Magnetohydrodynamic Viscous Flow Research Articles

Effects of heat source on the stagnation point flow of a nanofluid over a stretchable sheet with magnetic field and zero mass flux at the surface

In this paper, authors have investigated the heat transference rate of stagnation point flow of a nanofluid over a stretching sheet in a porous medium. The authors have examined the magnetohydrodynamic viscous flow of nanofluid. The transport equations involve Brownian motion and thermophoresis effects. The properties of heat transfer of nanofluids are acknowledged via a numerical algorithm. Diffusivity and conductivity characteristics of fluid are relying on nanoparticles volume fraction and the model is based on energy, momentum, mass conservation, and concentration equations. For the physical significance of the flow model, authors have utilized the zero mass flux condition at the surface. Similarity transformations are used to convert the PDEs (Nonlinear Partial Differential Equations) into a set of coupled ODEs (Ordinary Differential Equations). A built-in bvp4c algorithm in MATLAB software produces convergent implications of nonlinear systems. An exhaustive analysis of pertinent parameters, magnetic, porosity, heat source/sink parameter, etc, is done for clarification of the physical significance. The higher far-field velocity causes the temperature to rise but the heat transfer rate to reduce at the surface. The zero mass flux condition relates to the higher concentration of nanoparticles at the far field in comparison to the surface.

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.

An MHD viscous liquid stagnation point flow and heat transfer with thermal radiation and transpiration

The impact of kinematic parameters magnetohydrodynamic (MHD) and thermal radiation on the unsteady flow of a Newtonian liquid through stagnation point due to a linear sheet with mass transpiration is considered. The characteristics of heat and MHD impinging on the sheet are analyzed theoretically. The flow of an electrically conducting liquid through stagnation point has gained considerable interest due to its industrial relevance. In the chemical engineering applications involving cooling of the liquid namely glass blowing, food processing, metal thinning, polymer extrusion, silicon chip manufacturing and applications of similar kind. In all these chemical engineering applications, the interplay between the regulating kinematic parameters and the nature of the fluid is of at most priority. The flow problem is modelled into nonlinear unsteady Navier-Stokes’ partial differential equations. The similarity solution for the velocity distribution is obtained. Depending on the type of boundary heating, the analytical solutions for temperature distribution is derived by means of a power series (Gauss hypergeometric). Temperature distribution for two types of boundary heating processes viz., prescribed time-dependent constant surface temperature (PTDCST) and prescribed time-dependent wall heat flux (PTDWHF) is discussed. There found to exist branching of solutions for both velocity and temperature distribution for certain range of controlling parameters. In fact there exists dual solution for both cases of stretching/shrinking sheet and these are analyzed to see the impacts of various physical parameters on the solution domain. The impact of various regulating parameters on the velocity as well as temperature is analyzed by means of numerous plots.

A Mathematical Study on Non-Linear MHD Boundary Layer Past a Porous Shrinking Sheet with Suction

In this paper we discuss with magneto hydrodynamic viscous flow due to a shrinking sheet in the presence of suction. We also discuss two dimensional and axisymmetric shrinking for various cases. Using similarity transformation the governing boundary layer equations are converted into its dimensionless form. The transformed simultaneous ordinary differential equations are solved analytically by using Homotopy analysis method. The approximate analytical expression of the dimensionless velocity, dimensionless temperature and dimensionless concentration are derived using the Homotopy analysis method through the guessing solutions. Our analytical results are compared with the previous work and a good agreement is observed.

Ohmic Heating of Magnetohydrodynamic Viscous Flow over a Continuous Moving Plate with Viscous Dissipation Buoyancy and Thermal Radiation

This study extends previous investigation on ohmic heating of magnetohydrodynamic viscous fluid flow over a continuous moving plate to include radiative heat-loss, viscous dissipation and buoyancy effects. The mathematical formulation representing the modified physical model involves a system of three partial differential equations, which are transformed into a system of two coupled non-linear ordinary differential equations using suitable dimensionless variables. Thereafter, the resulting dimensionless system of equations governing modified model are solved via Homotopy Analysis Method (HAM). The accuracy and convergence of solutions are validated by comparing the results obtained with those in literature and they are in good agreement. Parametric study is performed to illustrate the effects of emerging parameters on fluid velocity and temperature, skin friction coefficient and Nusselt number. It is found that the impacts of pertinent parameters due to the extensions are significant and these are presented in graphs and tables. The results indicate that the skin friction coefficient and the heat transfer rate increase with the increasing values of thermal radiation and decrease with the increasing value of viscous dissipation parameter.

Steady Boundary Layer Magnetohydrodynamic Viscous Flow and Heat Transfer of Nanofluid Over Stretching Sheet in Presence of Radiation and Heat Source

Steady Boundary Layer Magnetohydrodynamic Viscous Flow and Heat Transfer of Nanofluid Over Stretching Sheet in Presence of Radiation and Heat Source

Dirichlet series and analytical solutions of MHD viscous flow with suction / blowing

Abstract This paper presents Dirichlet series and approximate analytical solutions of magnetohydrodynamic (MHD) flow due to a suction / blowing caused by boundary layer of an incompressible viscous flow. The governing nonlinear partial differential equations of momentum equations are reduced into a set of nonlinear ordinary differential equations (ODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel mathematical tools for their analysis. We use elegant fast converging Dirichlet series and approximate analytical solutions (method of stretching of variables) of these nonlinear differential equations. These methods have advantages over pure numerical methods for obtaining derived quantities accurately for various values of the parameters involved at a stretch and also they are valid in much larger parameter domains as compared with DTM-Padé and classical numerical schemes.

Hall Effect on MHD Flow Induced by Torsional Oscillation of a Porous Disc in a Rotating Fluid

This paper deals with the study of Hall effects on magnetohydrodynamic viscous flow induced by torsional oscillation of a porous disc in a rotating fluid. Constitutive equations of motion and energy have been developed using both hydrodynamic and electrodynamic equations. Expressions for velocity, temperature and phases are obtained by solving the equations of momentum and energy. The expression for skin-friction has also been derived alongwith its amplitude and phase. After computerization with the permitted numerical values of the fluid parameters, the velocity, temperature and shear stress profiles are obtained. It is observed that the radial velocity of the fluid increase with distance from the porous disc. However, the increase in Hall parameter is observed to reduces the axial velocity for, 0 2, it increases. The phase ϕ of the transverse shear stress decreases with the decrease of Hartmann number for n > p (frequency (n) greater than fluid pressure (p).

Influence of magnetohydrodynamic viscous flow on entropy generation within porous micro duct using the Lattice Boltzmann Method

In this work entropy generation and heat transfer for magnetohydrodynamic (MHD) forced convection flow in a micro duct filled with a porous medium are investigated using a modified axisymmetric Lattice Boltzmann Method.

Approximate analytical solutions of MHD viscous flow

The paper presents the semi-numerical solution for the magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet caused by boundary layer of an incompressible viscous flow. The governing three partial differential equations of momentum equations are reduced into ordinary differential equation (ODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel mathematical tools for their analysis. We use fast converging Dirichlet series and Method of stretching of variables for the solution of these nonlinear differential equations. These methods have the advantages over pure numerical methods for obtaining the derived quantities accurately for various values of the parameters involved at a stretch and also they are valid in much larger parameter domain as compared with HAM, HPM, ADM and the classical numerical schemes.

Numerical Solutions of MHD Viscous Flow of Newtonian Fluids due to a Shrinking Sheet by SOR Iterative Procedure

The problem of Magneto Hydrodynamic viscous flow due to a shrinking sheet of Newtonian fluids has been solved numerically by using SOR Iterative Procedure. The similarity transformations have been used to reduce the highly nonlinear partial differential equations of motion to ordinary differential equations. The results have been calculated on three different grid sizes to check the accuracy of the results. The numerical results for Newtonian fluids are found in good agreement with those obtained by the previous results.

MAGNETOHYDRODYNAMIC VISCOUS FLOW OVER A SHRINKING SHEET IN A SECOND-ORDER SLIP FLOW MODEL

In this paper, we investigate a magnetohydrodynamic viscous flow over a permeable shrinking surface by means of a second-order slip flow model. We have obtained a closed form of exact solution for the Navier−Stokes equations by using the similarity variable technique. The effects of slip, suction, and magnetic parameters have been investigated in detail. The results show that there are two solution branches, namely, a lower solution branch and an upper solution branch. The behavior of velocity and shear stress profiles at different values of slip, suction, and magnetic parameters has been discussed through graphs.

Magnetohydrodynamic viscous flow over a nonlinearly moving surface: Closed-form solutions

In this paper, the magnetohydrodynamic (MHD) flow over a nonlinearly (power-law velocity) moving surface is investigated analytically and solutions are presented for a few special conditions. The solutions are obtained in closed forms with hyperbolic functions. The effects of the magnetic, the wall moving, and the mass transpiration parameters are discussed. These solutions are important to show the flow physics as well as to be used as bench mark problems for numerical validation and development of new solution schemes.

Analytical Solutions of the Slip Magnetohydrodynamic Viscous Flow over a Stretching Sheet by Using the Laplace–Adomian Decomposition Method

In this research, the Laplace-Adomian decomposition method (LADM) is applied for the analytical and numerical treatment of the nonlinear differential equation that describes a magnetohydrodynamic (MHD) flow under slip condition over a permeable stretching surface. The technique is well applied to approximate the similarity solutions of the problem for some typical values of model parameters. The obtained series solutions by the LADM are combined with the Pad´e approximation to improve the accuracy and enlarge the convergence domain of the obtained results. Through tables and figures, the efficiency of the presented method is illustrated.

Analytic heat and mass transfer of the mixed hydrodynamic/thermal slip MHD viscous flow over a stretching sheet

In this paper, the heat and mass transfer characteristics of the magnetohydrodynamic (MHD) viscous flow over a permeable stretching surface is solved analytically. The flow considered is under both the hydrodynamic and thermal slip conditions. The magnetohydrodynamic flow and heat transfer of an electrically conducting fluid, taking into account the effects of Joule and viscous dissipation, internal heat generation/absorption, work done due to deformation and thermal radiation is studied. The solution is expressed in a closed form equation and is an exact solution of the full governing Navier–Stokes and energy equations. Thermal transport is analyzed for two types of non-isothermal boundary conditions, i.e. prescribed surface temperature (PST) and prescribed surface heat flux (PHF) varying as a power of the distance from the origin. Results for some special cases of the present analysis are in excellent agreement with those existing in the literature. The effects of various physical parameters, such as magnetic parameter, thermal radiation parameter, heat source/sink parameter, Prandtl number, Eckert number and suction/injection parameter on the velocity and temperature profiles, skin friction coefficient and Nusselt number are examined and discussed in detail. Results show that there is only one physical solution for any combination of the slip together with all the parameters. The velocity/shear stress profiles and the temperature/heat transfer profiles are greatly influenced by these parameters.

A new modified homotopy perturbation method with two free auxiliary parameters for solving MHD viscous flow due to a shrinking sheet

PurposeThe purpose of this paper is to introduce a new version of the homotopy perturbation method (HPM) for solving the magnetohydrodynamic viscous flow due to a shrinking sheet.Design/methodology/approachThree terms from HPM solution are used.FindingsThe results show that this method is very effective and simple and can be applied to other nonlinear problems.Research limitations/implicationsComparison between the HPM and homotopy analysis methods for the studied problem shows a remarkable agreement and reveals that the HPM needs less work.Practical implicationsIt is suggested that this method should be called HPM with auxiliary parameters. This paper uses two auxiliary parameters, three or more auxiliary parameters could be used for accuracy consideration.Originality/valueIn this paper, a two‐parameter HPM is applied which is useful for finding an approximate analytical solution of MHD viscous flow due to a shrinking sheet.

Effects of thermal radiation on MHD viscous fluid flow and heat transfer over nonlinear shrinking porous sheet

This paper investigates the effects of thermal radiation on the magnetohydrodynamic (MHD) flow and heat transfer over a nonlinear shrinking porous sheet. The surface velocity of the shrinking sheet and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent viscosity and the thermal conductivity are also assumed to vary as an inverse function and a linear function of the temperature, respectively. A generalized similarity transformation is used to reduce the governing partial differential equations to their nonlinear coupled ordinary differential equations, and is solved numerically by using a finite difference scheme. The numerical results concern with the velocity and temperature profiles as well as the local skin-friction coefficient and the rate of the heat transfer at the porous sheet for different values of several physical parameters of interest.

Existence results and numerical simulation of magnetohydrodynamic viscous flow over a shrinking sheet with suction

This paper presents an analysis and a semi-analytical study of the boundary value problem resulting from a self-similar transformation of the partial differential equations governing the magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet with suction. Existence of a solution is shown using the fixed point argument and the boundary value problem is solved. Galerkin–Legendre spectral method with domain truncation is used to obtain approximate analytical solutions. The approximate solutions computed confirm the theoretical analysis.

Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet

The magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet is examined analytically. The series solution is obtained using the Adomian decomposition method (ADM) coupled with Padé approximants to handle the condition at infinity. The numerical solutions agree very well with the results by the homotopy analysis method.

On the effect of chemical reaction, heat and mass transfer on nonlinear MHD boundary layer past a porous shrinking sheet with suction

This work is concerned with magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are numercally solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. numerical results for the dimensionless velocity, temperature and concentration profiles are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.