MHD Flow Of Micropolar Fluid Research Articles

Numerical treatment of MHD micropolar nanofluid flow with activation energy, thermal radiation, and Hall current past a porous stretching sheet

ABSTRACT This communication investigates the heat and mass transfer properties of MHD micropolar nanofluid fluid flow behaviour with activation energy, thermal radiation, and Hall current past a linear stretching sheet. The governing non-linear partial differential equations of the flow are transformed into non-linear ordinary differential equations using similarity transformation variables and solved using Runge Kutta 4th order in conjunction with the shooting methodology. The shooting approach in MAPLE is then employed to solve the associated system of ordinary differential equations. The impact of pertinent parameters is revealed and discussed on velocity, temperature, and concentration. Increasing micropolar parameters increases tangential velocity profiles while decreasing the transfer velocity profiles. The comparison table for local skin friction coefficient, Nusselt number, and Sherwood number are represented with the effects of pertinent non-dimensional variables. The model has undergone thorough validation using existing data and has shown outstanding performance. It is revealed in the study that an increase in the micropolar term increases the tangential velocity for an enhanced engineering working fluid. Also, a rise in the Hall current term boosts the heat transfer to strengthen thermal science fluids performance.

Significance of an incident solar energy toward the MHD micropolar fluid flow over a stretching sheet

This paper studies the mixed convective flow of a magnetohydrodynamic micropolar fluid over an extending sheet. The first-order velocity slip condition is taken to observe the slip flow of the fluid. The applications of solar radiation toward the micropolar fluid flow are analyzed in this paper. Furthermore, the Brownian motion, thermophoresis and Joule heating impacts are also studied. Also, the Cattaneo-Christov heat flux model, chemical reaction and activation energy are observed. The leading PDEs have been transformed to ODEs and then solved with the help of homotopy analysis technique. The impacts of different physical parameters have been evaluated theoretically. The outcomes exhibited that the material factors have augmented the microrotation and velocity profiles. Moreover, the velocity slip parameter has a reverse relation with velocity and microrotation profiles, while there is a direct relation of a velocity slip with the energy curve. The velocity profile has increased with higher thermal and mass Grashof numbers. With increasing Brownian motion parameter, the thermal profile is amplified while the concentration profile is declined. On the other hand, the thermal and mass profiles have been boosted with greater thermophoresis parameter. The velocity profile has decreased with higher magnetic parameter, whereas the temperature profile has augmented with higher magnetic parameter. The couple stress and skin friction have been augmented with material parameter, whereas the skin friction has been reduced with thermal and mass Grashof numbers.

Mathematical Study of MHD Micropolar Fluid Flow with Radiation and Dissipative Impacts over a Permeable Stretching Sheet: Slip Effects Phenomena

Mathematical Study of MHD Micropolar Fluid Flow with Radiation and Dissipative Impacts over a Permeable Stretching Sheet: Slip Effects Phenomena

An analytical approach to entropy production in MHD mixed convection micropolar fluid flow over an inclined porous stretching sheet

This analytical analysis examines the MHD micropolar fluid flow and mixed convection features using entropy production analysis of an inclined porous stretching sheet. Flow field and heat transfer analysis are presented to consider thermal radiation, heat source/sink, Lorentz, and buoyancy forces. The PDEs system is transformed by appropriate similarity variables, turned into a system of high non-linearity coupling ODEs, and then solved with the help of an analytical approach. An analytical approach can provide exact explicit solutions for the flow field, heat transport, entropy production, the local skin friction coefficient, the local couple stress coefficient, and the local Nusselt number. It is shown that the magnetic field, mixed convection, and sheet inclination effects can be incorporated together into a single parameter, which is called the magneto-buoyancy-inclination parameter here. In other words, this parameter controls the boundary layer flow. In addition, an experimental procedure called Box-Behnken design (BBD) was employed to analyze the influence of material (K), radiation (Rd), and buoyancy (Λ) parameters on entropy production in MHD micropolar fluid flow over the sheet. In order to estimate accurately the optimum entropy generation containing K, Rd, and Λ, we used a quadratic regression model. Based on the results of this investigation, the value of the entropy generation number became larger by decreasing the magneto-buoyancy-inclination parameter. Further, the magnitude of the local couple stress coefficient is reduced as the heat source parameter increases.

Effects of Soret and Dufour Numbers on the Three-Dimensional MHD Flow of Micropolar Fluid Containing Gyrotactic Microorganisms Over a Bidirectional Stretching Sheet With Cattaneo–Christov Heat and Mass Flux Model

Abstract Stretching flow problems have several real-world applications in engineering, biological, and industrial fields. The real-world applications of the stretching sheet flow problems are continuous cooling of fiber, manufacturing of rubber and plastics sheets, metal-working processes, crystal growth processes, drawing of the filaments through a quiescent fluid, and consideration of the liquid's films and many others. The present problem focuses on the study of heat and mass transmission phenomena of the magnetohydrodynamics flow of three-dimensional micropolar liquid over a bidirectional stretching surface. In the current analysis, the heat and mass transport mechanism are demonstrated by incorporating the Cattaneo–Christov heat and mass flux model. The micro-organisms are only used to stabilize suspended nanoparticles via bioconvection, which is caused by the combination of magnetic field and a buoyancy force. The current model is demonstrated in the system of higher order partial differential equations (PDEs), which are changed into nonlinear ordinary differential equations (ODEs) by the exploitation of appropriate similarity variables. For the analytical solution, the resulting nonlinear ODEs are simulated by employing the homotopy analysis scheme. The physical significance of velocities, microrotation, temperature, concentration, and micro-organism profiles of the fluid via various embedded parameters are calculated and discussed in a graphical form. The Nusselt number, Sherwood number and micro-organism density number are calculated via tables. Some major findings of the current problem are that the Nusselt number is weakened for the boosted estimation of radiation and thermal relaxation time parameter. The bioconvection Lewis number raised the micro-organism density number. The nanofluid microrotation profile is boosted with the augmentation of the microrotation parameter. The temperature of nanoliquid is lower for thermal relaxation time parameter and nanofluid concentration is lower the for solutal relaxation time parameter.

Numerical modeling of MHD micropolar fluid flow and melting heat transfer under thermal radiation and Joule heating

The purpose of this paper is to discuss the melting heat transfer and flow of a micropolar fluid due to an exponentially stretching sheet, analogous to ordinary fluid. The impacts of slip parameter, viscous dissipation, Joule heating, heat source, and thermal radiation are anticipated. The transport of heat, momentum, and angular momentum is expressed mathematically using a set of partial differential equations (PDEs). The PDEs are turned into a set of dimensionless ordinary differential equations by employing similarity variables adequately and interpreted numerically utilizing a well-known computer language in-built software bvp4c solver in MATLAB. It is noticed that the impacts of several parameters (Prandtl number, Eckert number, magnetic, heat generation parameters, etc.) on physical quantities and flow fields (velocity, temperature, and microrotation profiles) are remarkable and which are exhibited graphically and discussed in details. It is detected that, by enhancing the melting parameter, the microrotation profile appears to be dwindling near the wall; however, it is eventually lifted. Increasing the slip parameter depletes the velocity and microrotation fields, whereas it has reverse effect on the thermal field. Moreover, the thermal field is positively affected by viscous dissipation and heat generation, but slightly more enhancement has been seen for ordinary fluid compared to micropolar fluid.

Thermal Conductivity and Thermophoretic Impacts of Micropolar Fluid Flow by a Horizontal Absorbent Isothermal Porous Wall with Heat Source/Sink

Boundary layer analysis is invoked to clarify the aspects of variable thermal conductivity and thermophoretic forces on a steady state of MHD micropolar fluid flow in the existence of a uniform transverse magnetic field along an isothermal horizontal plate. The micropolar pattern permits the rotational freedom degrees that lead to couple stresses and a non symmetric stress tensor. The initiated PDEs governing the case pattern are mutated into a non-dimensional system due to proper transformations. The transformed mathematical governing equations are solved by implementing a very potent computer algebra software MATLAB code. The plotted graphs analyzed the attitude of multiple physical aspects involving factors on the flow attitude of micropolar velocity and angular velocity and temperature. Through the involved factors, the couple stress, skin friction and Nusselt number are manifested and interpreted amply. A new outcome for drag force and heat gradient experienced by the key factors is portrayed. Augmentation in Ω results in the thermophoretic forces that encapsulate the mass transmission. The local Nusselt number strengthened as the thermal conductivity, heat absorption factors or wall suction velocity were improved, and weakened due to the existence of viscous dissipation or heat generation impacts. As a particular case, the governing field equations of a classical Newtonian liquid are given by dropping the micropolar parameter impacts.

Numerical investigation of entropy generation on MHD flow of micropolar fluid over a stretching sheet in the presence of a porous medium

Various industrial operations involve frequent heating and cooling of electrical systems. In such circumstances, the development of relevant thermal devices is of extreme importance. During the development of thermal devices, entropy generation should be reduced significantly for realizing efficient performance of the devices. Hence, in the current study, the investigation of micropolar fluid with entropy generation over a stretching sheet is taken into account. The impacts of different physical parameters on the velocity profile, microrotation profile, and temperature profile are studied graphically. The effects of thermal radiation, porous medium, magnetic field, and viscous dissipation are also analyzed. The influences of various involved parameters on physical quantities like skin friction coefficient, couple stress coefficient, and Nusselt number are also illustrated numerically. Moreover, entropy generation and Bejan number are studied graphically. The governing equations are solved by implementing the built-in Newton’s shooting method and code in the Mathematica (Version-9) operating system.

Heat and mass transfer in mixed convection MHD micropolar fluid flow due to non-linear stretched sheet in porous medium with non-uniform heat generation and absorption

In this paper, mixed convection flow is considered with micropolar fluid in the presence of the magnetic field. In addition, the flow is defied with a non-linear stretching sheet through a porous medium. Non-uniform heat generation/absorption as well as chemical reaction are studied. The similarity transformation is used to change the governing equations. The Homotopy Analysis Method is used to solve the system of ODE. The impacts of several important parameters on velocity profiles, angular velocity profiles, temperature profiles and concentration profiles are represented graphically. With the help of tables, the coefficients of Skin friction, Nusselt number, and local Sherwood number are also anticipated and shown. When the new finding results were compared to earlier findings, they revealed a high-level agreement. The findings show that the velocity profile and angular velocity profiles are enhanced by thermal radiation parameter and material parameter. When Biot number and Eckert number are raised, the temperature profiles increase noticeably. Furthermore, when the chemical reaction parameter is raised, the concentration profile is reduced and it is improved as Soret number is increased. Heat transfer rate increased as thermal radiation parameter increased and decreased as Biot number decreased for both linear and non-linear stretching.

Influences of First Order Slip and Heat Source/Sink on the Entropy Generation of MHD Micropolar Fluid Flow Through a Porous Medium

Influences of First Order Slip and Heat Source/Sink on the Entropy Generation of MHD Micropolar Fluid Flow Through a Porous Medium

Ohmic heating and chemical reaction effect on MHD flow of micropolar fluid past a stretching surface

The current article discuss the interaction between the Ohmic heating and chemical reaction impact on MHD micropolar fluid flow past a stretching surface in the existence of chemical reaction using Runge–Kutta–Fehlberg method (RKF-45) along with the shooting procedure. By applying some similarity transformations, the governing equations were changed to ODEs. Numerical consequences were calculated for many values of pertinent factors on flow, angular velocity, thermal, mass transfer are exposed graphically and the numerical outcomes of the skin friction, couple stress at the wall, Nusselt number, Sherwood number are entered in tabulated form. With an increase of the material parameter, the velocity, couple stress, Sherwood number, Nusselt number, and temperature, concentration, and shear stress increase, while temperature, concentration, and shear stress decreases.

Influence of nonlinear radiation on MHD micropolar fluid flow with viscous dissipation

AbstractThis study takes account of the impact of the convective boundary conditions. The energy equation consists of Joule heating and thermal nonlinear radiation impacts. Contact between the solid and the fluid is also susceptible to a velocity slip. The resultant differential equations system is solved using homotopy analysis method. To find all numerical computations, Mathematica is utilized. The behavior, with graphical results, of pertinent parameters in micropolar fluid flow characteristics is studied. We look at the impact of the material parameter, magnetic parameter, slip parameter, and electrical parameter to grasp the physics of the problem better. Different values of skin friction, wall couple stress, and Nusselt and Sherwood numbers are discussed.

Mathematical Modeling and MHD Flow of Micropolar Fluid Toward an Exponential Curved Surface: Heat Analysis via Ohmic Heating and Heat Source/Sink

The main goal of the current article analyzed the influence of MHD flow of micropolar fluid via exponentially curved stretching surface. Heat transfer analysis is discussed with the impact of thermal radiation and Joule heating. For mathematical model curvilinear (u, v, r and s) is taken for governing flow problem. Viscous dissipation is also considered. Exponential similarity variables are used to transform partial differential equations to ordinary differential system. (ODEs). Numerical techniques have been used to solve the nonlinear ODEs. Effect of various physical variables like material parameter $$(K_{1} = 0.1, 0.2, 0.3, 0.4, 0.5)$$ , radius of curvature ( $$\delta = 1,2,3,4,5$$ ), magnetic parameter ( $$M = 0,0.1, 0.2, 0.3, 0.4$$ ), radiative parameter ( $$R_{d} = 1.0,2.0,3.0,4.0,5.0$$ ), heat generation parameter (Q = 0, 0.1, 0.2, 0.3, 0.4), surface friction, couple stress and surface temperature on the flow of velocity, temperature field and microrotation velocity has been examined through graphs. A good agreement of the present work has been noticed with a previous published result.

Second Law Analysis of MHD Micropolar Fluid Flow through a Porous Microchannel with Multiple Slip and Convective Boundary Conditions

The impact of space dependent heat source in the transport of micropolar fluid in the existence of magnetic dipole, Joule heating, viscous heating, thermal radiation, hydrodynamic slips and convective condition effects has been numerically investigated. The dimensioned governing equations are non-dimensionlzed by using dimensionless variables then non-dimensional forms of the corresponding equations are than tackled by the versatile Finite Element Method (FEM). The effects of pertinent physical parameters characterize the flow phenomena are presented through graphs and discussed. It is found that, the impact of thermal based heat source advances the heat transfer characteristics significantly than exponential to space dependent. The thermal performance can be improved through the effects of magnetic dipole, viscous heating, Joule heating and convective condition. Further, the present numerical results are compared with previously published results in the literature as a limiting case of the considered problem and found to be in good agreement with the existing results.

MHD Flow of Micropolar Fluid via Porous Medium Within the Rotating Frame of Reference

The present study reveals the heat and mass transfer on the MHD flow of micropolar fluid in a porous medium within a rotating frame. In order to facilitate osillatory plate velocity with constant suction and first order chemical reaction has been considered. Using small perturbation approximation, the governing non-dimensional equations are solved. The influence of pertinent physical quantities on the flow phenomena have been presented graphically. The skin friction coefficient, wall couple stress, Nusselt and Sherwood number have also computed for different flow parameters and have presented in table. In the study, the applied magnetic field sets in to produce the resistive force i.e. the Lorentz force that resists the fluid motion throughout the domain. Attenuation in the Prandtl number is because of the slower thermal diffusivity resulted in a sharp reduction in the thermal boundary layer thickness. The retardation in the polar fluid concentration is greater in amount for the influence of heavier species.

Analysis of Chemical Reaction on MHD Micropolar Fluid Flow over a Shrinking Sheet near Stagnation Point with Nanoparticles and External Heat

The present study investigates numerically MHD flow near the stagnation point of micropolar fluid through a shrinking sheet containing nanoparticles under the influence of chemical reaction and external heat. The study is an attempt to investigate the flow behaviour of micropolar nanofluid because of its importance in heat transfer process in industries as well as cooling systems. The governing equations are converted to nonlinear ordinary differential equations by implementing similarity transformations. Numerical results are investigated in the form of figures and tables by using MATLAB built in solver bvp4c for various dimensionless parameters. The impacts of external heat parameter on temperature and chemical reaction factor on concentration of the nanofluid are illustrated in the form of graphs. It is observed that the temperature of the nanofluid and nanoparticle volume distributions increase when Biot number attain larger values. Rise in Thermophoretic parameter increases the nanoparticles concentration in the boundary layer. Numerical data are presented for Nusselt number and Sherwood number.

Melting Heat Transfer of MHD Micropolar Fluid Flow Past An Exponentially Stretching Sheet with SLip and Thermal Radiation

The effects of velocity slip and radiation on MHD flow and melting heat transfer of a micropolar fluid due to an exponentially stretched sheet are presented. By means of similarity transformations the leading partial differential equations are changed to a set of ordinary differential equations which are nonlinear. Numerical solutions of the nonlinear system of equations are then obtained by changing the boundary value problem first to an initial value problem. It is observed that the pertaining parameters have significant effects on the flow and heat transfer characteristics, which are presented and talked about in detail through their illustrations. Due to boost in the melting parameter, the fluid velocity, angular velocity and temperature are found to decrease. Fluid velocity and angular velocity both decrease with a rise in slip at the boundary but quite opposite is the effect on the temperature.

Evaluating the unsteady MHD micropolar fluid flow past stretching/shirking sheet with heat source and thermal radiation: Implementing fourth order predictor–corrector FDM

The idea of the current investigation is to analyze the effect of thermal radiation and non-uniform heat source/sink on unsteady MHD micropolar fluid flow past a stretching/shirking sheet. The governing non-linear PDEs are transformed into a set of non-linear coupled ODEs which are then solved numerically by using the fourth order predictor–corrector finite difference method (PC4-FDM). The effect of non-dimensional governing parameters on momentum, angular momentum, energy and mass descriptions is examined and displayed with the aid of their graphical depictions. Also, friction factor, heat and mass transfer rates have been enumerated and shown through tables. Under some special conditions, current outcomes are compared with the existing outcomes to examine the exactness and validity of the current study. An excellent agreement is found with the existing outcomes. Finally, it is observed that velocity increases with an increase in both micro-polar parameter and thermal buoyancy parameter. In addition, for the temperature profiles opposite behavior is observed for increment in both unsteadiness parameter and thermal buoyancy parameter.

Magnetohydrodynamic Flow of Micropolar Fluid and Heat Transfer Between a Porous and a Non-Porous Disk

This paper presents a study of the MHD flow of micropolar fluid and also heat transfer between porous disk and a non-porous disk of infinite radii. The non-zero tangential slip velocity is considered at the porous disk. The self-similar ODEs are obtained using the Von-Karman similarity transformation from the governing PDEs. The resulting equations are then solved numerically by a very efficient Keller-box method based on a finite-difference scheme. The influence of various pertaining parameters on velocity,micro-rotation, temperature, skin friction, and couple stress coefficient have been analyzed. The obtained results agree well with the available literature for special cases. The analysis finds that the heat transfer rate at the surfaces of the disks increases with the increase in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field.

Novel solution for heat and mass transfer of a MHD micropolar fluid flow on a moving plate with suction and injection

Two new functions on the semi-infinite interval, namely Rational Gegenbauer (R) and Exponential Gegenbauer (E) functions are proposed to solve the heat transfer problem. The considered problem is flow of MHD micropolar over a moving plate with suction and injection boundary conditions. For applying Tau method efficiently, two matrices of derivative and product for both of rational and exponential Gegenbauer whose enable us to solve a system of nonlinear algebraic equations on the semi-infinite interval were introduced, and an error bound of these functions approximation was estimated which led to have an exponential convergence rate in this method. Moreover, the influence of the important physical parameters on heat and mass transfer phenomena are studied with details. Comparing the results of Rational Gegenbauer Tau and Exponential Gegenbauer Tau methods with available analytical and numerical solutions shows that the present methods are efficient and have fast convergence rate and high accuracy. This method can solve a set of coupled nonlinear and high-order differential equations on a semi-infinite domain by converting to a set of linear equations.