Search Results (30)

The present paper treats the problem of steady laminar MHD flow of an incompressible viscous fluid for mixed convection stagnation-point flow over a vertical stretching sheet in the presence of an externally magnetic field. By means of the Optimal Auxiliary Functions Method (OAFM), the resulting nonlinear ODEs are semi-analytically solved. The impact of various physical parameters, such as the velocity ratio parameter A, the Prandtl number $Pr$, and the Hartmann number $Ha$, on the behavior of velocity and temperature profiles is analyzed. Both assisting ($\lambda >0$) and opposing ($\lambda <0$) flows are considered. The influence of these parameters is tabulated and graphically presented. The originality of this work lies in the development of effective semi-analytical solutions and in the excellent agreement between these solutions and the corresponding numerical solutions. This highlights the accuracy of the proposed method applied to steady laminar MHD flow. A comparative analysis underlines the advantages of the OAFM compared to the iterative method. The obtained results confirm that the OAFM represents a competitive mathematical tool to explore a large class of nonlinear problems with applications in engineering. Full article

The present study aims to offer new numerical solutions and optimisation strategies for the fluid flow and heat transfer behaviour at a stagnation point through a nonlinear sheet that is expanding or contracting in water-based hybrid nanofluids. Most hybrid nanofluids typically use metallic nanoparticles. However, we deliver a new approach by combining single- and multi-walled carbon nanotubes (SWCNTs-MWCNTs). The flow is presumptively steady, laminar, and surrounded by a constant temperature of the ambient and body walls. By using similarity variables, a model of partial differential equations (PDEs) with the magnetohydrodynamics (MHD) effect on the momentum equation is converted into a model of non-dimensional ordinary differential equations (ODEs). Then, the dimensionless first-order ODEs are solved numerically using the MATLAB R2022b bvp4C program. In order to explore the range of computational solutions and physical quantities, several dimensionless variables are manipulated, including the magnetic parameter, the stretching/shrinking parameter, and the volume fraction parameters of hybrid and mono carbon nanotubes. To enhance the originality and effectiveness of this study for practical applications, we optimise the heat transfer coefficient via the response surface methodology (RSM). We apply a face-centred central composite design (CCF) and perform the CCF using Minitab. All of our findings are presented and illustrated in tabular and graphic form. We have made notable contributions in the disciplines of mathematical analysis and fluid dynamics. From our observations, we find that multiple solutions appear when the magnetic parameter is less than 1. We also detect double solutions in the shrinking region. Furthermore, the increase in the magnetic parameter and SWCNTs-MWCNTs volume fraction parameter increases both the skin friction coefficient and the local Nusselt number. To compare the performance of hybrid nanofluids and mono nanofluids, we note that hybrid nanofluids work better than single nanofluids both in skin friction and heat transfer coefficients. Full article

In the manufacturing sector, transport phenomena near the stagnation region are frequent, particularly in the polymer and extrusion processes, which require continuous improvement to raise the process’s quality standards. The aim of this study is to explore the improvement of heat and mass transmission using unsteady magnetohydrodynamic (MHD) hybrid nanofluid (HNF) flow over a stretching/shrinking cylinder with variable viscosity and Stefan blowing. The governed equations of heat and mass transfer processes are converted into ordinary differential equations (ODEs) using the appropriate transformations, and the resulting equations are then solved using the MATLAB package bvp4c. With an upsurge in the volume fraction of nanoparticles, the skin friction increases, but the reverse trend is detected with negative values for the unsteadiness constraint. The use of 2D graphs to show how important parameters affect the velocity, temperature, and concentration is thoroughly discussed. There is a discussion of the quantitative findings from the wall shear factor and the heat and mass transfer rates calculated for the stretching/shrinking cases. Full article

The magneto-hydrodynamic dual convection stagnation flow pattern behavior of a Tangent Hyperbolic (TH) fluid has been reported in this study. The radiation, Joule heating, and heat generation/absorption impacts have also been analyzed. The flow-narrating differential equations, which are constrained by a thermal and solutal stratified porous medium, are transmuted into a system of nonlinear differential equations. To provide a numerical solution to the flow problem, a computational model is created. Numerical solutions are obtained using the fifth-order exactness program (Bvp5c), and for validation of the results, a comparison is also made with the methodology of the Runge–Kutta fourth order. The physical implications are appraised and depicted using diagrams or tables against flow-controlling parameters, such as Hartmann number, porosity parameter, solutal stratification, the parameter of curvature, temperature stratification, local Weissenberg number, Schmidt number, etc. It has been observed that in the appearance of Joule heating phenomena, the fluid temperature is a lowering function of thermal stratification. The findings are compared to the existing literature and found to be consistent with earlier research. Full article

This study investigates the magnetohydrodynamics of a micropolar fluid consisting of a hybrid nanofluid with mixed convection effects. By using the dimensionless set of variables, the resulting equations of ordinary differential equations are solved numerically using the bvp4c solver in MATLAB. In the present work, the water-based alumina–copper hybrid nanofluid is analytically modeled with modified thermophysical properties. The study reveals that the highest critical value of opposing flow is the hybrid nanofluid (ϕ₁ = ϕ₂ = 2%). By comparing the hybrid nanofluid with Cu–water nanofluid (ϕ₁= 0%, ϕ₂= 1%) as well as water (ϕ₁= 0%, ϕ₂= 0%), hybrid nanoparticle volume fraction enhances the dynamic viscosity performance and surface shear stress. In addition, the augmentation of the nanoparticle volume fraction and magnetic field parameter will increase the physical quantities Re_x^1/2 C_f, Re_x M_x, and Re_x^−1/2 Nu_x. The result from the stability inquiry discloses that the first solution is more physically stable and trustworthy. It is proven that magnetohydrodynamics could contribute to controlling the fluid flow in a system, i.e., engineering operations and the medical field. In addition, this theoretical research can be a benchmark for experimental research. Full article

This paper discusses a numerical study performed in analysing the performance regarding the magnetic effect on the mixed convection stagnation-point flow of hybrid ferrofluid, examining the influence of viscous dissipation, convective boundary condition as well as Joule heating across a nonlinearly moving surface. Additionally, the hybrid ferrofluid exhibits an asymmetric flow pattern due to the buoyancy force affecting the flow. Water $\left({\mathrm{H}}_2\mathrm{O}\right)$ is employed as the base fluid collectively with the mixtures of nanoparticles containing magnetite $\left(\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4\right)$ and cobalt ferrite $\left(\mathrm{CoF}{\mathrm{e}}_2{\mathrm{O}}_4\right)$, forming a hybrid ferrofluid. The partial differential equation’s complexity is reduced by similarity transformation into a system of ordinary differential equations, which are then numerically solved by applying the MATLAB function bvp4c for a specific range of values regarding the governing parameters. Dual solutions were identified under both opposing and assisting flow conditions, and the stability analysis identified that the first solution was stable. Furthermore, it was also revealed that the addition of 1% $\mathrm{CoF}{\mathrm{e}}_2{\mathrm{O}}_4$ in hybrid ferrofluid led to a higher skin friction coefficient between 3.35% and 7.18% for both assisting and opposing flow regions. Additionally, the growth of magnetic fields results in a reduced heat transfer rate between 8.75% to 10.65%, whilst the presence of the suction parameter expands the range of solutions, which then delays the boundary layer separation. With the Eckert number included, the heat transfer rate continuously declined between 7.27% to 10.24%. However, it increased by about 280.64% until 280.98% as the Biot number increased. Full article

Recycling plastic waste (RPW) benefits the ecological footprint. Therefore, the authors test its mixing by magnetic hydrodynamic MHD nanofluid materials such as alumina in two sizes (${\beta }_{core}, {\beta }_{skin}$) prepared into a new device called the incubator installed in the desktop injection machine to enhance its solubility by taking advantage of the mixture’s heat via defining the oblique stagnation-point slip flow (OSPSF) of a nanofluid in two dimensions. The paper has been innovative in mathematically identifying the operating parameters’ values for the injection flow mechanism (IFM) via controlling in Riga magnetic field and piston orifice pressure using a meta-heuristic algorithm called WSA. The proposed (IFM) is used to experimentally enhance the mixture properties via parameters’ control to meet the output quality and predict the control equation for the Riga plate. IFM controls the amount of pushed nanoparticles in the mixture with a ratio of plastic to aluminum approximate by 96.1%: 3.9%. The defects were reduced by approximately 23.21%, with an increasing system performance of 70.98%. Full article

The present study explores the characteristics of 2D MHD melting with reference to mass and heat transportation upon stagnation point Powell–Eyring nanofluid flow on an extensible surface. Melting is an important phenomenon that is involved in many procedures such as permafrost melting, solidification of slag, defrosting frozen ground etc., all of which are examples of soil freezing and melting that involve heat trafficking through a coil in a grounded pump. A mathematical model is developed for the boundary layer flow. The differential equations are solved through a numerical algorithm which makes use of the boundary value problem solver bvp4c, applying MATLAB software. The numerical variations of embedded parameters on velocity lineation, temperature figuration, and concentration delineation are represented graphically, as are the width of the boundary layer value and the delineation rate for the increasing velocity parameter. The velocity function shows a decremental response for M while the opposite behavior is seen against the concentration field. Full article

This paper investigates the mixed convection flow related to ${\mathrm{Fe}}_3{\mathrm{O}}_4$-${\mathrm{CoFe}}_2{\mathrm{O}}_4/\mathrm{water}$ hybrid ferrofluids on stagnation point over an exponentially stretching/shrinking surface with the influence of magnetohydrodynamic (MHD), velocity slip, and heat source/sink. The proposed system of differential equations is reduced using the similarity transformation procedure that is numerically solvable using MATLAB. Dual solutions are obtained for various governing parameters, in which the first solution is found to be in a stable state via the stability analysis. The CoFe₂O₄ nanoparticles volume fraction increases the heat transfer rate and the skin friction coefficient while delaying the separation of the boundary layer at the bifurcation point. Adding CoFe₂O₄ nanoparticles in hybrid ferrofluids gives a better heat transfer rate than that obtained with ferrofluids. The presence of a magnetic field enhances the fluid flow velocity. The increased strengths of the heat sink and stretching parameters give better results on the heat transfer, while the results are reversed for the heat source and shrinking parameters. The presence of velocity slip does influence the skin friction and the fluid flow. Full article

Numerical simulations of hypersonic magnetohydrodynamics (MHD) flow over a typical sphere–cone blunt body are carried out based on the assumption of a low magnetic Reynolds number. The effects of an external dipole magnetic field on the surface heat flux are analyzed in detail, and multiple mechanisms of the MHD heat flux mitigation are revealed systematically for the first time. The following is found: (1) The external magnetic field can effectively reduce the stagnation point heat flux, and the increase in the boundary layer thickness due to the effect of counter-flow Lorentz force, which is equivalent to adding an adverse pressure gradient, is the main reason. (2) In the head region of the blunt body, the relative surface heat flux shows a complex trend of rising and falling because there are two mechanisms which could produce the opposite effects on the surface heat flux. One is that the counter-flow Lorentz force results in an increase in the boundary layer thickness, and the other is that the Joule heating increases the static temperature behind the shock wave. (3) In the shoulder region of the blunt body, the Lorentz force component, normal to streamline, could change the flow direction of the fluid elements, causing the streamline to deviate from the wall or even separate, thus affecting the surface heat flux. (4) In the large area downstream of the blunt body, the surface heat flux could still be reduced by more than 30% due to the “upstream historical effect”. Full article

This paper examines the unsteady separated stagnation point (USSP) flow and thermal progress of Fe₃O₄–CoFe₂O₄/H₂O on a moving plate subject to the heat generation and MHD effects. The model of the flow includes the boundary layer and energy equations. These equations are then simplified with the aid of similarity variables. The numerical results are generated by the bvp4c function and then presented in graphs and tables. The magnetic and acceleration (strength of the stagnation point flow) parameters are the contributing factors in the augmentation of the skin friction and heat transfer coefficients. However, the enhancement of heat generation parameter up to 10% shows a reduction trend in the thermal rate distribution of Fe₃O₄–CoFe₂O₄/H₂O. This finding reveals the effectiveness of heat absorption as compared to the heat generation in the thermal flow process. From the stability analysis, the first solution is the physical solution. The streamline for the first solution acts as a normal stagnation point flow, whereas the second solution splits into two regions, proving the occurrence of reverse flow. Full article

This article investigates the three-dimensional magneto stagnation-point flow of ternary hybrid nanofluid caused by a radially extended infinite gyrating disk with multiple slip effects. The main concern is to analyze the characteristics of heat transport when linear thermal radiation (LTR), quadratic thermal radiation (QTR), and full nonlinear thermal radiation (FNTR) are significant. Ternary fluid is a composition of water, spherical-shaped silver, cylindrical-shaped aluminum oxide, and platelet-shaped aluminum nanoparticles. Non-uniform heat source effects are taken into account. The governing equations are constructed using a single-phase nanofluid model using boundary layer theory and von Karman variables. The consequent nonlinear problem is solved with an efficient finite element method and the results are verified with the available data. The Nusselt number and friction factors are computed for both clean fluid and ternary nanofluid subjected to three different forms of Rosseland’s thermal radiation. Our results demonstrate that the rate of heat transport (Nusselt number) is higher in the FNTR case than in QTR and LTR, and it is even higher for ternary nanofluid compared to clean fluid. Further, the heat transport rate gets reduced for a higher heat source parameter. The rotation of the disk escalates the shear stress along both the radial and axial directions. The multiple slip boundary conditions lead to condensed boundary layers over a disk surface. Full article

The significance of radiation, Soret and Dufour’s effects on MHD flow in a porous media near a stagnation point past a vertical plate with slip, temperature, and concentration boundary conditions were investigated. Local similarity variables are used in the solution, which reduces the PDEs into analogous boundary value problem for ODEs. Symmetry analysis can be used to detect these variations in local similarity. To numerically explain the problem, a shooting approach and the MATLAB bvp4c solver are utilized. As the magnetic field and porous medium parameters are raised, the skin friction increases, and the temperature increases as the radiation pointer is increased. As the Soret number grows, the concentration profile rises. Full article

In this article, motivated by novel nanofluid solar energy coating systems, a mathematical model of hybrid magnesium oxide (MgO) and nickel (Ni) nanofluid magnetohydrodynamic (MHD) stagnation point flow impinging on a porous elastic stretching surface in a porous medium is developed. The hybrid nanofluid is electrically conducted, and a magnetic Reynolds number is sufficiently large enough to invoke an induced magnetic field. A Darcy model is adopted for the isotropic, homogenous porous medium. The boundary conditions account for the impacts of the velocity slip and thermal slip. Heat generation (source)/absorption (sink) and also viscous dissipation effects are included. The mathematical formulation has been performed with the help of similarity variables, and the resulting coupled nonlinear dimensionless ordinary differential equations have been solved numerically with the help of the shooting method. In order to test the validity of the current results and the convergence of the solutions, a numerical comparison with previously published results is included. Numerical results are plotted for the effect of emerging parameters on velocity, temperature, magnetic induction, skin friction, and Nusselt number. With an increment in nanoparticle volume fraction of both MgO and Ni nanoparticles, the temperature and thermal boundary layer thickness of the nanofluid are elevated. An increase in the porous medium parameter (Darcy number), velocity slip, and thermal Grashof number all enhance the induced magnetic field. Initial increments in the nanoparticle volume fraction for both MgO and Ni suppress the magnetic induction near the wall, although, subsequently, when further from the wall, this effect is reversed. Temperature is enhanced with heat generation, whereas it is depleted with heat absorption and thermal slip effects. Overall, excellent thermal enhancement is achieved by the hybrid nanofluid. Full article

This study is to investigate the magnetohydrodynamic (MHD) stagnation point flow and heat transfer characteristic nanofluid of carbon nanotube (CNTs) over the shrinking surface with heat sink effects. Similarity equations deduced from momentum and energy equation of partial differential equations are solved numerically. This study looks at the different parameters of the flow and heat transfer using first phase model which is Tiwari-Das. The parameter discussed were volume fraction nanoparticle, magnetic parameter, heat sink/source parameters, and a different type of nanofluid and based fluids. Present results revealed that the rate of nanofluid (SWCNT/kerosene) in terms of flow and heat transfer is better than (MWCNT/kerosene) and (CNT/water) and regular fluid (water). Graphically, the variation results of dual solution exist for shrinking parameter in range ${\lambda }_c<\lambda \le -1$ for different values of volume fraction nanoparticle, magnetic, heat sink parameters, and a different type of nanofluid. However, a unique solution exists at $-1<\lambda <1$, and no solutions exist at $\lambda <{\lambda }_c$ which is a critical value. In addition, the local Nusselt number decreases with increasing volume fraction nanoparticle when there exists a heat sink effect. The values of the skin friction coefficient and local Nusselt number increase for both solutions with the increase in magnetic parameter. In this study, the investigation on the flow and heat transfer of MHD stagnation point nanofluid through a shrinking surface with heat sink effect shows how important the application to industrial applications. Full article