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A novel type of heat transfer fluid known as hybrid nanofluids is used to improve the efficiency of heat exchangers. It is observed from literature evidence that hybrid nanofluids outperform single nanofluids in terms of thermal performance. This study aims to address the stagnation point flow induced by Williamson hybrid nanofluids across a vertical plate. This fluid is drenched under the influence of mixed convection in a Darcy–Forchheimer porous medium with heat source/sink and entropy generation.

By applying the proper similarity transformation, the partial differential equations that represent the leading model of the flow problem are reduced to ordinary differential equations. For the boundary value problem of the fourth-order code (bvp4c), a built-in MATLAB finite difference code is used to tackle the flow problem and carry out the dual numerical solutions.

The shear stress decreases, but the rate of heat transfer increases because of their greater influence on the permeability parameter and Weissenberg number for both solutions. The ability of hybrid nanofluids to strengthen heat transfer with the incorporation of a porous medium is demonstrated in this study.

The findings may be highly beneficial in raising the energy efficiency of thermal systems.

The originality of the research lies in the investigation of the Darcy–Forchheimer stagnation point flow of a Williamson hybrid nanofluid across a vertical plate, considering buoyancy forces, which introduces another layer of complexity to the flow problem. This aspect has not been extensively studied before. The results are verified and offer a very favorable balance with the acknowledged papers.

Ohmic heating generates temperature with the help of electrical current and resists the flow of electricity. Also, it generates heat rapidly and uniformly in the liquid matrix. Electrically conducting biofluid flows with Ohmic heating have many biomedical and industrial applications. The purpose of this study is to provide the significance of the effects of Ohmic heating and viscous dissipation on electrically conducting Casson nanofluid flow driven by peristaltic pumping through a vertical porous channel.

In this analysis, the non-Newtonian properties of fluid will be characterized by the Casson fluid model. The long wavelength approach reduces the complexity of the governing system of coupled partial differential equations with non-linear components. Using a regular perturbation approach, the solutions for the flow quantities are established. The fascinating and essential characteristics of flow parameters such as the thermal Grashof number, nanoparticle Grashof number, magnetic parameter, Brinkmann number, permeability parameter, Reynolds number, Casson fluid parameter, thermophoresis parameter and Brownian movement parameter on the convective peristaltic pumping are presented and thoroughly addressed. Furthermore, the phenomenon of trapping is illustrated visually.

The findings indicate that intensifying the permeability and Casson fluid parameters boosts the temperature distribution. It is observed that the velocity profile is elevated by enhancing the thermal Grashof number and perturbation parameter, whereas it reduces as a function of the magnetic parameter and Reynolds number. Moreover, trapped bolus size upsurges for greater values of nanoparticle Grashof number and magnetic parameter.

There are some interesting studies in the literature to explain the nature of the peristaltic flow of non-Newtonian nanofluids under various assumptions. It is observed that there is no study in the literature as investigated in this paper.

This study aims to analyze the two-dimensional ferrofluid flow in porous media. The effects of changes in parameters such as permeability parameter, buoyancy parameter, Reynolds and Prandtl numbers, radiation parameter, velocity slip parameter, energy dissipation parameter and viscosity parameter on the velocity and temperature profile are displayed numerically and graphically.

By using simplification, nonlinear differential equations are converted into ordinary nonlinear equations. Modeling is done in the Cartesian coordinate system. The finite element method (FEM) and the Akbari-Ganji method (AGM) are used to solve the present problem. The finite element model determines each parameter’s effect on the fluid’s velocity and temperature.

The results show that if the viscosity parameter increases, the temperature of the fluid increases, but the velocity of the fluid decreases. As can be seen in the figures, by increasing the permeability parameter, a reduction in velocity and an enhancement in fluid temperature are observed. When the Reynolds number increases, an increase in fluid velocity and temperature is observed. If the speed slip parameter increases, the speed decreases, and as the energy dissipation parameter increases, the temperature also increases.

When considering factors like thermal conductivity and variable viscosity in this context, they can significantly impact velocity slippage conditions. The primary objective of the present study is to assess the influence of thermal conductivity parameters and variable viscosity within a porous medium on ferrofluid behavior. This particular flow configuration is chosen due to the essential role of ferrofluids and their extensive use in engineering, industry and medicine.

This study aims to investigate the effect of externally applied magnetic force and heat transfer with a heat source/sink on the Couette flow with viscous dissipation in a horizontal rotating channel. The magnetic force is added to the governing equations. The effects of fluid flow parameters are observed under the applied magnetic force. In this system, the magnetic force is applied perpendicular to the plane of the fluid flow. In recent years, the magnetic field has renewed interest in aerospace technology. The physical and theoretical approach in the multidisciplinary field of magneto fluid dynamics (MFD) is applied in the field of aerospace vehicle design.

Authors use the perturbation method to solve and find the approximate solutions of differential equations. First, convert the partial differential equation to ordinary differential equation and calculate the approximate solutions in two cases. The first solution got by assuming heat generating in the fluid and the second one got when heat absorbing. After applying the external magnetic force, the effects of various fluid parameters velocity, temperature, skin friction coefficient and Nusselt number are found and discussed using tables and graphs.

It is found that the velocity of the fluid has decreased tendency when the rotation of the fluid and magnetic force on the fluid increases. The temperature of the fluid, Prandtl value and Eckert number increased when the heat source generated heat. When heat absorbs the heat, sink parameter increases and the temperature of the fluid decreases. Also, while heat absorbs, the temperature increases when the Prandtl value and Eckert number increase.

The skin friction coefficient on the surface increases, when the rotation parameter and the magnetic force parameter of the fluid increase. In the case of heat generating, the Nusselt number increased, while the Eckert number and Prandtl numbers increased. Also, the Nusselt number has larger values when the heat source parameter has near the constant temperature, and it has smaller values when the temperature varies. In the case of heat-absorbing, the Nusselt number decreased when the Eckert and Prandtl numbers increased. Also, the Nusselt number varies up and down while the heat absorbing parameter increases.

The purpose of this study is to investigate the Dynamics of micropolar – water B Fluids flow simultaneously under the influence of thermal radiation and Soret–Dufour Mechanisms.

The thermal radiation contribution, the chemical change and heat generation take fluidity into account. The flow equations are used to produce a series of dimensionless equations with appropriate nondimensional quantities. By using the spectral homotopy analysis method (SHAM), simplified dimensionless equations have been quantitatively solved. With Chebyshev pseudospectral technique, SHAM integrates the approach of the well-known method of homotopical analysis to the set of altered equations. In terms of velocity, concentration and temperature profiles, the impacts of Prandtl number, chemical reaction and thermal radiation are studied. All findings are visually shown and all physical values are calculated and tabulated.

The results indicate that an increase in the variable viscosity leads to speed and temperature increases. Based on the transport nature of micropolar Walters B fluids, the thermal conductivity has great impact on the Prandtl number and decrease the velocity and temperature. The current research was very well supported by prior literature works. The results in this paper are anticipated to be helpful for biotechnology, food processing and boiling. It is used primarily in refrigerating systems, tensile heating to large-scale heating and oil pipeline reduction.

All results are presented graphically and all physical quantities are computed and tabulated.