Magnetohydrodynamic Flow Of Micropolar Fluid Research Articles

Nonlinear radiative thermal analysis of magneto-micropolar fluid over a bidirectionally extending sheet with varied thermal conditions

Thermal fluid flow analysis occasioned by stretching surfaces offers practical industrial and engineering applications, such as extrusion and drawing processes and materials experiencing heating and cooling conditions. Thus, this study explores magnetohydrodynamic micropolar fluid flow under varied thermal conditions and nonlinear thermal radiation over a dually stretched sheet subject to surface mass flux and an internal heat source. The study thus provides insight into the dynamics of heat transfer mechanisms for improving material processing techniques in many engineering processes. The flow dynamics with the thermal analysis are evaluated by applying two thermal conditions in the heat equation: the prescribed surface temperature (PST) and the prescribed heat flux (PHF). The formulated partial derivative equations that describe the current problem are changed into ordinary derivatives using some similarity quantities, while the converted equations are tackled with the combined techniques of shooting and Runge–Kutta Fehlberg. Consequently, diverse tables and figures are displayed to deliberate on the impacts of the physical terms on the dynamics of flow and heat transmission processes. The consequence of the analysis reveals a higher heat gradient in the prescribed surface temperature case than the uniform temperature distribution, as the Prandtl number magnifies. The micropolar material term reduces the surface frictional factor and depletes heat transmission, but the magnetic field term raises the skin friction coefficient.

Magnetohydrodynamic micropolar slip flow due to an exponentially stretching sheet with chemical reaction and nonuniform heat generation

AbstractThe main focus of the current study is to examine the impact of melting heat transfer and chemical reaction on magnetohydrodynamic micropolar fluid flow over a sheet that is exponentially stretching and immersed in a porous medium. A nonuniform heat source is placed within this flow system. Other impacts like slip phenomena and thermal radiation are also taken into consideration. The governing partial differential equations are converted to a system of ordinary differential equations (ODEs) via similarity transformation and we also get the corresponding necessary boundary conditions. These nonlinear ODEs are resolved with the help of shooting technique and an Runge‐Kutta fourth order (RK‐4) iterative strategy. Also, we solve this problem using the Bvp4c approach for validating the results of the RK‐4 method. Both outcomes are consistent with previously published data. With the help of tables and graphs, we examine the influence of multiple physical parameters on velocity, thermal, microrotation, concentration, Nusselt number, Sherwood number, coefficient of skin friction, and wall couple stress. We see that the temperature distribution and velocity profiles decrease when the melting parameter increases. The temperature profile boosts when the heat source parameter is increased.

MHD micropolar fluid flow in porous media

The analysis of mass and heat transfer in magnetohydrodynamic (MHD) flows has significant applications in heat exchangers, cooling nuclear reactors, designing energy systems and casting and injection processes of different types of fluids. On the other hand, extraction of crude oil, the flow of human or animal blood, as well as other polymer fluids or liquid crystals are just some examples of micropolar fluid flows. Due to the broad application spectrum of the theory of micropolar fluid flows, and the significance the impact the external magnetic field has on the flow of these fluids, this paper considers the stationary flow of a micropolar fluid between two plates under the influence of an external magnetic field which is perpendicular to the direction of the flow. Stationary plates are maintained at constant and different temperatures, while the whole problem is considered in the non-inductive approximation. The equation system used to define the physical problem under consideration is reduced to the system of differential equations that have been solved analytically and the solutions of which are of general nature. In addition to the solutions for velocity, microrotation and temperature, the paper gives solutions for shear stress at plates, the Nusselt number and flow rate. The provided solutions have been applied in order to reach some general conclusions about the influence of the magnetic field and physical characteristics of a micropolar fluid and the characteristics of porous media on the nature of micropolar fluid flows in porous media by means of chart analysis. General conclusions, obtained in the result analysis in this paper, give us the opportunity to understand the flows of micropolar fluids and highlight their significance.

Illustration of reacting species on the magnetohydrodynamic flow of micropolar fluid through an expanding surface with ohmic heating

The existing investigation intended to expose the control of dissipative heat on the flow of micropolar fluid past a moving surface embedding with permeable medium. The flow profiles are considerably boosted by the Darcy-Forchheimer inertial drag associated with Joule and Darcy dissipation. Because of the magnetic interaction as well as the permeability of the medium it is not wise to neglect these effects. The application of the current study is vital in the production process of certain materials in industries, applied engineering vis-a-vis biomedical areas such as drug delivery system, peristaltic pumping, etc. The use of standard transformation rules for the stream function the profiles are get rid into ordinary nonlinear from the system of nonlinear partial. Further, the system of equations is solved by using approximate analytical technique generally known as ‘Adomian Decomposition Method’. Graphs are used to analyse many constraints affecting the flow phenomena, and tabular data is used to investigate on the simulated findings for the rate coefficients. Further, the important outcomes are; the non-Newtonian parameter favours in enhancing the fluid velocity in comparison to the Newtonian fluid whereas the inertial drag retards it significantly.

Application of Keller-Box Method to the Heat and Mass Transfer Analysis of Magnetohydrodynamic Flow of Micropolar Fluid between Porous Parallel Walls of Different Permeability

The present work seeks to investigate the problem of stable laminar micropolar fluid flow through porous walls of varying permeability. Furthermore, the effect of an external magnetic field is investigated. The resulting solution is extended to analyse the nonlinear differential equation of heat and mass transfer in the flow situation. The velocity and microrotation at the channel’s entrance are assumed to be those of Poiseuille flow. Using appropriate transformations, the governing nonlinear equations are transformed to a system of ordinary differential equations, which are then solved using a novel numerical technique based on a finite difference scheme termed the Keller-box method. The results show that the smooth and straightforward Keller-box method is an appropriate method for estimating solutions of complex governing equations since it is simple to implement. Graphs and tables are used to explain the effect of significant parameters such as the suction Reynolds number, micro rotation/angular velocity parameters, and Peclet number on the stream function, temperature distribution, and concentration properties of the fluid. The effect of wall permeability on longitudinal velocity and microrotation has been investigated. The couple stress and skin friction on the walls have also been calculated. The effect of variation in Reynolds number is showing the importance of inertial forces in comparison with viscous forces. The velocity boundary layer is observed to decrease when there is an increase in Reynolds number. Furthermore, the accuracy and convergence of the obtained solutions show that the Keller-box method is applicable to various nonlinear physical problems, even those with significant non-linearity.

Computational Treatment of Magnetohydrodynamic Micropolar Fluid Flow Through Porous Medium Over an Exponentially Stretching Sheet with Heat Sink and Chemical Reaction Effects

The purpose of this research is to look into the magnetohydrodynamic boundary layer flow of Maxwell fluid across an exponentially stretching sheet with chemical reaction, and radiation impacts, that involves a heat sink. The PDE governing equation is converted to an ODE governing system. A Successive Linearization Method is then used to solve the system numerically. Graphically, the numerical outputs of, temperature, concentration profiles, and velocity are displayed. The results of several parameters are explored and examined. The numerical outcomes for the skin friction coefficient, local Nusselt number, Deborah number, local Sherwood number, and porosity are reported and analyzed. Based on the results, many characteristics have a considerable effect on fluid flow profiles. The reaction rate parameter had a significant impact on the concentration profile and the thickness of the boundary layer dropped as the reaction rate parameter was increased. The analyses’ findings were compared to those of previous studies and found to be in great agreement.

MHD dissipative micropolar fluid flow past stretching sheet with heat generation and slip effects

The micropolar fluids apply to certain polymeric solutions, lubricating fluids, colloidal expansions and complexes. Due to these significant applications, the present study is devoted to the magneto-hydrodynamic micropolar fluid flow and heat transfer over a stretching sheet in the presence of viscous dissipation, heat generation and slips conditions effects. The proposed phenomenon in terms of partial differential eqautions is transformed to ordinary differential equations by using similiarity variable formulation and is solved by utilizing bvp4c solver. The numerical solutions for the velocity profile , angular velocity , temperature profile and mass concentration along with the skin friction , angular velocity , the rate of heat transfer and the rate of mass transfer for diverse values of pertinent parameters involved in the flow model are determined. It is noted that by increasing material parameter , the velocity field decreases. It is observed that owing to increasing the values of magnetic field parameter velocity field declines and angular velocity rises well. It is seen that an increase in heat generation parameter results in reduction in the velocity profile, and by increasing values of Eckert number, the temperature field increases.

Steady Magnetohydrodynamic Micropolar Fluid Flow and Heat and Mass Transfer in Permeable Channel with Thermal Radiation

The present work is devoted to the study of magnetohydrodynamic micropolar fluid flow in a permeable channel with thermal radiation. The Rosseland approximation for thermal radiation is taken into account in the modelling of heat transfer. The governing equations are expressed in non-dimensional form. The Homotopy Perturbation Method (HPM) is briefly introduced and applied to derive the solution of nonlinear equations. The effects of various involved parameters like Reynolds number, microrotation parameter and Prandtl number on flow and heat transfer are discussed. Further, their effects on Nusselt and Sherwood numbers are also investigated from the physical point of view. Analytic solutions of the problem are obtained by HPM and a numerical technique bvp4c package MATLAB is applied to predict the graphs between different parameters.

Unsteady 3D micropolar nanofluid flow through a squeezing channel: application to cardiovascular disorders

Micropolar fluids had many industrial applications such as polymer solutions, lubricant fluids, and biological structures. However, the present study deals with the drug delivery in the cardiovascular system where the blood particles are considered as microparticles included their self-rotation (mainly red blood cells) and interaction. The nanoparticles may be used as drug carrier particles. In the present problem, nanoparticles are considered as metallic oxides, e.g., Alumina ( $${\text {Al}} _2{\text {O}} _3$$ ), Titania ( $${\text {TiO}} _2$$ ), and Magnetite ( $${\text {Fe}} _3{\text {O}} _4$$ ) with water as base fluid. The magnetohydrodynamic micropolar fluid flow between two parallel squeezing plates is considered. Further, the analysis is carried out in the presence of viscous dissipation and Joule heating effects. With the aid of a similarity transformation, the flow governing Navier–Stokes equations is transformed into a system of coupled nonlinear ordinary differential equations. Fourth-order Runge–Kutta method with shooting approach is used to solve the nonlinear coupled boundary value problem. The profiles of flow field variables are acquired for key parameters arising in the present problem. It is noticed that, when the plates are fixed, the viscous drag of the base fluid is the same as that of nanofluid. Further, it is observed that increasing volume fraction results a decrement in microrotation and thereby causing an increase in temperature of Titania–water nanofluid which is in contrast to the behavior of other nanofluids.

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.

Computational study on the effects of variable viscosity of micropolar liquids on heat transfer in a channel

A numerical model is developed to study the effects of temperature-dependent viscosity on heat transfer in magnetohydrodynamic flow of micropolar fluid in a channel with stretching walls. The governing equations for linear and angular momenta and energy are transformed to a set of nonlinear ordinary differential equations by using similarity variables, and resulting problems are solved numerically by quasi-linearization. The effects of the various physical parameters on velocity, microrotation and temperature profiles are presented graphically and numerically. Finally, the effects of pertinent parameters on local skin-friction coefficient and local Nusselt number are also presented graphically. Some important observations regarding the effect of vortex viscosity parameter, microinertia density parameter, spin gradient viscosity parameter and couple stress on flow fields are noted and displayed. Numerical values of shear stress, couple stress and heat flux are computed and tabulated. The viscosity variation parameter enhances the shear stress and the couple stress. However, the heat transfer exhibits an opposite trend. The viscosity parameter is the most influential on thermal distribution. The magnetic field acts as a retarding force which reduces the normal and streamwise velocities as well as the microrotation distribution

Magnetohydrodynamic micropolar fluid flow in a porous medium with multiple slip conditions

Theoretically, micropolar fluids are used in the biomedical investigations. This study analyzes the flow, heat and mass transfer in a magneto-micropolar reactive fluid over a nonlinear stretching sheet in a saturated non-Darcy porous medium. The impact of velocity, thermal and concentration slips with prescribed surface temperature and concentration boundary conditions are examined. Mathematical models are formulated and solved using an iterative technique spectral quasi-linearization method. The results of numerical simulations are depicted graphically. The present results when cross-checked with earlier reported data in the literature for limiting conditions exhibit good agreement. The results show that the momentum and thermal boundary layer thicknesses fall as the nonlinear stretching parameter increases while the opposite occur with a rise in the thermal conductivity parameter.

Hybrid Solution for the Analysis of MHD Micropolar Fluid Flow in a Vertical Porous Parallel-Plates Duct

In this paper, we analyze the transient magnetohydrodynamic (MHD) flow of an incompressible micropolar fluid between a porous parallel-plates channel. The fluid is electrically-conducting subjected to radiation described by the Cogley-Vincent-Gilles formulation and with convective thermal boundary conditions at the plates. The solution methodology employed is the hybrid numerical-analytical approach known as the Generalized Integral Transform Technique (GITT). The consistency of the integral transform method in handling such a class of problem is illustrated through convergence analyses, and the influence of physical parameters such as radiation, and micropolar parameters, and Hartman number. The wall shear stress, the coupled stress coefficient, and heat flux at the walls were also calculated, demonstrating that increasing the gyroviscosity decreases the wall stresses magnitudes. Furthermore, the results show that increasing the radiation heat transfer decreases the fluid temperature distribution. Additionally, the velocity is damped, and the angular velocity is increased by the Lorentz force in the presence of a magnetic field.

Numerical Simulations of Unsteady 3D MHD Micropolar Fluid Flow over a Slendering Sheet

The purpose of the present analysis is to explore the numerical investigation on the time-dependent 3D magnetohydrodynamic flow of micropolar fluid over a slendering stretchable sheet. The prevailing PDEs are rehabilitated into coupled non-linear ODEs with the aid of appropriate similarity variables and then numerically calculated by applying the 4th RKM incorporate with shooting scheme. The contributions of various interesting variables are shown graphically. Emerging physical parameters on velocity, microrotation, and the surface drag coefficient are portrayed graphically. It is noticed that the microrotation profiles highly influenced by the vortex viscosity parameter and the micro-inertia density parameter. It is also concluded that the microrotation profiles (h2) are promoted by increasing the spin gradient viscosity parameter. Excellent accuracy of the present results is observed with the formerly published as a result of a special case.

Study of the Couple Stress Convective Micropolar Fluid Flow in a Hall MHD Generator System

The steady non-isothermal convective heat transfer in magnetohydrodynamic micropolar fluid flow over a non-linear extending wall is examined. The fluid flow is treated with strong magnetic field. The influence of magnetic field, Hall current, viscous dissipation, and couple stress are mainly focused in this work. The fluid flow problem is solved by analytical method. The impact of developing dimensionless parameters on primary, secondary, and angular velocity components and temperature profile are determined through graphs. The greater magnetic parameter, local Grashof number, Hall parameter, power-law index, Prandtl number, nonlinear wall geometric parameter, and couples stress parameter reduce the primary velocity component while the material parameter, and Eckert number escalates the primary velocity component. The greater local Grashof number, material parameter, power-law index, Prandtl number, and wall geometric parameter reduces the secondary velocity component while the greater magnetic parameter, Hall parameter, Eckert number, and couple stress parameter escalates the secondary velocity component.

Numerical Exploration of MHD Radiative Micropolar Liquid Flow Driven by Stretching Sheet with Primary Slip: A Comparative Study

Abstract The knowledge of thermal transport of magnetohydrodynamic (MHD) flows across a stretching sheet plays a crucial role for transportation, fiber coating, heat exchangers, etc. Due to this fact, we scrutinize the heat transfer features of MHD micropolar fluid flow via a stretching surface in the neighborhood of the stagnation point with Joule heating, by taking advantage of the classical Fourier law. The flow equations are transformed into dimensionless form with the help of suitable similarity transformations. The Runge–Kutta-based shooting method is utilized to solve the converted non-linear coupled equations. Impacts of various physical parameters on the flow fields are represented via graphs. The heat transfer rate, couple stress coefficient and friction factor are presented in a separate table. Results anticipate that fluid temperature is an increasing function of Eckert number, radiation and magnetic parameters, whereas an opposite outcome is noticed for the Prandtl number. It is interesting to notice that the maximum velocity is attained in the absence of slip but maximum temperature is detected in the presence of slip.

Magnetohydrodynamic micropolar fluid flow in presence of nanoparticles through porous plate: A numerical study

This study numerically investigates Magnetohydrodynamic (MHD) convective and chemically reactive unsteady micropolar fluid flow with nanoparticles through the vertical porous plate with mass diffusion, thermal radiation, radiation absorption and heat source. A flow model is established by employing the well-known boundary layer approximations. To obtain the non-similar equation, the boundary layer governing equations including continuity, momentum, energy and concentration balance were nondimensionalised by usual transformation. A non-similar approach is applied to the flow model. To optimize the parametric values, the stability and convergence analysis (SCA) have been analysed for the Prandtl number (Pr) and Lewis number (Le). It is observed that with initial boundary conditions, U =V =T = C= 0 and for Delta tau = 0.005, Delta X = 0.20 and Delta Y = 0.25, the system converged at Prandtl number, P-r >= 0.356 and Lewis number, L-e >= 0.16. The coupled non-linear partial differential equations are solved by explicit finite difference method (EFDM) and the numerical results have been calculated by Compaq Visual FORTRAN 6.6a. Evaluation of the thermal and momentum boundary layer thickness with isotherms and streamlines analysis of boundary layer flows have been shown for the thermal radiation parameter (R). The effects of various parameters entering the problem on velocity, angular velocity, temperature and concentration are shown graphically.

Finite Element Analysis of MHD Flow of Micropolar Fluid over a Shrinking Sheet with a Convective Surface Boundary Condition

This paper presents a numerical solution for the steady mixed convection magnetohydrodynamic (MHD) flow of an electrically conducting micropolar fluid over a porous shrinking sheet. The velocity of shrinking sheet and magnetic field are assumed to vary as power functions of the distance from the origin. A convective boundary condition is used rather than the customary conditions for temperature, i.e., constant surface temperature or constant heat flux. With the aid of similarity transformations, the governing partial differential equations are transformed into a system of nonlinear ordinary differential equations, which are solved numerically, using the variational finite element method (FEM). The influence of various emerging thermophysical parameters, namely suction parameter, convective heat transfer parameter, magnetic parameter and power index on velocity, microrotation and temperature functions is studied extensively and is shown graphically. Additionally the skin friction and rate of heat transfer, which provide an estimate of the surface shear stress and the rate of cooling of the surface, respectively, have also been computed for these parameters. Under the limiting case an analytical solution of the flow velocity is compared with the present numerical results. An excellent agreement between the two sets of solutions is observed. Also, in order to check the convergence of numerical solution, the calculations are carried out by reducing the mesh size. The present study finds applications in materials processing and demonstrates excellent stability and convergence characteristics for the variational FEM code.

Flow visualization using heat lines for unsteady radiative hydromagnetic micropolar convection from a vertical slender hollow cylinder

The present study aims to investigate the thermal radiation heat transfer effect on unsteady magnetohydrodynamic flow of micropolar fluid over a uniformly heated vertical hollow cylinder using Bejan's heat function concept. The normalized conservation equations emerge as a system of time-dependent non-linear coupled partial differential equations. Under appropriate wall and free stream conditions these equations are solved with an efficient unconditionally stable implicit scheme of Crank-Nicolson type. Important thermo-physical parameters featured include the magnetic body force parameter (M), Grashof (free convection) parameter (Gr), Eringen micropolar material parameter (K), Prandtl number (Pr), conjugate heat transfer parameter (P) and radiative-conductive Rosseland parameter (N), are analyzed on the flow-field with ranges 0–3, 105–106, 0–1.2, 0.7–7.0, 0–0.5 and 0–15, respectively. The time-histories of average values of momentum and heat transport coefficients, as well as the steady-state flow variables are presented for selected values of these non-dimensional parameters. With elevation in magnetic parameter or radiation parameter, the time taken for the flow-field variables to attain the time-independent state increases. The dimensionless thermal radiative heat function values are closely correlated with the overall rate of heat transfer on the outer hot cylindrical wall. Bejan's heat flow visualization implies that the thermal radiative heat function contours are compact in the neighbourhood of leading edge of the boundary layer on the outer hot cylindrical wall. Increasing radiation or magnetic parameter values result in an increase in the deviation of heat lines from the hot wall. Also, the heat lines are observed to depart slightly away from the hot wall with greater values of vortex viscosity. Furthermore, the deviations of flow variables from the hot wall for a micropolar fluid are significant compared to the Newtonian fluid (vanishing micropolar vortex viscosity).

Slip Flow in Porous Medium of Micropolar Fluid in a Rectangular Microchannel under the Effect of a Magnetic Field

The magnetohydrodynamic flow of micropolar fluid through porous medium inside the rectangular microchannel is investigated. The flow is subjected to a uniform magnetic field. This phenomenon is modulated mathematically by a system of linear differential equations which describe the continuity, momentum and angular momentum equations of the considered fluid. The system of differential equations has been solved analytically. We have obtained the velocity and microrotation vectors in terms of a Fourier series. The volumetric flow rate is calculated and the effect of various parameters like medium permeability, magnetic field, the Knudsen number, the microrotation parameter and coupling parameter are discussed and illustrated graphically through a set of figures.