Steady Magnetohydrodynamic Flow Research Articles

Magnetohydrodynamic flow of Casson fluid on an inclined permeable moving plate with viscous dissipation, thermal radiation, joule heating and Soret effect

Here, a steady magnetohydrodynamic flow of Casson fluid on an inclined permeable moving plate through a porous medium is investigated. The influence of viscous dissipation, thermal radiation, Joule heating, heat sink, Soret effect with first order chemical reaction is considered. The impact of relevant flow parameters on fluid speed, temperature, species concentration, skin-friction and Sherwood number are deliberated. It is noticed that the flow velocity intensifies with an increase in the Soret number and inclination angle while the Casson parameter and Magnetic parameter decreases the fluid flow. In addition, the Prandtl number and the radiation parameter slow down the temperature and Schmidt number declines the concentration field.

Dual solutions of magnetized radiative flow of Casson Nanofluid over a stretching/shrinking cylinder: Stability analysis

The enhanced thermal efficiency exhibited by Casson nanofluids offers significant practical applications across various industrial and engineering sectors. This study focuses on the mathematical investigation of the steady magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid through a stretched/shrinking cylinder, taking into account the effects of suction and thermal radiation. The governing partial differential equations (PDEs) have been subjected to a similarity transformation, resulting in a set of nonlinear ordinary differential equations (ODEs). These ODEs were solved numerically utilizing the code of bvp4c in the software of Matlab which offers high accuracy (4th order). The employed nanofluid model incorporates the effects of Brownian motion and thermophoresis. The present study illustrates the graphical depictions of the impacts of different governing parameters, namely Hartmann (M) number, curvature (γ) parameter, Brownian motion (Nb) parameter, mass suction (S) parameter, thermal radiation (Rd) parameter, and thermophoresis (Nt) parameter, on heat transfer, flow, and mass transfer characteristics. Comprehensive determination and visual presentation of the coefficient of skin friction, local Nusselt number, and local Sherwood number were conducted for a range of estimates of applied parameters. Based on our examination, it has been determined that dual similarity solutions are present within a specific range of mass suction parameters. The relationship between the Casson parameter and various fluid dynamic properties, such as skin friction coefficient, heat transfer rate, and mass transfer rates, has been found to exhibit a decreasing trend. Furthermore, the stability analysis discovered that the first solution exhibits linear stability, whereas the second solution displays linear instability. Additionally, the motivation behind this study is to enhance industrial performance through the optimization of thermal power generation systems, thereby increasing their overall efficiency.

Analytical solution of the steady magnetohydrodynamic (MHD) free convection flow over a semi-infinite flat vertical plate moving in a porous medium with viscous dissipation

Analytical solution of the steady magnetohydrodynamic (MHD) free convection flow over a semi-infinite flat vertical plate moving in a porous medium with viscous dissipation

MHD Hybrid Nanofluid Flow Past A Stretching/Shrinking Wedge With Heat Generation/Absorption Impact

Heat transfer is commonly utilized in diverse industrial applications, including the manufacturing of paper, the cooling of electrical devices, and the synthesis of new substances. Hence, this study aims to investigate the effect of heat generation/absorption on the steady magnetohydrodynamic (MHD) flow and heat transfer of Al2O3-Cu/H2O hybrid nanofluids over a permeable stretching/shrinking wedge. By using similarity transformation techniques, the governing equations of the hybrid nanofluids are transformed into similarity equations. The similarity equations are numerically solved using the MATLAB software's built-in bvp4c package. The findings show that hybrid nanofluids are seen to improve thermal efficiency in comparison to conventional fluid. In relation to heat transfer rate, the increase of magnetic parameters from 0.00 to 0.10 and 0.15 contributes approximately 12.3% and 18.8%, respectively. Meanwhile, as the heat generation parameter increases, the heat transfer rate decreases leading to an inefficient thermal system. The findings of this study are anticipated to contribute to the knowledge base of scientists and researchers in the field.

Numerical solution of magnetohydrodynamic flow through duct with perturbated boundary using RBF-FD method

This paper explores the magnetic field and velocity profile within a square and rectangular duct that experiences a perturbation in the steady magnetohydrodynamic flow. The magnetic field applied forms an angle with the x-axis. To solve for the solutions, a radial basis function-based finite difference approach is employed, known as one of the most efficient numerical methods. The Hartmann number and the perturbation magnitude in the region with insulated walls are adjusted to compute the findings. Numerical solutions are obtained by varying the angles of the applied magnetic field. The results are computed by varying the width and magnitude of the perturbation on the wall. The computed results of the induced magnetic field and velocity are represented through contours.

DRBEM solution of singularly perturbed coupled MHD flow equations

In this study, the numerical solution of singularly perturbed magnetohydrodynamic (MHD) flow in a square duct with no-slip, and insulated or perfectly conducting walls is investigated by using the Dual Reciprocity Boundary Element Method (DRBEM). The steady, laminar and fully-developed MHD flow of an incompressible, viscous, and electrically conducting fluid in a long channel of square cross-section (duct) is driven by a pressure gradient. The governing MHD flow equations are convection–diffusion type and coupled in terms of the velocity V(x,y) and induced magnetic field B(x,y). When the intensity of horizontally applied external magnetic field is high, the Hartmann number (Ha) which is the coefficient of convection terms becomes large, that is, the coupled MHD flow equations become convection dominated. In other words, the coefficient of the diffusion terms is very small giving singularly perturbed MHD duct flow which exhibits thin boundary layers. The numerical scheme uses Shishkin mesh which depends on the number of points on one side and Ha. Numerical results obtained by DRBEM reveal that the well-known characteristics of the MHD flow problem are found as Ha increases and it is possible to obtain V(x,y) and B(x,y) for large values of Hartmann number up to Ha=1000.

Impacts of radiative heat flux and heat acquisition on steady Magneto hydrodynamics with viscous and ohmic dissipation, Free convection casson fluid flow between porous plates

An investigation was conducted on a steady magnetohydrodynamic (MHD) free convection flow of a Casson fluid across a parallel vertical plate immersed in a porous medium with viscous and magnetic dissipation. In addition, the energy equation contains terms for radiational heat flow, heat injection, and suction. The perturbation approach provides an analytical solution to the governing nonlinear partial differential equations underlying this phenomenon. The numerical approach in the Maple program was used to verify the correctness of the outcomes produced by the perturbation technique. The Grashof and Prandtl numbers, Casson fluid, magnetic field, and porosity parameters as well as radiation parameter, and heat injection/suction parameter impact on the flow is discussed graphically. Skin friction coefficient and Nusselt number are tabulated for a range of magnetic and radiative parameter values. The other physical factors listed above accelerate the fluid velocity, but the magnetic field decreases it. Furthermore, the wall shear stress and heat transfer were significantly impacted by the magnetic and radiative factors.

Significance of chemically reactive magnetized Eyring-Powell nanofluid flow comprising gyrotactic moment of microorganism and radiative analysis

The emerging attention in nano-technology and thermal engineering has led to the concept of nanoparticles with improved theoretical mechanisms and accomplished influenced innovative usages in cooling and heating conveniences, air conditioning arrangements, heat carrying systems, bio-medical applications such as cancer cure, micromechanics, solar energy, artificial heart surgery etc. Currently, peristaltic movements joined with non-Newtonian fluids have enlarged innumerable devotion due to their enormous applications in physical, medical, engineering processes and medical. Eyring - Powell is unique type of non-Newtonian model consequential commencing the theory of motion of fluids. This research work inspects the 3D steady magnetohydrodynamic flow (MHD) containing microorganisms of a Powell-Eyring nanofluid with double stratification over a bidirectional stretched surface. Furthermore, the characteristics of the heat transfer phenomenon are prescribed out by means of thermal radiation. For changing nonlinear PDEs to nonlinear ODEs, we use the appropriate transformations and then numerically solve them with the help of bvp4c procedures. The possessions of several parameters modulating the heat and mass transfer properties are graphically depicted and illustrated in particular. It is interesting to perceived that the temperature field deteriorates for established estimates of the stretching parameter and the Prandtl number. The microorganism as well as concentration field improve for increasing estimates of magnetic parameter and the Biot number.

Dual solutions of magnetite/cobalt/manganese-zinc-aqueous nano-ferrofluids from a stretching sheet with magnetic induction effects: MHD stagnation flow computation and analysis

A theoretical study is presented for the steady magnetohydrodynamic (MHD) boundary layer stagnation point flow of a nano-ferrofluid along a linearly moving stretching sheet, as a simulation of functional magnetic materials processing. Due to having imerging applications in heat transfer, the nano-ferrofluids draw the attention which comprise an aqueous base fluid doped with a variety of magnetic nanoparticles, i.e. magnetite (Fe3O4), cobalt ferrite (CoFe2O4) and Manganese-zinc (Mn-Zn) ferrite. A partial differential equation mathematical model is developed for mass, momentum, magnetic field continuity (induction), and energy with appropriate wall and free stream boundary conditions. Following similarity transformations, the dimensionless resultant nonlinear ordinary differential boundary value problem is solved numerically using the robust bvp4c function in MATLAB which features very efficient 4th order optimized Runge–Kutta quadrature. Dual solutions for the upper branch and lower branch separated by a critical point are identified. Visualization of velocity, temperature, and induced magnetic field function are presented graphically including validation of solutions with previous studies. Furthermore, skin-friction coefficient and the local Nusselt number are also computed. The impact of the controlling parameters, i.e. Prandtl number nanoparticle volume fraction parameter reciprocal of magnetic Prandtl number magnetic parameter and stretching rate ratio parameter have been illustrated through graphs and evaluated when a desire heat transfer can occur. Furthermore, resistance between fluid and the plate can be increased with the growing magnetic Prandtl number values. Increment in magnetic parameter () produces an elevation in the induced magnetic field magnitudes. Skin friction and Nusselt number are found to be greater for cobalt nanoparticles when compared to magnetite and Mn-Zn ferromagnetic nanoparticles when there is an increase in reciprocal magnetic Prandtl number. The simulations provide a deeper insight into the manufacturing flows of functional nano-ferromagnetic materials of relevance to deposition and coating systems.

MHD Effect on the Thermocapillary Silicon Melt Flow in Various Annular Enclosures

AbstractTo simulate thermocapillary magnetohydrodynamic (MHD) convection in different shallow annular enclosures filled with silicon melt, a 3D numerical approach using an implicit finite volume formulation is used. Radiation is emitted upward from the annular enclosure's free top surface, the bottom one heated vertically and is subjected to an external magnetic field. The steady and unsteady thermocapillary MHD flow in four annular enclosures (R = 0.5, 0.6, 0.7, and 0.8) field is studied. The effects of varying the annular gaps, R, on the hydrothermal wave number and azimuthal pattern are obtained. The effects of the magnetic field on azimuthal velocity, temperature disturbances, and the transition from oscillatory to steady flow are also depicted. The results reveal that: hydrothermal waves m = 4, m = 6 and m = 8 are observed in steady flow for R = 0.7, R = 0.6 and R = 0.5, respectively. Oscillatory flows dominated by a hydrothermal wave m = 3 are found also when R = 0.8. The azimuthal velocity and temperature fluctuations at the free surface decrease as the magnitude of the magnetic field (Ha) increases, and the oscillatory flow would turn steady when Ha exceeds a critical value.

Motile micro-organism based trihybrid nanofluid flow with an application of magnetic effect across a slender stretching sheet: Numerical approach

The steady magnetohydrodynamic ternary hybrid nanofluid flow over a slender surface under the effects of activation energy, Hall current, chemical reactions, and a heat source has been reported. A numerical model is developed to increase the rate of energy transfer and boost the efficiency and outcome of heat energy dissemination for a diverse range of biological applications and commercial uses. The rheological properties and thermal conductivity of the base fluids are improved by framing an accurate combination of nanoparticles (NPs). The ternary hybrid nanofluid has been prepared, in the current analysis, by the dispersion of magnesium oxide, titanium dioxide (TiO2), and cobalt ferrite (CoFe2O4) NPs in the base fluid. The physical phenomena have been expressed in the form of a system of nonlinear PDEs, which are degraded to a dimensionless system of ODEs through the similarity replacement and numerically solved by employing the MATLAB software package bvp4c. The graphical and tabular results are estimated for velocity, mass, and energy curves vs distinct physical factors. It has been noticed that the variation in the magnetic effect enhances the energy profile while the increasing number of ternary nanocomposites (MgO, TiO2, and CoFe2O4) in water lowers the energy curve. Furthermore, the effect of both Lewis and Peclet numbers weakens the motile microbe’s profile.

Numerical simulation of nanofluid flow due to a stretchable rotating disk

In this study, a steady magnetohydrodynamic (MHD) flow due to stretchable rotating disk in the presence of gyrotactic microorganisms is investigated. The governing equations modeling the flow are solved numerically using the newly introduced simple iteration method (SIM) that seeks to linearize a system using relaxation technique that effectively decouples the system. To verify the convergence and accuracy of the method, solution error and residual error analysis are carried out, respectively. The obtained results suggest that the SIM is a highly efficient method that produces convergent and highly accurate solutions. The effects of various parameters as well as combined parameter effects on the solution profiles are also investigated. An increase in the Hall and permeability parameters leads to a corresponding rise in the microorganism?s density and nanoparticle volume fraction.

MHD Casson Nanofluid in Darcy-Forchheimer Porous Medium in the Presence of Heat Source and Arrhenious Activation Energy: Applications of Neural Networks

ABSTRACT The present study investigates the significance of activation energy during chemical reactions, thermal radiations and temperature gradient of 3-D steady Magnetohydrodynamic Casson nanofluid flow (MHDCNFM) in Darcy−Forchheimer medium over an oscillating disk by using an intelligent numerical-based computing solver through the Levenberg-Marquardt backpropagation neural network scheme (LMBNNS). The adjusted Buongiorno model is utilized to develop the system of partial differential equations (PDEs) for MHDCNFM, and further, by invoking Von Karman similarity transformation, the system of governing PDEs is turned out into ordinary differential equations (ODEs). First, a data set for the magnetohydrodynamic Casson nanofluid flow model (MHDNNFM) is generated for a range of sundry parameters for the radial velocity, tangential velocity, heat distribution and concentration profile by the variations of Casson parameter, magnetic parameter, Brownian motion parameter, thermophoresis parameter, Forchheimer parameter, activation energy parameter, chemical reaction parameter, stretching parameter, porosity parameter and Schmidt number through the Lobatto IIIA technique, and after this, by applying an intelligent computing algorithm through nftool training, testing and validation steps are taken into account to find out the approximate solution for various cases. The designed solver LMBNNS is used to solve the MHDCNFM through mean squared error (MSE), regression, gradient analysis and histogram studies.

Energy dissipative MHD Cu-AA7072/water-based hybrid nanofluid flow over a perpetually moving slender needle

Right now, numerous nanoparticles are available in literature amidst these Copper, Aluminium and their alloys are sole feature nanoparticles with high physical, thermal and chemical possessions. These are enormously utilized in aircraft parts, generating space crafts and production of rocket climbing frames etc. This paper describes the steady and two-dimensional magnetohydrodynamic boundary layer flow of a hybrid nanofluid past a moving slandering needle. Copper (Cu) and Alumina Alloy (AA7072) are used as hybrid nanoparticles by considering water, a base fluid. The fundamental partial differential equations are transfigured to a set of nonlinear ordinary differential equations, then numerically solved with the help of MATLAB solver (bvp4c). The profiles of velocity, temperature and physical variables like skin friction coefficient and the local Nusselt number are displayed through figures for various parameters. The results are explored with nanofluid (Water + AA7072, Water + Cu) and hybrid nanofluid (Water + Cu + AA7072). The highest heat transfer rate can perceive in the case of Copper nanoparticles than AA7072 and hybrid cases (Water + Cu + AA7072) whereas skin friction is more in the case of Water + AA7072.

A novel approach for assessment of MHD mixed fluid around two parallel plates by consideration hybrid nanoparticles and shape factor

In the presence of a uniform magnetic field, the heat and mass transmission mechanisms of steady magnetohydrodynamic nanofluid flows between two parallel plates are presented in this paper. Ethylene glycol and water are mixed in equal proportions in the fluid. The hybrid nanoparticle is analyzed in this work, utilizing MWCNT and Ag as the particles. As a novelty, the nonlinear equations were solved using the Radial Basis Function methodology for the first time, and the numerical fourth-order Runge–Kutta method was used to compare the results, which were then illustrated in figures. The end result demonstrates that the numerical method and the Radial Basis Function approach are in excellent accord. Furthermore, the impact of various shape factors was investigated. The impact of a variety of active parameters, such as the magnetic parameter, viscosity coefficient, thermophoretic parameter, Brownian parameter, and nanofluid shape factor, on non-dimensional velocity, temperature, and concentration profiles has been shown. The Nusselt number drops as the thermophoretic and Brownian parameters are increased, but the viscosity coefficient has the reverse tendency.

Effects of Heat Generation/Absorption on Magnetohydrodynamics Flow Over a Vertical Plate with Convective Boundary Condition

Heat generation effect in a steady two-dimensional magnetohydrodynamics (MHD) flow over a moving vertical plate with a medium porosity has been studied. By similarity transformation variables, the coupled non-linear ordinary differential equations describing the model are obtained. The resulting equation is then solved, using Galerkin Weighted Residual Method (GWRM), where the effect of heat generation, Magnetic Parameter as well as other physical parameters encountered were examined and discussed. Some of the major findings were that increase in heat generation and convective heat parameter enhances the plate surface temperature as well as temperature field which allows the thermal effect to penetrate deeper into the quiescent fluid.

Effects of Inclination angle and Free Convection on Velocity Profile for a Steady 2-Dimensional Magnetohydrodynamic Fluid Flow in an Inclined Cylindrical Pipe

Effects of inclination and free convection on velocity profile for magnetohydrodynamic (MHD) fluid flow in an inclined cylindrical pipe has been investigated. The governing partial differential equations are the equations of continuity, momentum and energy which are converted into ordinary differential equation by employing similarity transformation and solved numerically by the Runge- Kutta fourth order scheme with shooting method. The findings, which are presented in the form of tables and graphs reveal that; when Hartmann number, Grashoff number and Gamma are decreased, the velocity of the fluid increases. The results of the study may be useful for the different model investigations, especially, in various areas of science and technology in which optimal inclination and free convection are utilized.

Steady magnetohydrodynamic Poiseuille flow of two immiscible non‐Newtonian and Newtonian fluids in a horizontal channel with Ohmic heating

AbstractIn this paper, an analytical study has been carried out on a steady magnetohydrodynamics (MHD) Poiseuille flow of two immiscible fluids in a horizontal channel with ohmic heating in the presence of an applied magnetic field. The channel is divided into two sections, Region I and Region II, respectively. Region I contains an electrically conducting, third grade, non‐Newtonian fluid while Region II is a Newtonian fluid. The regular Perturbation series method is used to transform the coupled nonlinear differential equations governing the flow into a system of linear ordinary differential equations in both fluid regions. Suitable interface matching conditions were chosen to obtain separate solutions for each fluid in both regions and the results were displayed graphically for various values of physical parameters, such as pressure gradient, suction parameter, Hartmann number, Prandtl number, viscosity, and conductivity ratios to show their effects on the flow. The effect of skin friction and Nusselt number was shown with the aid of tables. The results obtained among other findings clearly shows that as the value of the magnetic parameter increases, the velocity and temperature of the fluid decrease.

Spectral relaxation computation of electroconductive nanofluid convection flow from a moving surface with radiative flux and magnetic induction

Abstract A theoretical model is developed for steady magnetohydrodynamic viscous flow resulting from a moving semi-infinite flat plate in an electrically conducting nanofluid. Thermal radiation and magnetic induction effects are included in addition to thermal convective boundary conditions. Buongiorno’s two-component nanoscale model is deployed, which features Brownian motion and thermophoresis effects. The governing nonlinear boundary layer equations are converted to nonlinear ordinary differential equations by using suitable similarity transformations. The transformed system of differential equations is solved numerically, employing the spectral relaxation method (SRM) via the MATLAB R2018a software. SRM is a simple iteration scheme that does not require any evaluation of derivatives, perturbation, and linearization for solving a nonlinear system of equations. Effects of embedded parameters such as sheet velocity parameter$\lambda$, magnetic field parameter$\beta$, Prandtl number$Pr$, magnetic Prandtl number$Prm$, thermal radiation parameter$Rd$, Lewis number$Le$, Brownian motion parameter$Nb$, and thermophoresis parameter$Nt$ on velocity, induced magnetic field, temperature, and nanoparticle concentration profiles are investigated. The skin-friction results, local Nusselt number, and Sherwood number are also discussed for various values of governing physical parameters. To show the convergence rate against iteration, residual error analysis has also been performed. The flow is strongly decelerated, and magnetic induction is suppressed with greater magnetic body force parameter, whereas temperature is elevated due to extra work expended as heat in dragging the magnetic nanofluid. Temperatures are also boosted with increment in nanoscale thermophoresis parameter and radiative parameter, whereas they are reduced with higher wall velocity, Brownian motion, and Prandtl numbers. Both hydrodynamic and magnetic boundary layer thicknesses are reduced with greater reciprocal values of the magnetic Prandtl number Prm. Nanoparticle (concentration) boundary layer thickness is boosted with higher values of thermophoresis and Prandtl number, whereas it is diminished with increasing wall velocity, nanoscale Brownian motion parameter, radiative parameter, and Lewis number. The simulations are relevant to electroconductive nanomaterial processing.

Numerical study of Magnetohydrodynamic flow through annular duct with Neumann’s boundary condition

This paper investigates the magnetic field and velocity profile in an annular duct for steady Magnetohydrodynamic flow. The applied magnetic field makes an angle α with the x-axis. The numerical solution is obtained by the ‘Finite Element Method’ which is one of the efficient numerical methods. Computations are done by increasing Hartmann number in the annular region with partially conducting walls. Numerical Solution is evaluated for different angles in which the magnetic field is applied. By changing the thickness of the annular region and wall conductivity the results are computed. Computed results are presented in the form of contours for the magnetic field and velocity plot. Thus FEM enables one to portray the effect of Hartmann number and conductivity parameter on the behaviour of both the velocity and the induced magnetic field at a small expense.