Magnetohydrodynamic Stagnation Point Flow Research Articles

Physical aspects on unsteady MHD‐free convective stagnation point flow of micropolar fluid over a stretching surface

AbstractThe unsteady magnetohydrodynamic (MHD) stagnation point flow of micropolar fluid across a vertical stretching surface with second‐order velocity slip is the main concern of the present paper. The influence of electrical energy, temperature‐dependent thermal conductivity, thermal radiation, Joule heating, and heat sink/source is investigated. The basic partial differential equations are changed into ordinary differential equations with the help of appropriate similarity variables and then solved by the fourth‐order Runge‐Kutta–based shooting technique. The impact of physical parameters on the velocity, microrotation, and temperature as well as friction factor, couple stress, and local Nusselt number is thoroughly explained with the support of graphs and tables. The results divulge that the heat source/sink and thermal radiation parameters have a propensity to enhance the fluid temperature. The distribution of velocity is an increasing function of an electric field and unsteadiness parameter. The numerical results are also compared with the results available in the literature.

Magnetohydrodynamics (MHD) stagnation point flow past a shrinking/stretching surface with double stratification effect in a porous medium

The present work emphasizes the MHD mixed convective stagnation point flow over a shrinking/stretching surface saturated in a porous medium. The double stratification with heat source effects are also considered while the magnetic field is imposed normal to the sheet. The governing model (partial differential equations) is converted into a system of ordinary (similarity) differential equations using similarity transformations. The boundary value problem solver (bvp4c) in the MATLAB software is utilized for the numerical computations. Numerical results are graphically illustrated in the form of velocity, temperature and concentration profiles for several values of buoyancy, magnetic, thermal and solutal stratification parameters. The graphs of skin friction coefficient, local Nusselt and Sherwood numbers portray that the dual solutions are achievable within a certain range of the buoyancy and velocity ratio parameters. Both assisting and opposing flow cases can generate two solutions, whereas the forced convective flow only produces a unique solution. The execution of stability analysis affirms the reliability of the first solution. Both heat and mass transfer rates intensify with the increment of the velocity ratio parameter for all type of convective flows. The fluid temperature and concentration decrease with the increment of the thermal and solutal stratification parameters, respectively, whereas the magnetic and buoyancy parameters reduce both temperature and concentration profiles.

Magnetohydrodynamics Stagnation-Point Flow of a Nanofluid Past a Stretching/Shrinking Sheet with Induced Magnetic Field: A Revised Model

The revised Buongiorno’s nanofluid model with the effect of induced magnetic field on steady magnetohydrodynamics (MHD) stagnation-point flow of nanofluid over a stretching or shrinking sheet is investigated. The effects of zero mass flux and suction are taken into account. A similarity transformation with symmetry variables are introduced in order to alter from the governing nonlinear partial differential equations into a nonlinear ordinary differential equations. These governing equations are numerically solved using the bvp4c function in Matlab solver, a very adequate finite difference method. The influences of considered parameters ( P r , M, χ , L e , N b , N t , S, and λ ) on velocity, induced magnetic, temperature, and concentration profiles together with the reduced skin friction and heat transfer rate are discussed. Results from these criterion exposed the existence of dual solutions when magnetic field and suction are applied for a specific range of λ . The stability of the solutions obtained is carried out by performing a stability analysis.

MHD stagnation point flow of viscous nanofluid over a curved surface

In this article, we have examined the steady 2D magnetohydrodynamic (MHD) stagnation point flow of an incompressible viscous nanofluid over a curved surface based on mass suction. Alumina () is taken to be a nanoparticle while ethylene glycol is considered a base fluid. The developed flow and heat equations are changed into coupled ordinary differential equations through dimensionless variables, which are resolved numerically via the bvp4c scheme in MATLAB. The graphical results for temperature, velocity, Nusselt number and skin friction have been obtained under the effect of various parameters, such as suction parameter Hartmann number curvature parameter and nanoparticle volume fraction From these results, it is noticed that and act directly on the skin friction and heat transfer rate, although the reverse effect has been shown by Furthermore, increasing leads to lower fluid velocity and higher temperature field.

Impact of heat generation/absorption on the unsteady magnetohydrodynamic stagnation point flow and heat transfer of nanofluids

Purpose The purpose of this study is to describe the unsteady three-dimensional magnetohydrodynamic stagnation point flow of nanofluids with heat generation/absorption. Design/methodology/approach The comprehensive numerical simulations in this study accommodate a physical insight into the heat transfer and flow problem. The use of finite difference method through the bvp4c function in Matlab provides the numerical results and graphical illustrations for the heat transfer rate and shear stress. Findings Dual solutions are discovered in this study. Thus, stability analysis is implemented and the first solution complies the stability behavior. Silver nanoparticles dominate the highest thermal conductivity. Accretion of the rate of heat transfer is obtained with an increment in the magnitude of heat absorption, suction parameter and nanoparticle volume fraction. A stronger magnetic field and larger unsteadiness parameter contribute to the increase of the surface shear stress. Practical implications Many practical fluid mechanics problems involve the time-dependent element. Practically, an unsteady flow of nanofluid can be implemented in the micro-manufacturing, periodic heat exchanges process, nano drug delivery system and nuclear reactors. Originality/value In spite of numerous studies on the unsteady flow, none of the researchers combined the effect of heat generation/absorption and magnetic field in the nanofluid model. The behavior of the flow and heat transfer have been analyzed thoroughly with the variations in the unsteadiness parameter, heat source/sink and nanoparticle volume fraction. Moreover, the discovery of dual solutions in this model strengthens the novelty of this study. Subsequently, the implementation of stability analysis leads to a remarkable revelation where the first solution is found to be stable.

MHD Stagnation-point Flow over a Stretching/ Shrinking Sheet in Nanofluids

In this study, we investigated the problem of steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow over a linearly stretching/shrinking sheet in nanofluids. There are three types of metallic nanoparticles considered such as copper (Cu), alumina (Al2O3) and titania (TiO2) in the base fluid of water with the Prandtl number Pr = 6.2 to investigate the effect of the nanoparticles volume fraction parameter φ of the nanofluids. In this problem, the governing nonlinear partial differential equations are transformed into the nonlinear ordinary differential equations by using a similarity transformation and then solved numerically using the boundary value problems solver bvp4c in Matlab software. The influence of magnetic field parameter, M on the skin friction coefficient Cf, local Nusselt number Nu and the velocity and temperature profiles are presented graphically and discussed. The results show that the velocity and temperature are influenced by the magnetic field and nanoparticles volume fraction. The dual solutions exist for shrinking sheet case and the solutions are non-unique, different from a stretching sheet. The numerical values of and for M=0 are also computed, which show a favourable agreement with previous work.

Effect of Nonlinear Thermal Radiation on Magnetohydrodynamic Stagnation Point Flow of Williamson Fluid Induced by Nonlinear Stretching Sheet in the Presence of Non Uniform Heat Generation/Absorption

Effect of Nonlinear Thermal Radiation on Magnetohydrodynamic Stagnation Point Flow of Williamson Fluid Induced by Nonlinear Stretching Sheet in the Presence of Non Uniform Heat Generation/Absorption

MHD Stagnation-Point Flow of a Nanofluid Past a Stretching Sheet with a Convective Boundary Condition and Radiation Effects

In this paper, the investigation of magnetohydrodynamic (MHD) stagnation point flow of a nanofluid past a stretching sheet with a convective boundary condition and radiation effects is carried out numerically. Similarity transformation is used to reduce the governing partial differential equations into third and second order non-linear ordinary differential equations. These equations are then being solved numerically using a problem solver built in the MATLAB software. The numerical solutions for the skin friction coefficient, local Nusselt number, velocity and temperature profiles for different values of the physical parameters are presented graphically and discussed further. The results indicate that the velocity and the temperature are influenced by the magnetic parameter M, Brownian motion parameter Nb and radiation parameter Nr. The local Nusselt number and the skin friction coefficient are affected significantly in the presence of suction at the boundary.

MHD Stagnation Point Flow with Heat Transfer Past a Porous Sheet along with Viscous Dissipation and Thermal Radiation

In this article, we study the magnetohydrodynamics stagnation point flow for the upper-convected Maxwell fluid with the viscous dissipation and thermal radiation effects using the Cattaneo-Christov heat flux model. The flow equations are reconstructed and the obtained set of partial differential equations is then converted into an arrangement of nonlinear, coupled O.D.E. by utilising some reasonable similarity transformations. After this, the set of O.D.E. is solved by applying shooting method. Graphs and tables describe the behavior of physical parameters.

A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow with Zero Nanoparticles Flux Condition and Anisotropic Slip

The numerical study of nanofluid stagnation point flow coupled with heat and mass transfer on a moving sheet with bi-directional slip velocities is emphasized. A magnetic field is considered normal to the moving sheet. Buongiorno’s model is utilized to assimilate the mixed effects of thermophoresis and Brownian motion due to the nanoparticles. Zero nanoparticles’ flux condition at the surface is employed, which indicates that the nanoparticles’ fraction are passively controlled. This condition makes the model more practical for certain engineering applications. The continuity, momentum, energy and concentration equations are transformed into a set of nonlinear ordinary (similarity) differential equations. Using bvp4c code in MATLAB software, the similarity solutions are graphically demonstrated for considerable parameters such as thermophoresis, Brownian motion and slips on the velocity, nanoparticles volume fraction and temperature profiles. The rate of heat transfer is reduced with the intensification of the anisotropic slip (difference of two-directional slip velocities) and the thermophoresis parameter, while the opposite result is obtained for the mass transfer rate. The study also revealed the existence of non-unique solutions on all the profiles, but, surprisingly, dual solutions exist boundlessly for any positive value of the control parameters. A stability analysis is implemented to assert the reliability and acceptability of the first solution as the physical solution.

Heat transfer on magnetohydrodynamic stagnation point flow through a porous shrinking/stretching sheet: A numerical study

This article examines the numerical study of heat transfer analysis on MHD stagnation point flow past a permeable shrinking/stretching sheet through a porous media. The governing equations have been reduced to the ODE by utilizing similarity variables. The obtained highly non-linear coupled differential equations have been solved by implementing a numerical scheme labeled as successive linearization method. The influences for the pertinent parameters on velocity profile and temperature profile is debated and demonstrated graphically. Numerical comparisons in some special cases have been brought along the prevailing literature, and it is noticed that the current outcomes are in good concord.

Thermal radiation and slip effects on magnetohydrodynamic (MHD) stagnation point flow of Casson fluid over a convective stretching sheet

Current study examines the combined effect of thermal radiation and velocity slip along a convective heated stretching sheet. magnetohydrodynamic (MHD) effect near the stagnation point is also under consideration. The main structure of partial differential equations attained in the form of momentum, energy and concentration equations. For a self-similar solution, the system of governing PDEs assimilated into the set of nonlinear ordinary differential equations by applying suitable similarity transformation. Resulting nonlinear ODEs are successfully solved via Runge-Kutta-Fehlberg method. All obtained unknown functions are discussed in detail after plotting the numerical results against different arising physical parameters. The validations of numerical results have been taken into account with two different numerical approaches and it is found to be in excellent agreement with the numerical results. The study reveals that concentration boundary layer thickness decreases by increasing the values of Schmidt number and increases by increasing the chemical reaction parameter.

Stability Analysis of MHD Stagnation-point Flow towards a Permeable Stretching/Shrinking Sheet in a Nanofluid with Chemical Reactions Effect

The magnetohydrodynamic (MHD) stagnation-point flow of a nanofluid towards a permeable stretching/shrinking sheet with chemical reaction effect is investigated. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which are then solved numerically using the boundary value problem solver, bvp4c built in Matlab software. The numerical results are obtained for the skin friction coefficient, local Nusselt number, local Sherwood number as well as the velocity, temperature and concentration profiles for some values of the governing parameters, namely suction/injection parameter and chemical reaction parameter. Dual solutions are found to exist for a certain range of the stretching/shrinking parameter. A stability analysis is performed to determine which solutions are stable and physically reliable. It is found that the first solutions are stable and the second solutions are unstable.

Unsteady magnetohydrodynamic stagnation point flow—closed-form analytical solutions

This paper investigates the unsteady stagnation point flow and heat transfer of magnetohydrodynamic (MHD) fluids over a moving permeable flat surface. The unsteady Navier-Stokes (NS) equations are transformed into a similarity nonlinear ordinary differential equation, and a closed form solution is obtained for the unsteadiness parameter of 2. The boundary layer energy equation is transformed into a similarity equation, and is solved for a constant wall temperature and a time-dependent uniform wall heat flux case. The solution domain, velocity, and temperature profiles are calculated for different combinations of parameters including the Prandtl number, mass transfer parameter, wall moving parameter, and magnetic parameter. Two solution branches are obtained for certain combinations of the controlling parameters, and a stability analysis demonstrates that the lower solution branch is not stable. The present solutions provide an exact solution to the entire unsteady MHD NS equations, which can be used for validating the numerical code of computational fluid dynamics.

MHD Stagnation Point Flow of Viscoelastic Nanofluid Past a Convectively Heated Stretching Surface

A mathematical model is established to examine the influence of viscous dissipation and joule heating on magnetohydrodynamic (MHD) flow of an incompressible viscoelastic nanofluid over a convectively heated stretching sheet. Brownian motion and thermophoresis effects have been introduced in this nanofluid model. The governing equations are transformed into ODE’s by using suitable similarity conversions and are then solved numerically by the most robust shooting technique. The significance of numerous physical flow constraints is performed for, and distributions through graphs. It is noticed that, the increases for higher values of and reduces for rising values of heat source and Biot numbers. An outstanding contract was found between our numerical results and previously publicised results.

Stability Analysis on Magnetohydrodynamic Flow of Casson Fluid over a Shrinking Sheet with Homogeneous-Heterogeneous Reactions.

Two-dimensional magnetohydrodynamic (MHD) stagnation point flow of incompressible Casson fluid over a shrinking sheet is studied. In the present study, homogeneous-heterogeneous reactions, suction and slip effects are considered. Similarity variables are introduced to transform the governing partial differential equations into non-linear ordinary differential equations. The transformed equations and boundary conditions are then solved using the bvp4c solver in MATLAB. The local skin friction coefficient is tabulated for different values of suction and shrinking parameters. The profiles for fluid velocity and concentration for various parameters are illustrated. It was found that two solutions were obtained at certain ranges of parameters. Then, the bvp4c solver was used to perform stability analysis on the dual solutions. Based on the results, the first solution was more stable and physically meaningful than the other solution. The skin friction coefficient increased when suction increased, but decreased when the magnitude of shrinking parameter increased. Meanwhile, the velocity and concentration profile increased in the presence of a magnetic field. It is also noted that the higher the strength of the homogeneous-heterogeneous reactions, the lower the concentration of reactants.

Thermal and velocity slip effects on MHD mixed convection flow of Williamson nanofluid along a vertical surface: Modified Legendre wavelets approach

The purpose of the present work is to carry out the numerical simulation of magnetohydrodynamic (MHD) stagnation-point flow of non-Newtonian Williamson nanofluid towards a vertical moving surface. The focus of present work is to analyze the nanofluid characteristics for both buoyancy assisting and opposing flow regions. The stretching sheet is subject to uniform normal magnetic field and three types of slip conditions: velocity, thermal and solutal slip are applied. The governing equations are derived in the form of nonlinear partial differential equations. Using suitable transformation variables such equations are converted into favorable nonlinear ordinary differential equations. New modification in Legendre wavelets method is proposed and applied to investigate the numerical solution of the reduced set of nonlinear ordinary differential equations. The simulation is performed for the emerging physical parameter on the nanofluid velocity, temperature, concentration, coefficient of skin friction, heat and mass transfer rate. The study concludes that the Modified Legendre Wavelets Method (MLWM) reduces the computational cost and very accurate to find the solution and can be extended for nonlinear diversify problems of physical nature. Moreover, skin friction at the stretching surface is increased due to increase in non-Newtonian Williamson fluid parameter which subsequently decreases the nanofluid velocity in the boundary layer.

Simultaneous effects of melting heat and internal heat generation in stagnation point flow of Jeffrey fluid towards a nonlinear stretching surface with variable thickness

This paper investigates the magnetohydrodynamic (MHD) stagnation point flow of Jeffrey material towards a nonlinear stretching surface with variable surface thickness. Heat transfer characteristics are examined through the melting process, viscous dissipation and internal heat generation. A nonuniform applied magnetic field is considered. Boundary-layer and low magnetic Reynolds number approximations are employed in the problem formulation. Both the momentum and energy equations are converted into the non-linear ordinary differential system using appropriate transformations. Convergent solutions for resulting problems are computed. Behaviors of various pertinent parameters on velocity and temperature distributions are studied in detail. Further the heat transfer rate is also computed and analyzed.

Magnetohydrodynamics Stagnation-Point Flow of Sisko Liquid With Melting Heat Transfer and Heat Generation/Absorption

This research concentrates on melting heat transfer in magnetohydrodynamics (MHD) flow of Sisko fluid bounded by a sheet with nonlinear stretching velocity. Modeling and analysis have been carried out in the presence of heat generation/absorption and magnetic field. Transformation procedure is implemented in obtaining nonlinear differential system. Convergence series solutions are developed. The solution for different influential parameters is analyzed. Skin friction coefficient and heat transfer rate are analyzed. It is observed that the qualitative results of magnetic field and melting heat transfer on velocity are similar.

Stagnation point flow of viscoelastic nanomaterial over a stretched surface

Abstract Present communication aims to discuss magnetohydrodynamic (MHD) stagnation point flow of Jeffrey nanofluid by a stretching cylinder. Modeling is based upon Brownian motion, thermophoresis, thermal radiation and heat generation. Problem is attempted by using (HAM). Residual errors for h-curves are plotted. Convergent solutions for velocity, temperature and concentration are obtained. Skin friction coefficient, local Nusselt number and Sherwood number are studied. It is examined that velocity field decays in the presence of higher estimation of magnetic variable. Furthermore temperature and concentration fields are enhanced for larger magnetic variable.