Unsteady Hydromagnetic Flow Research Articles

Unsteady Hydromagnetic Flow of a Heat Absorbing Dusty Fluid Past a Permeable Vertical Plate with Ramped Temperature

The unsteady flow and heat transfer of a viscous incompressible, electrically conducting dusty fluid past vertical plate under the influence of a transverse magnetic field is studied with a view to examine the combined effects of suction, heat absorption and ramped wall temperature. The temperature of the wall is assumed to have a temporarily ramped profile which goes on increasing up to a certain time limit and then becomes constant. To investigate the effect of rampedness in wall temperature, the solution for the flow past an isothermal wall is also obtained. The governing partial differential equations are solved using Laplace transformation technique in which the inversion is obtained numerically using Matlab. To validate the results of numerical inversion a comparison between the numerical and analytical values of fluid and particle temperatures and Nusselt number is also presented. The effects of pertinent flow parameters affecting the flow and heat transfer are investigated with the help of graphs and tables. It is found that the increase in suction, heat absorption and particle concentration contribute in thinning the thermal and momentum boundary layers and the velocity and temperature for both the fluid and particle phases are higher in the case of a flow past an isothermal plate than that of a flow past a plate with ramped temperature.

Unsteady hydromagnetic slip flow and heat transfer of nanofluid over a moving surface with prescribed heat and mass fluxes

An unsteady two-dimensional laminar boundary layer flow of viscous, incompressible nanofluid over a vertical stretching surface with hydromagnetic field has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of partial slip on the velocity field. Two types of general heating processes namely, the prescribed surface temperature and concentration and the prescribed wall heat and nanoparticle flux are imposed on the stretching surface. By applying similarity analysis, the governing partial differential equations are transformed into a set of time-dependent nonlinear coupled ordinary differential equations and they are solved by Runge–Kutta–Fehlberg method along with shooting technique. The effects of governing parameters on the dimensionless velocity, temperature and concentration distributions are discussed. Moreover, the numerical results obtained in this study is compared with the existing literature and found that they are in good agreement.

Hydromagnetic natural convection flow with heat and mass transfer of a chemically reacting and heat absorbing fluid past an accelerated moving vertical plate with ramped temperature and ramped surface concentration through a porous medium

Abstract Unsteady hydromagnetic natural convection flow with heat and mass transfer of an electrically conducting, viscous, incompressible, chemically reacting and heat absorbing fluid past an accelerated moving vertical plate with ramped temperature and ramped surface concentration through a porous medium in the presence of thermal and mass diffusions is studied. The exact solutions of momentum, energy and concentration equations, under the Boussinesq approximation, are obtained in closed form by Laplace Transform technique. The expressions for skin friction, Nusselt number and Sherwood number are also derived. The variations in fluid velocity, fluid temperature and species concentration are displayed graphically whereas numerical values of skin friction, Nusselt number and Sherwood number are presented in tabular form for various values of pertinent flow parameters. Natural convection flow near a ramped temperature plate with ramped surface concentration is also compared with the flow near an isothermal plate with uniform surface concentration.

Effect of Hall Current on Hydromagnetic Boundary Layer in Rotating Dusty Fluid with Exponential Pressure Gradient

An asymptotic analysis of an unsteady hydromagnetic boundary layer flow of an incompressible viscous conducting fluid with uniform distribution of dust particle bounded by semi-infinite plate in the presence of exponential decaying pressure gradient is investigated. The exact solutions of the boundary layer equations are obtained by asymptotic behaviour of Laplace transform treatment. The structure of velocity distribution is investigated and the effect of various physical parameters likes magnetic parameter, Ekman parameter and Hall current parameter on velocities of both fluid and dust phase are depicted graphically.

Unsteady Hydromagnetic Flow of Radiating Fluid Past a Convectively Heated Vertical Plate with the Navier Slip

This paper investigates the unsteady hydromagnetic-free convection of an incompressible electrical conducting Boussinesq’s radiating fluid past a moving vertical plate in an optically thin environment with the Navier slip, viscous dissipation, and Ohmic and Newtonian heating. The nonlinear partial differential equations governing the transient problem are obtained and tackled numerically using a semidiscretization finite difference method coupled with Runge-Kutta Fehlberg integration technique. Numerical data for the local skin friction coefficient and the Nusselt number have been tabulated for various values of parametric conditions. Graphical results for the fluid velocity, temperature, skin friction, and the Nusselt number are presented and discussed. The results indicate that the skin friction coefficient decreases while the heat transfer rate at the plate surface increases as the slip parameter and Newtonian heating increase.

Unsteady hydromagnetic couette flow due to ramped motion of one of the porous plates

An unsteady flow formation in Couette motion of an electrically conducting fluid subject to transverse magnetic field has been analyzed in the presence of suction/injection through the porous plates when one of the porous plates is in ramped motion. It is assumed that the porous plates are uniformly permeable and the fluid is entering the flow region through one of the porous plates at same rate as it is leaving through the other porous plate. The resulting boundary value problem has been solved exactly under the assumption of a negligible induced magnetic field, external electric field and pressure gradient. Unified closed form expressions for the velocity field and skin-friction corresponding to the case of a magnetic field fixed relative to the fluid or to the moving porous plate have been presented. In order to highlight the impact of the ramp motion of the porous plate on the fluid flow, it has also been compared with Couette flow between porous plates when one of the porous plates has been set into an impulsive motion.

Effects of Radiation and Magnetic Field on Unsteady Boundary Layer Flow of a Nanofluid Past an Exponentially Stretching Sheet in the Presence of Heat Source/Sink

An analysis has been carried out to investigate an unsteady two-dimensional hydromagnetic nanofluid flow past an exponentially stretching sheet in the presence of thermal radiation and heat generation/absorption. The governing time-dependent partial differential equations are transformed into ordinary differential equations, using an appropriate similarity transformation. The resulting ordinary differential equations are solved numerically using the shooting method. The effects of the governing parameters on the flow and heat transfer characteristics are analyzed and presented graphically. Different types of nanoparticles, namely, Cu, Ag, CuO, Al2O3 and TiO2 with water as the base fluid, are studied. It is found that the flow field and temperature are significantly influenced by the volume fraction of nanoparticles, radiation, heat generation, heat absorption and the magnetic effects. Comparisons with previously published works are performed in some special cases, and found to be in good agreement.

Effects of Hall current, radiation and rotation on natural convection heat and mass transfer flow past a moving vertical plate

An investigation of the effects of Hall current and rotation on unsteady hydromagnetic natural convection flow with heat and mass transfer of an electrically conducting, viscous, incompressible and optically thick radiating fluid past an impulsively moving vertical plate embedded in a fluid saturated porous medium, when temperature of the plate has a temporarily ramped profile, is carried out. Exact solution of the governing equations is obtained in closed form by Laplace transform technique. Exact solution is also obtained in case of unit Schmidt number. Expressions for skin friction due to primary and secondary flows and Nusselt number are derived for both ramped temperature and isothermal plates. Expression for Sherwood number is also derived. The numerical values of primary and secondary fluid velocities, fluid temperature and species concentration are displayed graphically whereas those of skin friction are presented in tabular form for various values of pertinent flow parameters.

Explicit numerical study of unsteady hydromagnetic mixed convective nanofluid flow from an exponentially stretching sheet in porous media

A numerical investigation of unsteady magnetohydrodynamic mixed convective boundary layer flow of a nanofluid over an exponentially stretching sheet in porous media, is presented. The transformed, non-similar conservations equations are solved using a robust, explicit, finite difference method (EFDM). A detailed stability and convergence analysis is also conducted. The regime is shown to be controlled by a number of emerging thermophysical parameters i.e. combined porous and hydromagnetic parameter (R), thermal Grashof number (G r ), species Grashof number (G m ), viscosity ratio parameter (Λ), dimensionless porous media inertial parameter (∇), Eckert number (E c ), Lewis number (L e ), Brownian motion parameter (Nb) and thermophoresis parameter (Nt). The flow is found to be accelerated with increasing thermal and species Grashof numbers and also increasing Brownian motion and thermophoresis effects. However, flow is decelerated with increasing viscosity ratio and combined porous and hydromagnetic parameters. Temperatures are enhanced with increasing Brownian motion and thermophoresis as are concentration values. With progression in time the flow is accelerated and temperatures and concentrations are increased. EFDM solutions are validated with an optimized variational iteration method. The present study finds applications in magnetic nanomaterials processing.

Unsteady Hydromagnetic Natural Convection Flow of a Dusty Fluid Past an Impulsively Moving Vertical Plate With Ramped Temperature in the Presence of Thermal Radiation

Unsteady hydromagnetic natural convection boundary layer flow of a viscous, incompressible, and electrically conducting dusty fluid past an impulsively moving vertical plate with ramped temperature in the presence of thermal radiation and transverse magnetic field is studied. Exact solutions of the governing equations for fluid and particle velocities and fluid and particle temperatures are obtained in closed form by Laplace transform technique. To compare the results obtained in this case with that of an isothermal plate, exact solutions of the governing equations are also obtained for an isothermal plate. The expressions for the skin friction and Nusselt number are also derived for both ramped temperature and isothermal plates. Numerical values of fluid and particle velocities and fluid and particle temperatures are displayed graphically for various values of pertinent flow parameters for both ramped temperature and isothermal plates, whereas numerical values of skin friction and Nusselt number for both ramped temperature and isothermal plates are presented in tabular form for pertinent flow parameters.

Similarity solutions and conservation laws for rotating flows of an Oldroyd-B fluid

In this paper, similarity reduction arising from classical Lie point symmetries of unsteady hydromagnetic flows of a rotating Oldroyd-B fluid under influence of Hall currents is carried out. By employing different combinations of translation and rotational symmetries, a class of new exact solutions under certain initial and boundary conditions has been obtained. A detailed comparative study of these solutions for different cases in perspective of previous literature is also presented. Solutions in existing literature have turned out to be special cases of similarity solutions obtained here. Finally, some nontrivial conservation laws of underlying system of the model are computed.

Unsteady Flow and Heat Transfer of a MHD Micropolar Fluid Over a Porous Stretching Sheet in the Presence of Thermal Radiation

AbstractA non-linear analysis has been made to study the unsteady hydromagnetic boundary layer flow and heat transfer of a micropolar fluid over a stretching sheet embedded in a porous medium. The effects of thermal radiation in the boundary layer flow over a stretching sheet have also been investigated. The system of governing partial differential equations in the boundary layer have reduced to a system of non-linear ordinary differential equations using a suitable similarity transformation. The resulting non-linear coupled ordinary differential equations are solved numerically by using an implicit finite difference scheme. The numerical results concern with the axial velocity, micro-rotation component and temperature profiles as well as local skin-friction coefficient and the rate of heat transfer at the sheet. The study reveals that the unsteady parameter S has an increasing effect on the flow and heat transfer characteristics.

Hydromagnetic flows of a mixture of two Newtonian fluids between two parallel plates

The paper aims to study the flow of a binary mixture of electrically conducting, incompressible and viscous fluids between two parallel plates in the presence of a transverse uniform magnetic field. The solution of such a flow model has many applications in magnetohydrodynamic (MHD) power generators, MHD pumps, MHD accelerators, and MHD flowmeters. Exact solutions have been obtained for the following four problems: (1) steady hydromagnetic Couette flow, (2) unsteady hydromagnetic Couette flow, (3) steady hydromagnetic Poiseuille flow, (4) unsteady hydromagnetic Poiseuille flow. The mean velocity of the mixture is drawn for different values of magnetic parameters and results are interpreted with the aid of graphs. The previous solutions involving single Newtonian fluid appear as the special cases of the present analysis.

Numerical Solution of Unsteady Hydromagnetic Natural Convection Flow of Heat Absorbing Fluid past an Impulsively Moving Vertical Plate with Ramped Temperature

A numerical investigation of unsteady hydromagnetic natural convection flow of a viscous, incompressible, electrically conducting and heat absorbing fluid past an impulsively moving vertical plate with ramped temperature embedded a porous medium in the presence of thermal diffusion is carried out. The governing equations are solved numerically by Crank-Nicolson implicit finite difference scheme. The numerical solution for fluid velocity and fluid temperature are depicted graphically whereas the numerical values of skin friction and Nusselt number are presented in tabular form for various values of pertinent flow parameters. Natural convection flow near a ramped temperature plate is also compared with the flow near an isothermal plate.

Effects of Hall Current and Ion-Slip on MHD Flow Induced by Torsional Oscillations of a Disc in a Rotating Fluid

AbstractThe unsteady hydromagnetic flow due to torsional oscillations of a rotating disc in a viscous incompressible electrically conducting fluid which is also rotating is studied taking the effects of the Hall current and ion-slip into consideration. The governing equations are solved analytically. The results show that the inclusion of the Hall current and ion slip have important effects on the velocity distributions as well as shear stresses at the disc. The flow is characterized by two opposite circularly polarized waves, travelling with different velocities. It is found that there is a formation of two-deck boundary layers, thicknesses of which increase with increase in either Hall parameter or ion-slip parameter. The radial velocity increases with an increase in Hall parameter and the azimuthal velocity increases with an increase in either Hall parameter or ion-slip parameter. Further, it is found that the amplitude of the transverse shear stress at the disc decreases with an increase in either Hall parameter or ion-slip parameter.

Unsteady Hydromagnetic Rotating Flow through an Oscillating Porous Plate Embedded in a Porous Medium

This paper investigates unsteady hydromagnetic flow of a viscous fluid in a rotating frame. The fluid is bounded by an oscillating porous plate embedded in a porous medium. The Laplace transform and Fourier sine transform methods are employed to find the exact solutions. They satisfy all imposed initial and boundary conditions and as special cases are reduced to some published results from the literature. The graphical results are plotted for different values of pertinent parameters and some interesting conclusions are made.

Unsteady Hydromagnetic Flow Due to Concentric Rotation of Eccentric Disks

AbstractThe unsteady hydromagnetic flow of a viscous incompressible electrically conducting fluid between two parallel disks rotating with the same angular velocity initially about non-coincident axes, which are suddenly made coincident, has been studied. An analytical solution describing the flow at large and small times after the start is obtained by the use of Laplace transform technique. The physical interpretations for the emerging parameters are discussed with the help of graphs. The shear stresses obtained from the general solution and from the solution for small time are compared.

EFFECTS OF HALL CURRENT AND ROTATION ON UNSTEADY HYDROMAGNETIC COUETTE FLOW WITHIN A POROUS CHANNEL

Unsteady hydromagnetic Couette flow of a viscous, incompressible and electrically conducting fluid between two parallel porous plates taking Hall current into account in a rotating system is studied. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel and is permeated by a uniform transverse magnetic field which is fixed relative to the moving plate. Solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving plate due to primary and secondary flows is also derived. Asymptotic behavior of the solution valid for small and large values of time t is analyzed to gain some physical insight into the flow pattern. Numerical values of primary and secondary velocities and that of shear stress at the moving plate due to primary and secondary flows are displayed graphically for various values of Hall current parameter m, rotation parameter K2, magnetic parameter M2, suction/injection parameter S and time t.

Effects of Hall Current and Rotation on Unsteady MHD Couette Flow in the Presence of an Inclined Magnetic Field

Unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid in a rotating system in the presence of an inclined magnetic field taking Hall current into account is studied. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel. Exact solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving plate is also derived. Asymptotic behavior of the solution is analyzed for small and large values of time t to highlight (i) the transient approach to the final steady state flow and (ii) the effects of Hall current, magnetic field, rotation and angle of inclination of magnetic field on the flow-field. It is found that Hall current and rotation tend to accelerate fluid velocity in both the primary and secondary flow directions. Magnetic field has retarding influence on the fluid velocity in both the primary and secondary flow directions. Angle of inclination of magnetic field has accelerating influence on the fluid velocity in both the primary and secondary flow directions.

Computational modelling of MHD unsteady flow and heat transfer toward a flat plate with Navier slip and Newtonian heating

The combined effects of Navier slip and Newtonian heating on an unsteady hydromagnetic boundary layer stagnation point flow towards a flat plate in the presence of a magnetic field are studied. The self-similar equations are obtained using similarity transformations and solved numerically by a shooting algorithm with a Runge-Kutta Fehlberg integration scheme. The velocity profiles, temperature profiles, the local skin friction coefficient, and the local Nusselt number are computed and discussed in details for various values of the different parameters. Numerical results are presented both in tabular and graphical forms, illustrating the effects of these parameters on the thermal and concentration boundary layers. It is revealed that the thermal boundary layer thickens with a rise in the flow unsteadiness and as Newtonian heating intensifies, while the local skin friction and the rate of heat transfer at the plate surface change significantly due to the slip parameter.