Unsteady Magnetohydrodynamic Free Convection Flow Research Articles

Unsteady magnetohydrodynamic free convection and heat transfer flow of Al2O3‒Cu/water nanofluid over a non-linear stretching sheet in a porous medium

This article investigates the impact of time-dependent magnetohydrodynamics free convection flow of a nanofluid over a non-linear stretching sheet immersed in a porous medium. The combination of water as a base fluid and two different types of nanoparticles, namely aluminum oxide (Al2O3) and copper (Cu) is taken into account. The impacts of thermal radiation, viscous dissipation and heat source/sink are examined. The governing coupled non-linear partial differential equations are reduced to ordinary differential equations using suitable similarity transformations. The solutions of the prin-cipal equations are computed in closed form by applying the MATLAB bvp4c method. The velocity and temperature pro-files, as well as the skin friction coefficient and Nusselt number, are discussed through graphs and tables for various flow parameters. The current simulations are suitable for the thermal flow processing of magnetic nanomaterials in the chemical engineering and metallurgy industries. From the results, it is noticed that the results of copper nanofluid have a better impact than those of aluminium nanofluid.

Study of an unsteady magnetohydrodynamic‐free convective flow under parabolic ramped temperature and concentration in the presence of Soret and heat sink

AbstractThe purpose of this paper is to investigate the effects of Soret, thermal radiation, and chemical reaction on an unsteady magnetohydrodynamic free convective flow past an impulsively initiated semi‐infinite vertical plate with heat sink under parabolic ramped temperature and parabolic ramped concentration. Using some nondimensional parameters, the flow boundary equations in this case are first converted to dimensionless equations. The closed‐form Laplace transform technique is employed here to solve the partial differential equations and get the solutions for fluid velocity, temperature, and concentration. The velocity, temperature, and concentration of the fluid tend to vary with the effect of various flow factors. These changes are graphically represented and analyzed. Differences in skin friction, Nusselt number, and Sherwood number for the different relevant parameters are also recorded. The Soret number hikes the fluid velocity and concentration. The rate of heat transfer, mass transfer, and momentum transfer improves due to the application of parabolic ramped conditions.

Heat and mass transfer on unsteady MHD Casson fluid flow past an infinite vertical porous plate with chemical reaction

The most excellent applications on the practice and status of research in environmental science and technology, both natural and human made, with respect to the concepts of chemical reaction are heat absorption and Newtonian heating. For this purpose, in this paper, the numerical investigation of Newtonian heating effect on unsteady magnetohydrodynamic free convective flow of radiating and chemically reacting Casson fluid past an infinite oscillating vertical porous plate embedded in a porous medium is conducted by considering the effects of heat sink and viscous dissipation. The fluid motion is persuaded due to the periodic oscillations of the plate along its length. This phenomenon is represented as non-linear partial differential equations with initial and boundary conditions. By introducing suitable non-dimensional variable and parameters, the leading equation with initial and boundary conditions are converted into dimensionless form, which are then solved numerically using a finite difference method. The effects of several relevant parameters on the velocity, temperature and concentration are displayed graphically whilst the effects of these parameters on the skin friction, Nusselt and Sherwood numbers are exhibited in tabular format and then discussed in detail.

MHD oscillatory flow of hybrid nanofluid along a vertical plate with ramped wall temperature, heat source, and thermal radiation: An exact solution

AbstractThe study looks at the characteristics of an unsteady magnetohydrodynamic (MHD) free convective hybrid nanofluid flow with heat transfer to an oscillating vertical plate. The impacts of thermal radiation and internal heat generation, as well as ramped wall temperature conditions at the boundary, are included in the study. The base fluid water is combined with alumina and copper nanoparticles to model fluid flow. A flow issue like this can occur in a variety of industrial and technical processes, such as aerodynamic heating, polymer manufacturing, and so on. The built dimensional controlling equations are transformed into the nondimensional form of equations using feasible similarity variables. The Laplace transform technique is used to solve the nondimensional equations analytically. Pictorial representations are used to investigate the sway of physical characteristics on velocity and temperature distributions. For all of the implanted parameters, the values of the local skin‐friction coefficient and local rate of heat transfer are determined at the boundary and displayed in tables. The velocity profile increases as the thermal Grashof number and time increase, but the magnetic parameter has the opposite effect on the ramping surface temperature and the isothermal plate. Similarly, the temperature profile of nanofluids has been discovered to have a direct relationship with characteristics such as thermal radiation, time, and internal heat generation.

Unsteady MHD free convection flow of an exothermic fluid in a convectively heated vertical channel filled with porous medium

Utilizing porous media in a new mathematical model to improve convective heat transfer characteristics in a variety of applications, such as radiation nuclear disposal storing, evaporation cooling, sieving, geological extraction, crude petroleum refining, and building heating and cooling, is becoming increasingly important. This study proposed a numerical analysis of the unsteady magnetohydrodynamic free convection flow of an exothermic fluid with Newtonian heating. This discovery reveals two types of solutions: steady state and unsteady state. After transforming the governing equation from dimensional form to dimensionless form, the steady state governing equation was solved by the Homotopy Perturbation Method. However, the implicit finite difference approach is used to solve the time-dependent governing equations numerically. The impact of various emerging parameters, namely the Hartmann number, Boit number, Darcy number, Navier slip parameter, and the Frank-Kamenetskii parameter, was discussed and graphically analyzed. During the computations and analysis, it was discovered that a minor rise in the Hartman number results in the Lorentz force, which streamlines the momentum barrier layer and hence slows the fluid flow. The fluid velocity, on the other hand, rose as the porous medium, thermal Biot number, slip parameter, and temperature field increased as the viscous reactive fluid parameter and Newtonian heating increased. The skin friction and Nusselt number were also examined and reported. By comparing the finding to an existing work, a great agreement was revealed.

Effects of Dufour and thermal diffusion on unsteady MHD free convection and mass transfer flow through an infinite vertical permeable sheet

In this paper, the effects of Dufour and thermal diffusion and on unsteady MHD (magnetohydrodynamic) free convection and mass transfer flow through an infinite vertical permeable sheet have been investigated numerically. The non-dimensional governing equations are solved numerically by using the superposition method with the help of “Tec plot” software. The numerical solution regarding the non-dimensional velocity, temperature, and concentration variables against the non-dimensional coordinate variable has been carried out for various values of pertinent numbers and parameters like the suction parameter left( {v_{0} } right), Prandtl number left( {P_{r} } right), magnetic parameter left( M right), Dufour number left( {D_{f} } right), Soret number left( {S_{0} } right), Schmidt number left( {S_{c} } right), and for constant values of modified local Grashof number left( {G_{{text{m}}} } right) and local Grashof number left( {G_{r} } right).The velocity field decreases for increasing the suction parameter which is focusing on the common fact that the usual suction parameter stabilizing the effect on the boundary layer growth. The thermal boundary layer thickness becomes thinner for rising values of the Dufour and Soret numbers. The skin friction enhances for uplifting values of Soret number and Dufour number but reduces for moving suction parameter, Magnetic force number, Prandtl number, and Schmidt number. The heat transfer rate increases for increasing the suction parameter, Dufour number, Prandtl number, and Soret number. The mass transfer rate increases for enhancing the values of suction parameter, Magnetic force number, Soret number, and Prandtl number but decreases for Dufour number and Schmidt number.

A Study of Two Dimensional Unsteady MHD Free Convection Flow over a Vertical Plate in the Presence of Radiation

This paper compacts with an exact analysis of radiative effects on the magnetohydrodynamic (MHD) free convection flow of an electrically conducting incompressible viscous fluid over a vertical plate. The non-dimensional continuity, momentum, and energy equations are solved using appropriate transformation. The dimensionless momentum and energy equations are solved numerically through an explicit finite difference method. The stability and convergence analysis also discussed. Finally, outcomes of the parameters on velocity and temperature profiles are displayed graphically and qualitatively.

An exact analysis of unsteady MHD free convection flow of some nanofluids with ramped wall velocity and ramped wall temperature accounting heat radiation and injection/consumption

This article investigates the influence of ramped wall velocity and ramped wall temperature on time dependent, magnetohydrodynamic (MHD) natural convection flow of some nanofluids close to an infinitely long vertical plate nested in porous medium. Combination of water as base fluid and three types of nanoparticles named as copper, titanium dioxide and aluminum oxide is taken into account. Impacts of non linear thermal radiation flux and heat injection/consumption are also evaluated. The solutions of principal equations of mass and heat transfer are computed in close form by applying Laplace transform. The physical features of connected parameters are discussed and elucidated with the assistance of graphs. The expressions for Nusselt number and skin friction are also calculated and control of pertinent parameters on both phenomenons is presented in tables. A comparative study is performed for ramped wall and isothermal wall to evaluate the application extent of both boundary conditions.

Influence of relative motion of magnetic field on time‐dependent MHD natural convection flow

AbstractThe effects of relative motion of magnetic field on unsteady magnetohydrodynamic free convection flow with ramped motion and temperature‐dependent heat source/sink have been analyzed. The motion of the inner cylinder is ramped while the motion of the outer cylinder is fixed. The momentum and energy equations are solved using the well‐known Laplace transform. The time‐domain solution is obtained using the Riemann‐sum approximation method. The influence of the governing parameters on fluid velocity, fluid temperature, volume flow rate, and rate of heat transfer are discussed with the help of line graphs. It is found that Hartmann number has a retarding effect on fluid velocity, skin friction at the outer surface of the inner cylinder, and mass flow rate when the magnetic field is fixed with the fluid and when the velocity of the magnetic field is less than the velocity of the moving cylinder. Whereas, the reverse effect is noticed when the magnetic field is fixed with the moving cylinder.

MHD effect on unsteady flow of tangent hyperbolic nano-fluid past a moving cylinder with chemical reaction

This study presents the exploration of unsteady magnetohydrodynamic (MHD) free convection flow of tangent hyperbolic nano-fluid flow on a moving cylinder with Brownian motion and thermophoresis effects. The current flow analysis yields nonlinear partial differential equations. The governing equations such as continuity, momentum, temperature and concentration are converted into dimensionless form and then solved numerically by adopting explicit finite difference method where Compaq Visual FORTRAN 6.6.a was also used for simulating the fluid flow system. The numerical outcomes are showed graphically to understand the result clearly. For the accurateness of the numerical technique a stability and convergence analysis was carried out. The aim was to illustrate the physical impacts of chemical reaction parameter, thermal radiation and viscous dissipation on various fluid fields along with the advanced visualization through streamlines. By comparing with the previous studies it was found that this fluid influenced the mass and heat properties more significantly rather than the other fluid. Additionally, this model predicts the shear thinning attitude significantly and describes the blood flow accurately. It has also applications in biological sciences, bio-engineering maneuver, and petroleum industries. Eventually the obtained outcomes were validated with previously published articles.

Unsteady MHD free convective flow past a permeable vertical plate with periodic movement and slippage in the presence of Hall current and rotation

The present investigation aims to analyze unsteady magnetohydrodynamic free convective flow of an electrically conducting and incompressible fluid past a permeable and periodically moving infinite flat plate with slippage at the surface in the presence of Hall current, rotation, thermal radiation and internal heat generation/absorption. The model equations are converted into non-dimensional form using suitable dimensionless variables and parameters. Exact analytical solutions, in closed form, for the velocity and temperature fields have been obtained upon solving these non-dimensional equations with the help of Laplace transform technique. The impact of various physical parameters on the velocity and temperature fields are illustrated and depicted in graphical form. Moreover, numerical values of coefficient of skin friction measuring the shear stress at the surface and Nusselt number measuring the rate of heat transfer at the surface are analyzed and shown in the form of tables.

Unsteady Magnetohydrodynamic Free Convection Flow of Nanofluid Through an Exponentially Accelerated Inclined Plate Embedded in a Porous Medium with Variable Thermal Conductivity in the Presence of Radiation

Unsteady Magnetohydrodynamic Free Convection Flow of Nanofluid Through an Exponentially Accelerated Inclined Plate Embedded in a Porous Medium with Variable Thermal Conductivity in the Presence of Radiation

Buoyancy Effects on MHD Unsteady Convection of a Radiating Chemically Reacting Fluid Past a Moving Porous Vertical Plate in a Binary Mixture

In this paper, the problem of unsteady magnetohydrodynamic free convective flow with thermal radiation and chemical reaction past a porous vertical plate moving through a binary mixture in an optically thin environment is investigated. The viscosity of the fluid is assumed to vary linearly with temperature. Due to the nature of corresponding dimensionless variable for temperature and its boundary condition as in the case of binary mixture, Boussinesq approximation and temperature dependent viscosity model were modified. The governing boundary layer equations are transformed using suitable similarity transformation and solved numerically. A parametric study of selected parameters is conducted and results for velocity, temperature, concentration, local skin friction coefficient, local Nusselt number and local Sherwood number are illustrated and physical aspects of the problem are discussed. Increasing the temperature dependent variable fluid viscosity leads to increase in the velocity of the fluid and heat transfer rate at the surface when Grashof related parameters are greater than one-tenth.

Hall effects on unsteady MHD oscillatory free convective flow of second grade fluid through porous medium between two vertical plates

The effects of radiation and Hall current on an unsteady magnetohydrodynamic free convective flow in a vertical channel filled with a porous medium have been studied. We consider an incompressible viscous and electrically conducting incompressible viscous second grade fluid bounded by a loosely packed porous medium. The fluid is driven by an oscillating pressure gradient parallel to the channel plates, and the entire flow field is subjected to a uniform inclined magnetic field of strength Ho inclined at an angle of inclination α with the normal to the boundaries in the transverse xy-plane. The temperature of one of the plates varies periodically, and the temperature difference of the plates is high enough to induce the radiative heat transfer. The effects of various parameters on the velocity profiles, the skin friction, temperature field, rate of heat transfer in terms of their amplitude, and phase angles are shown graphically.

Heat and Mass Transfer of Unsteady Hydromagnetic Free Convection Flow Through Porous Medium Past a Vertical Plate with Uniform Surface Heat Flux

AbstractSimultaneous effects of thermal and concentration diffusions in unsteady magnetohydrodynamic free convection flow past a moving plate maintained at constant heat flux and embedded in a viscous fluid saturated porous medium is presented. The transport model employed includes the effects of thermal radiation, heat sink, Soret and chemical reaction. The fluid is considered as a gray absorbing-emitting but non-scattering medium and the Rosseland approximation in the energy equations is used to describe the radiative heat flux for optically thick fluid. The dimensionless coupled linear partial differential equations are solved by using Laplace transform technique. Numerical results for the velocity, temperature, concentration as well as the skin friction coefficient and the rates of heat and mass transfer are shown graphically for different values of physical parameters involved.

Unsteady MHD free convection flow of rotating Jeffrey fluid embedded in a porous medium with ramped wall temperature

The effect of radiative heat transfer on unsteady magnetohydrodynamic (MHD) free convection flow of rotating Jeffrey fluid past an infinite vertical plate saturated in a porous medium with ramped wall temperature is investigated. The incompressible fluid is taken electrically conducting under influence of transverse magnetic field which perpendicular to the flow. An appropriate dimensionless variables are employed to the governing equations and solved analytically by Laplace transform technique. The results of several controlling parameters for both ramped wall temperature and an isothermal plate are presented graphically with comprehensive discussions. It has been observed that, an increase in rotation parameter, reduced the primary velocity, but an opposite behaviour is noticed for the secondary velocity. Moreover, large values of Hartmann number tends to retard the fluid flow due to the Lorentz force.

Porosity effect on unsteady MHD free convection flow of Jeffrey fluid past an oscillating vertical plate with ramped wall temperature

The unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid embedded in porous medium past an oscillating vertical plate generated by thermal radiation with ramped wall temperature is investigated. The incompressible fluid is taken electrically conducting under the action of transverse magnetic field towards the flow. Constitutive relation of Jeffrey fluid is employed to model the governing equations in terms of partial differential equations with some physical conditions. The transformed dimensionless governing equations are solved analytically using Laplace transform technique. The impact of various pertinent parameters namely material parameter of Jeffrey fluid , dimensionless parameter of Jeffrey fluid , phase angle , Hartmann number , permeability parameter , Grashof number , Prandtl number , radiation parameter and dimensionless time on velocity and temperature distributions are presented graphically and discussed in details. It is observed that, the permeability parameter tend to retard the fluid velocity for ramped wall temperature but enhance the velocity for an isothermal plate. Besides that, this study shows, the amplitude of velocity and temperature fields for ramped wall temperature are always lower than isothermal plate. A comparison with the existing published work is also provided to confirm the validity of the present results and an excellent agreement are found.

Exact and numerical solutions for unsteady heat and mass transfer problem of Jeffrey fluid with MHD and Newtonian heating effects

The combined heat and mass transfer of unsteady magnetohydrodynamic free convection flow of Jeffrey fluid past an oscillating vertical plate generated by thermal radiation and Newtonian heating is investigated. The incompressible fluid is electrically conducting in the presence of a uniform magnetic field which acts in a direction perpendicular to the flow. Mathematical formulation of the problem is modeled in terms of partial differential equations with some physical conditions. Some suitable non-dimensional variables are introduced to transform the system of equations. The dimensionless governing equations are solved analytically for exact solutions using the Laplace transform technique. Numerical solutions of velocity are obtained via finite difference scheme. Graphical results for velocity, temperature and concentration fields for various pertinent parameters such as material parameter of Jeffrey fluid \(\lambda_{1}\), dimensionless parameter of Jeffrey fluid \(\lambda\), Newtonian heating parameter \(\xi\), phase angle \(\omega t\), Grashof number \(Gr\), modified Grashof number \(Gm\), Hartmann number or magnetic parameter \(Ha\), Prandtl number \(Pr\), radiation parameter \(Rd\), Schimdt number \(Sc\) and dimensionless time \(t\) are displayed and discussed in detail. This study showed that the magnetic field resists the fluid flow due to the Lorentz force, whereas the thermal radiation and Newtonian heating parameters lead to the enhancement of velocity and temperature fields. Present results are also compared with the existing published work, and an excellent agreement is found.

Magnetohydrodynamic Conjugate Flow of Casson Fluid Over a Vertical Plate Embedded in a Porous Medium with Arbitrary Wall Shear Stress

The influence of thermal radiation on unsteady magnetohydrodynamic (MHD) free convection flow of Casson fluid over a vertical plate embedded in porous medium with arbitrary wall shear stress has studied. Casson fluid is a non-Newtonian fluid. The partial differential equations that govern the flow, heat and mass transfer are transformed to non-dimensional by using suitable non-dimensional variables, which are then solved analytically by using the Laplace transform technique. Analytical expressions for velocity, temperature and concentration fields are determined. Additionally, the exact expressions of the Nusselt number and Sherwood number are also obtained. Numerical results of velocity, temperature and concentration profiles with various values of embedded flow parameters are graphically shown and the influences to the characteristic of the fluid flow are discussed in detail. The variations in Nusselt number and Sherwood number are displayed in tabular form.

Free Convection Heat and Mass Transfer Flow for Magnetohydrodynamic Chemically Reacting and Radiating Elastico-Viscous Fluid Past a Vertical Permeable Plate with Gravity Modulation

An analysis of a two-dimensional unsteady magnetohydrodynamic free convective heat and mass transfer flow of an electrically conducting, optically thin, incompressible, and radiating elastico-viscous fluid (characterised by Walters’ liquid $${B}'$$ ) past a vertical permeable infinite plate embedded in a uniform porous medium with gravity modulation is considered. It is assumed that there exists a homogeneous first-order chemical reaction. Analytical solutions for velocity, temperature and concentration field have been derived. The effects of gravity modulation, radiation, and chemical reaction on velocity profile and shear stress for both Newtonian and elastico-viscous fluid have been studied and presented graphically. It was observed that velocity distribution increases with an increase in gravity modulation parameter and radiation parameter for both Newtonian and elastico-viscous fluid, where as it shows reverse effects in the case of magnetic field parameter and viscoelastic parameter. It is seen that viscous drag on the plate is reduced under the effect of chemical reaction parameter, where as it shows reverse effect in the case of gravity modulation parameter and radiation parameter.