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Computational Assessment of Magneto-Radiative and Activation Energy Influences on Heat and Mass Transmission in Williamson Hybrid Nanofluid Ag- SiC/Water Flow over a Permeable Stretching Cylinder

This study computationally investigates the coupled effects of magneto-radiative forces, activation energy, and various physical parameters on the heat and mass transfer characteristics of an Ag–SiC/Water Williamson hybrid nanofluid flowing over a permeable stretching cylinder using a validated numerical framework.

Original authors: Asra Anjum, G Swamy Reddy, S. S. Zafar, Samdani Peerusab, Han Liu, M. Faizan Ahmed, Asna Sadaf, Abdul Faiz Ansari, Farhan Ali

Published 2026-09-28

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CC BY 4.0

Original authors: Asra Anjum, G Swamy Reddy, S. S. Zafar, Samdani Peerusab, Han Liu, M. Faizan Ahmed, Asna Sadaf, Abdul Faiz Ansari, Farhan Ali

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Heat is a constant companion in the machinery of the modern world, moving through pipes, cooling engines, and regulating the temperature of electronic devices. To manage this heat, engineers rely on fluids—liquids that carry thermal energy from one place to another. For decades, the standard choice has been simple liquids like water or oil. However, these conventional fluids have a limitation: they are not very good at conducting heat compared to solid materials. To overcome this, scientists developed a technique of suspending tiny solid particles, often metals or ceramics, within a liquid. These mixtures, known as nanofluids, act as superior heat carriers. When two different types of particles are mixed together in a single liquid, the result is called a hybrid nanofluid, which offers even greater thermal efficiency. Yet, the fluids used in complex industrial processes are rarely simple. Many behave in ways that defy standard rules, thickening or thinning depending on how fast they are pushed. Understanding how these complex, particle-laden liquids move and transfer heat under the influence of magnetic fields and porous materials is essential for designing better cooling systems for everything from nuclear reactors to advanced manufacturing.

In a recent computational study, researchers set out to map the behavior of such a complex fluid in a specific, challenging environment. They focused on a hybrid nanofluid made of silver and silicon carbide particles suspended in water, flowing over a cylinder that is being stretched. This setup mimics real-world industrial processes like the extrusion of plastic sheets or the drawing of metal wires, where materials are pulled and stretched while being cooled. The fluid in question is a "Williamson fluid," a type of liquid that becomes less viscous, or thinner, as it is forced to move faster. This shear-thinning behavior is common in many industrial substances, from paints to biological fluids, but it makes predicting their movement difficult. The researchers simulated this flow while subjecting it to a magnetic field, a porous medium that acts like a sponge to slow the fluid down, and various thermal effects like radiation and internal heat generation. Their goal was to see how these competing forces interact to change the speed of the fluid, its temperature, and the concentration of chemical species within it.

The study revealed that the forces acting on the fluid create a delicate balance. When a magnetic field is applied, it generates a resistive force that pushes back against the moving fluid, effectively acting as a brake. As the strength of this magnetic field increases, the fluid slows down significantly. Similarly, when the fluid moves through a porous medium, the solid obstacles within the material create friction that further reduces the flow speed. However, the geometry of the cylinder itself plays a surprising role. As the curvature of the cylinder increases, the fluid is pulled more strongly toward the surface, which actually accelerates the flow. The unique nature of the Williamson fluid also matters; because this fluid thins out as it moves faster, increasing the parameter that defines this behavior allows the fluid to flow more easily, resulting in higher speeds near the stretching surface.

While the magnetic field and porous material slow the fluid down, they have the opposite effect on its temperature. The resistance created by the magnetic field converts the fluid's kinetic energy into heat, a process known as Joule heating, which raises the overall temperature. This warming effect is amplified by thermal radiation, where the fluid absorbs energy from its surroundings, and by viscous dissipation, where the internal friction of the fluid layers rubbing against each other generates additional heat. The researchers found that factors like the presence of a heat source or the specific angle at which the magnetic field is applied further influence how hot the fluid gets. Interestingly, the chemical reaction occurring within the fluid also plays a part; if the energy required to start a reaction is high, the reaction slows down, allowing more heat to accumulate in the fluid rather than being consumed by the chemical process.

The movement of the fluid also dictates how heat and chemical substances are transferred. The study showed that while the magnetic field and porous medium slow the fluid, they also reduce the rate at which heat and mass are transferred away from the surface. In contrast, increasing the thermal radiation or the temperature difference between the fluid and its surroundings enhances these transfer rates. The concentration of chemical species within the fluid is highly sensitive to the speed of the reaction. When the chemical reaction rate is high, the concentration of the solute drops quickly as it is consumed. However, if the energy barrier for the reaction is raised, the reaction slows, and the concentration of the solute remains higher for longer. The researchers also noted that the specific combination of silver and silicon carbide particles in the water created a hybrid fluid that performed differently than fluids with just one type of particle, offering distinct advantages in heat management.

These findings, derived entirely from computer simulations using advanced mathematical models, provide a detailed picture of how complex fluids behave under extreme conditions. The results suggest that by carefully adjusting the magnetic field, the porosity of the material, and the composition of the fluid, engineers can fine-tune the cooling and heating processes in industrial systems. The study confirms that hybrid nanofluids offer a powerful tool for managing thermal energy, but their performance is deeply tied to the non-Newtonian nature of the fluid and the external forces acting upon it. While the work is theoretical and has not yet been tested in a physical laboratory, the consistency of the simulation results with previous studies gives confidence in the predictions. This research lays the groundwork for designing more efficient thermal systems, potentially leading to better cooling for electronic devices, more effective energy storage, and improved manufacturing processes where precise control of heat and fluid flow is critical.

Technical Summary: Computational Assessment of Magneto-Radiative and Activation Energy Influences on Heat and Mass Transmission in Williamson Hybrid Nanofluid Ag-SiC/Water Flow

Problem Statement
This research investigates the steady-state, laminar, incompressible flow of a Williamson hybrid nanofluid (Ag–SiC nanoparticles suspended in water) over a permeable stretching cylinder. The study addresses a gap in existing literature regarding the simultaneous influence of multiple physical phenomena on non-Newtonian hybrid nanofluids. Specifically, the model integrates magnetohydrodynamics (MHD), porous media effects, thermal radiation, viscous dissipation, heat source/sink mechanisms, and chemical reactions involving activation energy. While previous studies have examined these factors individually or in simpler Newtonian contexts, this work focuses on the coupled effects within a shear-thinning Williamson fluid framework, a configuration relevant to industrial processes such as polymer extrusion, wire drawing, and nuclear reactor cooling.

Methodology
The study employs a mathematical modeling approach based on conservation laws for mass, momentum, energy, and species concentration.

Governing Equations: The system is described by non-linear partial differential equations (PDEs) incorporating the effective thermophysical properties of the Ag–SiC/water hybrid nanofluid using classical mixture theory. The Williamson fluid model is utilized to characterize the shear-thinning behavior of the base fluid.
Similarity Transformations: Appropriate similarity variables are applied to transform the governing PDEs into a system of coupled non-linear ordinary differential equations (ODEs).
Numerical Solution: The resulting boundary value problem (BVP) is solved numerically using the bvp5c solver in MATLAB. This method utilizes a Runge-Kutta scheme combined with a shooting technique to handle the non-linear ODEs.
Validation: The numerical scheme is validated by comparing the current results with previously published data (Nadeem et al. and Malik et al.) under specific limiting conditions, showing a 99.9% match and confirming the accuracy of the computational approach.
Parameters: The study analyzes the impact of dimensionless parameters including the magnetic parameter ( $M$ ), porosity parameter ( $\lambda$ ), curvature parameter ( $\gamma$ ), Williamson parameter ( $Wi$ ), radiation parameter ( $Rd$ ), Eckert number ( $Ec$ ), heat source/sink ( $Q$ ), Schmidt number ( $Sc$ ), chemical reaction parameter ( $Rc$ ), and activation energy ( $Ea$ ).

Key Contributions
The primary novelty of this work lies in the comprehensive, unified computational framework that captures the interplay between non-Newtonian rheology and multi-physics transport phenomena.

Hybrid Nanofluid Modeling: The study specifically models an Ag–SiC/water hybrid nanofluid, distinguishing it from single-particle nanofluid studies.
Multi-Physics Integration: It simultaneously accounts for MHD, porosity, thermal radiation, viscous dissipation, and activation energy-driven chemical reactions, which are often treated separately in prior literature.
Shear-Thinning Dynamics: The research explicitly investigates how the shear-thinning nature of the Williamson fluid interacts with magnetic and porous resistances, a critical aspect for non-Newtonian industrial applications.
Comprehensive Parametric Analysis: The paper provides detailed graphical and tabular data on velocity, temperature, and concentration profiles, as well as skin friction, Nusselt, and Sherwood numbers, under varying physical conditions.

Results and Discussion
The numerical analysis yields the following key findings regarding the transport mechanisms:

Velocity Profiles: The velocity distribution decreases with increasing magnetic parameter ( $M$ ), porosity ( $\lambda$ ), and aligned angle ( $\beta$ ) due to increased resistive forces (Lorentz force and drag). Conversely, velocity increases with higher curvature ( $\gamma$ ) and Williamson parameter ( $Wi$ ), as the shear-thinning effect reduces effective viscosity near the surface.
Temperature Profiles: Temperature increases with higher magnetic parameter, radiation ( $Rd$ ), porosity, curvature, Eckert number ( $Ec$ ), Biot number ( $Bi$ ), heat source ( $Q$ ), and activation energy ( $Ea$ ). These factors either add thermal energy (radiation, viscous dissipation, heat source) or reduce convective cooling. Conversely, the Williamson parameter ( $Wi$ ) leads to a decrease in temperature due to reduced viscous heating.
Concentration Profiles: The concentration of the solute decreases with increasing chemical reaction parameter ( $Rc$ ), temperature difference parameter ( $\delta$ ), and Schmidt number ( $Sc$ ). However, increasing activation energy ( $Ea$ ) raises the concentration profile by slowing the reaction rate, thereby reducing solute consumption.
Transport Rates:
- Skin Friction ( $C_f$ ): Decreases with increasing magnetic and porosity parameters but increases with the Williamson parameter.
- Nusselt Number ( $Nu$ ): Generally decreases with magnetic and porosity parameters but increases with thermal radiation.
- Sherwood Number ( $Sh$ ): Decreases with magnetic and porosity parameters. Increasing activation energy reduces mass transfer rates, while thermal radiation enhances them.
3D Visualizations: Surface plots illustrate the coupled effects of parameters like Prandtl number, Biot number, and heat source on heat transfer, and Schmidt/chemical reaction parameters on mass transfer, highlighting the complex gradients in the boundary layer.

Significance and Claims
The authors claim that this study fills a critical research gap by providing a generalized predictive platform for hybrid nanofluid transport in complex, multi-physics environments. The findings are presented as directly applicable to advanced thermal systems, including:

Cooling of electronic devices and nuclear reactors.
Chemical reactors and energy storage systems.
Biomedical heat transfer and industrial processes involving magnetically controlled fluid flows.
Polymer extrusion and wire drawing operations.

The paper emphasizes that the developed model offers improved predictive capabilities for thermal management systems by accounting for the complex relationships between radiative heat transport, MHD influences, and non-Newtonian behavior. It asserts that the inclusion of hybrid nanoparticles (Ag-SiC) significantly enhances heat and mass transfer rates compared to conventional fluids, provided the non-Newtonian and magnetic effects are properly managed. The study concludes that while the numerical results are robust and validated against existing literature, future work should aim to extend these findings to turbulent regimes, unsteady flows, and experimental validation to further bridge the gap between simulation and practical industrial design.

Technical Summary: Computational Assessment of Magneto-Radiative and Activation Energy Influences on Heat and Mass Transmission in Williamson Hybrid Nanofluid Ag-SiC/Water Flow

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