Magnetohydrodynamic Stagnation Point Flow Research Articles

Stability analysis of electrical magneto hydrodynamic stagnation point flow of Ag-Cu/water hybrid nanofluid over a permeable stretching/shrinking slendering sheet: Entropy generation

The current study emphasises the stability test of electrical magneto hydrodynamic stagnation point flow of hybrid nanofluids with entropy generation in the existence of velocity and thermal slips over a porous slendering stretchable sheet. A mathematical modelling of [Formula: see text]/water hybrid nanofluid has been explored. Heat transfer proficiency of airplane wings is evaluated with the inclusion of distinguished effects like viscous dissipation and solar-based thermal radiation, so we included them in this article. Using suitable self-similarity transformations, the system of the fluid transport equations are converted into an ordinary differential system, which are determined by utilising the bvp4c in MATLAB software. The achieved outcomes are expressed as the skin friction, Nusselt number, velocity, temperature, Bejan number, entropy generation and streamlines with an influence of diverse physical parameters. The boundary-layer separation happens when the number of results fails to happen ahead of the critical value of the contracting parameter. To show the effect on flow and heat transfer of appropriate parameters, graphs are used. Stability is shown to be better in solution one than in the second, according to the results. The wall thickness variable augmented the velocity profile of the hybrid nanofluid for the first solution and a contrary for the second solution. Higher values of the thermal radiation parameter resulted in enhanced temperatures in the first and second solutions. It is also observed that the rate of heat transfer in the first solution increased as the electric field value increased.

MHD Stagnation-Point Flow and Heat Transfer in a Micropolar Fluid over an Exponentially Vertical Sheet

This paper examines the magneto hydrodynamic (MHD), stagnation-point flow and heat transfer caused by an exponentially stretching/shrinking vertical sheet and the presence of mixed convection (buoyancy effect) in a micropolar fluid. A set of variables is employed to transform the system of partial differential equations (PDEs) to ordinary differential equations (ODEs). The ODEs are then numerically solved in MATLAB software using BVP4c. There are a lot of agreements when compared to previous findings. The impacts of different parameters, such as micropolar, magnetic, mixed convection, radiation, temperature, and stretching/shrinking parameters are displayed graphically. It is found that contradictory phenomena between Micropolar and mixed convection for fluid velocity, angular velocity and temperature distribution profiles. The velocity profile at the vertical plate increases due to the increasing buoyancy, magnetic and radiation parameters. The particle rotation occurs in two phenomena for buoyancy and magnetic parameters and it is reversible for micropolar. The temperature of the fluid decreases with buoyancy and magnetic parameters.

Entropy Generation and Regression Analysis of Magnetohydrodynamic Stagnation Point Flow of a Casson Fluid with Radiative and Dissipative Heat Transfer and Hall Effects

The phenomenon of heat transfer is prevalent in industries and has an extensive range of applications. However, mostly the discussion of heat transfer problems is limited to the study of the first law of thermodynamics, which deals with energy conservation. It is just restricted to the quantity of energy, not to its quality; i.e., there is no difference between the work (high‐grade energy) and the heat (low‐grade energy). A measurement of the degree of randomness of energy in a system is known as entropy. It is unavailable for doing useful work because work takes place only from ordered molecular motion. Even though many boundary layer models exist in the literature to investigate the flow and heat transfer of various fluids along a stretching surface, they have not yet been used at their maximum ability. The main motive of the current research is to discuss entropy generation or its minimization during heat transfer. This work presents an entropy generation analysis for the transient three‐dimensional stagnation point flow of a hydromagnetic Casson fluid flowing over a stretching surface in the existence of Hall current, viscous dissipation, and nonlinear radiation. The physical configuration of the present work is described in terms of partial differential equations (PDEs) of nonlinear nature. Furthermore, these PDEs are converted into ordinary differential equations by using some relevant similarity transformations. An efficient numerical method named as the spectral quasilinearization method (SQLM) is used to solve this model. The expression of the Bejan number and volumetric entropy generation rate is also computed. A parametric analysis, including the essential physical parameters, is performed to examine the influences of distinct flow parameters on the velocity profile, temperature profile, Bejan number, entropy generation number, and the coefficients of skin friction and the Nusselt number. In order to further insight into the emerging physical quantities of engineering interest, multiple quadratic regression models are used to estimate the coefficients of skin friction and heat transfer.

Magnetohydrodynamics stagnation point flow and heat transfer over a non‐isothermal permeable shrinking sheet with variable surface temperature

AbstractThe present study is intended to analyse the effect of heat and mass transfer on boundary layer stagnation point flow of a viscous fluid over a non‐isothermal shrinking sheet subject to transverse magnetic field and variable surface temperature. The medium of flow is considered to be porous. Further, the effect of variable surface temperature and concentration are also taken care of in the present analysis. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by suitable similarity transformations. The numerical simulation is carried out using Runge–Kutta method of fourth order with shooting technique. The physical significance of pertinent parameters of the flow phenomenon is studied with the help of graphs and tables. One striking outcome of the present analysis is that the unstable velocity profiles with inflection points are marked due to power law variation of temperature and concentration of the linearly stretchable bounding surface leaving aside the smooth fall in temperature and concentration (span wise) across the flow field. Further, it is noted that increase in magnetic field intensity, suction and thermal as well as mass buoyancy parameters enhance the skin friction concomitantly favouring the effective momentum transport.

Radiation effect on MHD three-dimensional stagnation-point flow comprising water-based graphene oxide nanofluid induced by a nonuniform heat source/sink over a horizontal plane surface

This research aims to study the 3D magnetohydrodynamics stagnation-point flow (SPF) over a horizontal plane surface (HPS) carrying water-based graphene oxide (GO) nanoparticles caused by an irregular heat source/sink used in heat transfer procedures. In addition, a Tiwari–Das model is used to inspect the dynamics of fluid flow behavior and heat transmission features of the nanoparticles with experiencing the impacts of thermal radiation. The acquired nonlinear set of partial differential equations (PDEs) is transfigured to a system of ordinary differential equations (ODEs) using similarity transformations. The accumulative dimensionless ODEs are then further tackled in MATLAB using the bvp4c solver. Tables and figures are prepared for the execution of several relevant constraints along with nodal/saddle indicative parameter, internal heat source/sink parameter, radiation parameter and nanoparticles volume fraction which divulges and clarify more accurately the posited quantitative data and graphical findings. Also, the velocity profile decelerated in the axial and transverse coordinate axes for a higher value of the nanoparticle volume fraction but the dimensionless temperature distribution is augmented. Additionally, thermal boundary layer thickness and profile of temperature enriches with higher impressions of radiation constraint. However, the internal heat sink factor declines the profiles of temperature while escalating with the superior value of the internal heat source parameter.

MHD stagnation point flow of a water-based copper nanofluid past a flat plate with solar radiation effect

Due to many biological and technical applications, including microelectronics, heat exchangers, cancer therapy, process industries, solar collectors and power production, researchers have been more interested in the mechanism of heat transfer involving nanomaterials. A contemporary method to increase the thermal conductivity of various cooling fluids is the use of nanomaterials. Many researches suggest that the thermal conductivity of nanoliquids; solid nanoparticles combined with a base fluid, is expressively greater than that of conventional fluids. This work presents the theoretical investigation of magnetohydrodynamic stagnation point flow of non-Newtonian nanofluid flow past flat plate. The applications of solar radiation towards water-based copper nanoparticles are highlighted in this study. The system of PDEs is transmuted into the system of ODEs by mean of suitable similarity variable. Analytical solution of the present analysis has been performed with the help of HAM technique. The impacts of physical factors on the flow profiles, skin friction coefficient, heat, and mass transfer rates are calculated. It is significant to note that the default concentration is weighted by 4% throughout this analysis. Also in this analysis, we examined the temperature and heat transfer rate for the presence and absence of solar radiation. It is found that the greater nanoparticles volume fraction of the water-based copper nanoparticles has accelerated the flow profiles for the absence of magnetic field. However, for the presence of strong magnetic field, the velocity, and temperature of the water-based copper nanoparticles have significantly reduced. Due to the incidence of Lorentz force, the velocity of the water-based copper nanoparticles has deteriorated, while the temperature profile has augmented. It is found that the solar radiation has always dominant impression on temperature of the water based copper nanoparticles.

Convected heat and mass transport in magnetic burgers’ nanoliquid subject to chemical responses

This paper investigates the effect of Burgers' nanofluid convinced as a stretching cylinder on heat source about magnetohydrodynamic stagnation point flow. Effect of the heat source/sink and chemical reaction are more appropriate to consider mass and heat transportation to the flow of Burgers’ fluid. Additionally, the effects of different convective actions i.e. convective condition by the exterior subordinate as two mass and heat transport arejoined in the analysis. The mathematical formulation was collected as the absorbing boundary layer theory and later coincidence transformations were imported in governing partial differential equations. The solutions of velocity, solutal, and thermal equations were declined to results, and graphs are interpreted from practical judgments. Fundamental physical announcement to the flow figure by Burgers' nanofluid improvement the lowering ideals magnetic force parameter. Also, The flow pattern of Burgers fluid parameters is contrary to the fluid detention time parameter. Furthermore, it was derived the thermal sketch and thermal density to the boundary layer of nanofluid enhance values of thermal Biot number and heat source parameter. The current examination was guaranteed to be recognised as study with previously presented scheduled.

Unsteady MHD stagnation point flow of ternary hybrid nanofluid over a spinning sphere with Joule heating

Practical Applications: Numerous technical applications, including as polymer deposition, electrolysis control, medication delivery, spin-stabilized missile cooling and cooling of rotating machinery slices have sparked considerable interest in studying stagnation point flow. Nuclear power plants, photovoltaic panels and heat exchangers as well as microfluidic heating devices use them. Purpose: To better understand the unsteady [Formula: see text]–[Formula: see text]–[Formula: see text] ternary hybrid nanofluid stream at the stagnation zone with Joule heating, this research examines the unique prospective applicative properties. Methodology: The flow equations will be modeled. By using similarity transformation, it is possible to transform nonlinear partial differential equations (PDEs) that are not precisely solvable into ordinary differential equations (ODEs) that can be numerically resolved. Runge–Kutta-IV and the shooting technique in MATHEMATICA have been demonstrated to have a significant effect on the predominance of heat exchange and the mobility features of ternary hybrid nanofluids. Findings: Results show that the unsteadiness parameter influences the [Formula: see text]-direction velocity and mono nanofluid has a larger velocity than other nanofluids, while the opposite is true for the [Formula: see text]-direction velocity. Nanoparticle concentrations, magnetic and Eckert number characteristics increase the thermal distribution, whereas the unsteadiness and rotation parameter decreases it. Unsteadiness, rotation and magnetic factors all improve heat transfer, while the Eckert number parameter has the reverse effect. The ternary hybrid nanofluid also has a greater heat transfer rate than the hybrid and normal nanofluids. Originality: Unsteady [Formula: see text]–[Formula: see text]–[Formula: see text] ternary nanofluid stream generated by magneto hydrodynamic (MHD) in the stagnation zone was studied in detail in this study. To avoid any errors in heat transfer, it may assist other researchers in selecting critical parameters for modern industrial heat transfer and the right parameters for developing nonunique solutions.

Slip and temperature jump effects of MHD stagnation point flow towards a translating plate considering nonlinear radiations

AbstractThis article investigates the combined effects of nonlinear radiation and magnetic parameter under the velocity slip and temperature jump conditions on the boundary layer flow, arising in magnetohydrodynamics stagnation point flow toward a horizontal moving plate with constant velocity, . The governing mass, momentum, and energy equations are reduced into nonlinear ordinary differential equations with boundary conditions using the relevant similarity variables. The reduced boundary value problem is regulated by the magnetic parameter, slip parameter, temperature jump parameter, Prandtl number, radiation parameter, and temperature ratio parameter. In the absence of an analytic solution, the reduced equations are then demonstrated numerically using the shooting technique. The effects of parameters on the flow domain are analyzed using tables and figures. Moreover, two‐dimensional streamlines are plotted for visualizing fluid flow. It is found that the temperature decreases as the magnetic parameter, slip parameter, temperature jump parameter, and Prandtl number increase, but the opposite scenario is observed when the radiation parameter and temperature ratio parameter increase.

Unsteady MHD Stagnation Point Flow of Al2O3-Cu/H2O Hybrid Nanofluid Past a Convectively Heated Permeable Stretching/Shrinking Sheet with Suction/Injection

The numerical investigation of unsteady magnetohydrodynamic (MHD) stagnation point flow of Al2O3-Cu/H2O hybrid nanofluid past a convectively heated permeable stretching/shrinking sheet with suction/injection effect is underlined. The characteristic of MHD and boundary condition with suction/injection has received a lot of consideration due to its across-the-board application in mechanical and chemical engineering. The governing continuity, momentum and energy equations are transformed into a system of nonlinear ordinary differential equations using similarity transformation, which is then solved using the bvp4c routine. Numerical results are obtained for the skin friction coefficient, local Nusselt number as well as the velocity and temperature profiles for certain values of the governing parameters, namely suction/injection parameter, copper nanoparticle volume fraction parameter and MHD parameter. Results showed that both velocity profile and temperature increase as the suction/injection parameter increases for the first solution and decreases for the second solution. Similarly, when increase the value of MHD parameter M, the velocity and temperature profiles are decreases for both solutions. The magnitude of the reduced skin friction coefficient and the local Nusselt number are notably increased for the first solution with increasing values of the suction/injection and MHD parameters. Finding also revealed that the skin friction coefficient is intensified in conjunction with the local Nussel number by adding up the copper nanoparticle volume fraction. In general, dual solutions are found to exist to a particular extent of the stretching/shrinking sheet.

MHD stagnation-point flow of nanofluid due to a shrinking sheet with melting, viscous dissipation and Joule heating effects

Nanofluids have received a lot of interest in recent years because of their prospective uses in industrial applications; therefore, a progressive study on flow control is requirable. The primary goal of this study is to elucidate the magnetohydrodynamic (MHD) stagnation point flow of alumina-water nanofluid due to a shrinking sheet with the inclusion of viscous dissipation, melting and Joule heating effects. The similarity transformation reduces the complexity of the model into the similarity (ordinary) differential equations. The findings are numerically acquired by programming the resultant equations in MATLAB and processing them via the bvp4c tool. The findings show that at the shrinking condition, two solutions are conceivable, with the separation of the flow occurring within this area. The examination of stability reveals that only one solution remains stable, while the other is not. By boosting the melting effect and decreasing the nanoparticle volume fraction as well as the Eckert number, it is possible to accelerate the heat transmission in the fluid flow system. The temperature profile is decelerated as the nanoparticle volume fraction amplifies, and this is accompanied by a decrease in Joule heating. This study also suggests considering 2% of alumina volume fraction instead of 1% so that the flow separation process can be delayed, and simultaneously sustain the laminar flow. The increment of melting effect by 25%, reducing the skin friction approximately by 5% at a certain degree of shrinking. This study can be referred as guidance in managing the relevant parameters imposed on the nanofluid flow, which has the capability to give significant advantages, especially in monitoring the flow performance.

Convective heat transfer in magnetohydrodynamic TiO2–CuO/ethylene glycol hybrid nanofluid flow toward stagnation point on a radially stretching disk with thermal radiation

AbstractA prime concern of this analysis is to investigate a steady, two‐dimensional, axisymmetric magnetohydrodynamic (MHD) stagnation point flow of TiO2–CuO/ethylene glycol (TiO2–CuO/EG) hybrid nanofluid through a radially stretched disk. Effects of thermal radiation, viscous dissipation, and Joule heating along convective boundary conditions have been taken into consideration. Suitable similarity conversions have been employed to simplify the set of flow controlling partial differential equations of the arising model. Subsequently, the finite element method has been utilized for computational results of the obtained set of ordinary differential equations with associated boundary conditions. The influence of various pertinent parameters, stretching parameter, solid volume fraction, magnetic parameter, Biot number, radiation parameter, and Brinkman number on dimensionless velocity and temperature have been displayed graphically. Subsequently, the responses of hybrid nanofluid (TiO2–CuO/EG) and regular nanofluid (CuO/EG) for these parameters have been compared pairwise, and it has been observed that nanoparticles in ethylene glycol are both controlling the temperature and improving the fluid velocity. Moreover, variations in local skin friction and local Nusselt number for certain values of embedded parameters have been illustrated in tabulated form. It is comprehended that augmented solid volume fraction, magnetic parameter, local Biot number, radiation parameter, and Brinkman number have improved the temperature profile. The velocity profile has been enhanced for the stretching parameter, while the reverse trend has occurred in the case of solid volume fraction and magnetic parameter. The outcomes of this study may be applicable in solar thermal systems.

Entropy generation on the variable magnetic field and magnetohydrodynamic stagnation point flow of Eyring–Powell hybrid dusty nanofluid: Solar thermal application

The prime intention of this study is to analyse the significance of the variable magnetic field and magnetohydrodynamic stagnation point flow of Eyring–Powell hybrid dusty nanofluid over a Darcy–Forchheimer sheet. The hybrid nanofluid was formulated by suspending the nanoparticles of copper ( Cu) and zirconium dioxide ( ZrO2) into a base fluid mixture of ( C2 H6 O2) ethylene glycol (50%) + ( H2 O) water (50%). The mixture of two different base fluid properties has notable results compared to using a single base fluid. Because when we used the mixture of both base fluids, we obtained better heat conductivity than pure ethylene glycol and a lower freezing point than water. Glycol water has several applications in solar heating installation and antifreeze in automobiles. The suitable self-similarity transformations are employed to convert the hybrid and dusty nanofluids transport equations into ordinary differential equations and then resolved using the Runge–Kutta fourth order with the shooting method in the MATLAB solver. The calculated results are plotted graphically through velocity, temperature, entropy generation, local skin friction coefficient and rate of heat transfer. The velocity profile enhances with the higher values of the Eyring–Powell fluid parameter. Entropy generation ( N G) and Bejan number ( Be) have an opposite nature on the Brinkman number ( Br). The rate of heat transfer rises for the higher values of the radiation parameter and opposite behaviour is observed to the magnetic field parameter. It is noticed that hybrid nanofluids have a higher heat transfer process than dusty nanofluids.

Computational Framework of Magnetized MgO-Ni/Water-Based Stagnation Nanoflow Past an Elastic Stretching Surface: Application in Solar Energy Coatings.

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.

MHD stagnation point flow over a stretching or shrinking sheet in a porous medium with velocity slip

Magnetohydrodynamics (MHD) stagnation point flow in a porous medium with velocity slip is investigated in this study. The governing system of partial differential equations is transformed into a set of non-linear ordinary differential equations by using the similarity transformation. Subsequently, the transformed equations are numerically solved by using the shooting method in MAPLE software. The skin friction coefficient and the local Nusselt number are obtained and presented graphically. The effects of the governing parameters including the velocity slip, magnetic and permeability parameters, are examined. It is found that both the skin friction coefficient and the local Nusselt number increase as magnetic and permeability parameters increase.

EFFECT OF HEAT SOURCE ON STAGNATION-POINT MHD TANGENT HYPERBOLIC FLUID FLOW ON A STRETCHED SHEET IN A POROUS MEDIUM

EFFECT OF HEAT SOURCE ON STAGNATION-POINT MHD TANGENT HYPERBOLIC FLUID FLOW ON A STRETCHED SHEET IN A POROUS MEDIUM

Magnetohydrodynamic Flow Past a Nonlinear Stretching or Shrinking Cylinder in Nanofluid with Viscous Dissipation and Heat Generation Effect

The Tiwari-Das model is used to investigate magnetohydrodynamic stagnation point flow and heat transfer past a nonlinear stretching or shrinking cylinder in nanofluid with viscous dissipation and heat generation using. The partial differential equations, also known as governing equations, were reduced to nonlinear ordinary differential equations using similarity transformation. MATLAB with the bvp4c solver is used for numerical computing. The controlling parameter, such as nanoparticle volume fraction, magnetic, curvature, nonlinear, radiation, and heat generation parameters, as well as Eckert and Grashof numbers, influence the skin friction coefficient, heat transfer rate, velocity, and temperature profiles. The results are presented as graphs to show the influence of the variables studied. In some circumstances of stretching and shrinking cases, dual solutions can be obtained.

Spline collocation for magnetohydrodynamic stagnation-point flow towards a stretching sheet

Steady two-dimensional stagnation-point flow of an incompressible viscous electrically con– ducting fluid over a flat deformable sheet is investigated when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. Using similarity variables, the governing partial differential equations are transformed into a set of non-dimensional ordinary differential equations. These equations are then solved numerically using Spline collocation method. It is shown that the velocity at a point decreases/increases with increase in the magnetic field when the free stream velocity is less/greater than the stretching velocity. Temperature distribution in the flow is obtained when the surface is held at a constant temperature. In the present reported work the effect of magnetic field parameter and Prandtl number on flow have been discussed.

Impact of nanoparticle shape on magnetohydrodynamic stagnation-point flow of Carreau nanoliquid: A comparative study

In this paper, a numerical computational work is carried out to investigate the significance of nanoparticle shape on magnetohydrodynamic stagnation-point flow of Carreau nanoliquid caused by a horizontally moving thin needle. The drive and thermal transport nature of Ti6Al4V+Ethylene glycol nanoliquid under the stimulus of space-dependent heat source and magnetized force is discussed numerically. The novelty of this work is to obtain the simultaneous solutions for three different shapes of nanoparticles namely spherical, cylindrical and laminar. The flow governing partial differential equations are transformed into ordinary differential equations with appropriate similarity variables and solved numerically by using Runge–Kutta and Newton's approach. Numerical outcomes of velocity and thermal distributions under the influence of different physical parameters are illustrated via graphical trends, wall friction and rate of heat transfer are interpreted using tabular values. It reveals from results that the thermal transfer performance of the Carreau nanoliquid is advanced when spherical shaped nanoparticles are used as compared with cylindrical and laminar-shaped nanoparticles. Also, it is witnessed that needle thickness parameter plays vital role in augmenting thermal transport rate of the nanoliquid.

Radiation and slip effects on MHD point flow of nanofluid towards a stretching sheet with melting heat transfer

AbstractIn the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth‐order method using appropriate similarity transformations. Temperature and velocity fields are presented for various flow pertinent parameters. Nondimensional physical parameters such as Prandtl number, radiation parameter, Brownian motion parameter, Lewis number, thermophoresis parameter, magnetic parameter, and melting parameter on fluid velocity, heat, concentration, skin friction, Sherwood number, and Nusselt number are presented graphically and discussed numerically. Heat transfer rate can be increased by increasing slip, melting, or radiation parameter. Mass transfer increases for greater values of melting parameter or slip parameter while radiation parameter shows the opposite impact on mass transfer.