
solar collectors heat transfer Brinkman-type fluid fractal fractional operator hybrid nanoparticles

Heat Transfer Capability Analysis of Hybrid Brinkman-Type Fluid on Horizontal Solar Collector Plate

Research Background and Problem Statement

With the growing global demand for clean energy, solar energy, as a renewable, clean, and low-pollution resource, has gained widespread attention. However, traditional solar collectors (such as flat-plate solar collectors) face efficiency bottlenecks in absorbing solar radiation and converting thermal energy. To address this issue, researchers have proposed using nanofluids as working fluids. Nanofluids are suspensions formed by dispersing nanoparticles in base fluids (such as water or ethylene glycol), and their thermal performance is significantly superior to that of traditional fluids. Nevertheless, single-type nanofluids still have limitations, which has led to the emergence of hybrid nanofluids as a research hotspot in recent years.

Hybrid nanofluids further enhance thermal conductivity and heat transfer efficiency by combining different types of nanoparticles (such as single-walled carbon nanotubes, SWCNTs, and multi-walled carbon nanotubes, MWCNTs). However, accurately modeling and predicting the heat transfer behavior of hybrid nanofluids under complex conditions remains a challenge. To this end, Dolat Khan et al. proposed a generalized Brinkman-type fluid model based on fractal fractional operators to more precisely analyze the heat transfer capability of hybrid nanofluids on horizontal solar collector plates and explore their potential applications.

Paper Source and Author Information

This paper, titled “Heat Transfer Capability Analysis of Hybrid Brinkman-Type Fluid on Horizontal Solar Collector Plate Through Fractal Fractional Operator,” was co-authored by Dolat Khan, Gohar Ali, and Zareen A. Khan from King Mongkut’s University of Technology Thonburi (KMUTT) in Thailand, City University of Science and Information Technology in Pakistan, and Princess Nourah Bint Abdulrahman University in Saudi Arabia. The paper was accepted on December 30, 2024, and published in the journal Optical and Quantum Electronics in 2025, with the article number 57:154 and DOI 10.1007/s11082-024-08025-8.

Research Content and Workflow

a) Research Workflow and Methods

This study is divided into the following main steps:

1. Model Construction

The research team first extended the classical Brinkman-type fluid model by introducing fractal fractional derivatives to broaden its applicability. This new approach better describes fluid flow behaviors with memory effects and long-range interactions. The fluid was assumed to be an incompressible Newtonian viscous hybrid nanofluid containing SWCNTs and MWCNTs, with water as the base fluid. The model analyzed the geometric structure between two infinite parallel plates, where one plate was heated while the other remained stationary.

The governing equations included: - Momentum equations to describe the velocity distribution of the fluid; - Energy equations to analyze the temperature distribution of the fluid.

Additionally, dimensionless variables were defined to simplify the equation forms for subsequent numerical solutions.

2. Numerical Solution

To solve the aforementioned fractal fractional model, the Crank–Nicolson method (a commonly used implicit finite difference method) was adopted. This method offers high numerical stability and accuracy, making it suitable for solving nonlinear partial differential equations. The research team developed discretization formulas to transform the time-fractional derivative and spatial second-order derivative into discrete forms and performed numerical calculations using Maple-15 software.

3. Parameter Analysis

The study systematically analyzed the effects of various parameters on the fluid’s velocity and temperature distributions, including fractal fractional parameters, nanoparticle volume fractions, Grashof numbers, and time variables. These parameters were tested individually to reveal their specific impacts on heat transfer efficiency.

b) Main Results

1. Impact of Fractal Fractional Parameters

The study found that fractal fractional parameters significantly affect the velocity and temperature distributions of the fluid. Specifically, as the fractal fractional parameter increases, both the temperature and velocity of the fluid decrease. This is due to changes in fluid viscosity and diffusivity caused by the power-law kernel in the fractional derivative, which affects the fluid’s motion characteristics.

2. Role of Nanoparticle Volume Fractions

The results showed that as the volume fractions of SWCNTs and MWCNTs increase, the fluid’s viscosity significantly improves, leading to slower flow but enhanced heat absorption. For example, when the volume fraction of SWCNTs increases from 0.01 to 0.04, the viscous forces of the fluid significantly increase, thereby improving the efficiency of flat-plate solar collectors.

3. Influence of Grashof Number

The Grashof number reflects the influence of buoyancy-driven convection on fluid flow. The study demonstrated that as the Grashof number increases, the fluid velocity significantly improves. This is because larger Grashof numbers enhance buoyancy forces while reducing viscous resistance.

4. Advantages of Hybrid Nanofluids

Compared to single nanofluids, hybrid nanofluids exhibit higher heat transfer efficiency. Particularly in terms of solar radiation absorption, hybrid nanofluids can significantly improve the performance of flat-plate solar collectors.

c) Conclusions and Implications

Scientific Value

This study is the first to apply fractal fractional derivatives to the heat transfer analysis of hybrid nanofluids, providing new ideas for modeling complex fluid systems. The fractal fractional model not only more accurately describes the memory effects and long-range interactions of fluids but also lays a theoretical foundation for future research.

Application Value

The results indicate that hybrid nanofluids have tremendous potential in solar collector applications. By optimizing the composition and volume fractions of nanoparticles, the thermal efficiency of collectors can be significantly improved, thereby reducing equipment size and cost. Additionally, this technology can be extended to other heat transfer fields, such as electronic cooling and industrial thermal management systems.

d) Research Highlights

  1. Novel Fractal Fractional Model
    The study is the first to apply fractal fractional derivatives to the heat transfer analysis of hybrid nanofluids, providing more precise modeling tools for complex fluid systems.

  2. Superiority of Hybrid Nanofluids
    Hybrid nanofluids outperform traditional nanofluids in enhancing the efficiency of solar collectors, offering important references for practical applications.

  3. Combination of Experiment and Theory
    The study not only established mathematical models through theoretical derivation but also verified the reliability of the models through numerical simulations, demonstrating scientific rigor.

Summary

This paper successfully analyzed the heat transfer capability of hybrid Brinkman-type fluids on horizontal solar collector plates by introducing fractal fractional derivatives. The study not only revealed the significant potential of hybrid nanofluids in improving solar energy utilization efficiency but also provided new methods for modeling and analyzing complex fluid systems. The research findings are of great significance for advancing solar energy technology and also open new directions for the application of nanofluids in other fields.