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

Effects of Thermal Radiation and Rotation on Unsteady Hydromagnetic Free Convection Flow past an Impulsively Moving Vertical Plate with Ramped Temperature in a Porous Medium

The effects of radiation and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving infinite vertical plate with ramped temperature in a porous medium are investigated. Exact solution of momentum and energy equations, under Boussinesq approximation, is obtained in closed form by Laplace transform technique. To compare the results obtained in this case with that of isothermal plate, exact solution of the governing equations is also obtained for isothermal plate. The expressions for the primary and secondary skin frictions and Nusselt number are also derived. It is noticed that, for both ramped temperature and isothermal plates, rotation retards fluid flow in the primary flow direction whereas it accelerates fluid flow in the secondary flow direction in the boundary layer region while radiation exerts accelerating influence on the fluid flow in both the primary and secondary flow directions. For ramped temperature plate radiation reduces primary skin friction whereas it tends to increase secondary skin friction. For isothermal plate radiation has tendency to reduce secondary skin friction. Radiation tends to increase fluid temperature for both ramped temperature and isothermal plates. With the increase in time the rate of heat transfer at the plate is reduced for isothermal plate while it is increased for ramped temperature plate

Effects of Rotation and Magnetic Field on Unsteady Couette Flow in a Porous Channel

Unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid in a rotating system in the presence of a uniform transverse magnetic field is studied. The plates of the channel are considered porous and fluid flow within the channel is induced due to the impulsive movement of the upper plate of the channel. General solution of the governing equations is obtained which is valid for every value of time t. For small values of time t, the solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the stationary plate due to the primary and secondary flows is obtained in both the cases. It is found that the solution obtained by Laplace transform technique converges more rapidly than the general solution when time t is very small. Magnetic field retards the fluid flow in both the primary and secondary flow directions. Rotation retards primary flow whereas it accelerates secondary flow. There exists incipient flow reversal near the stationary plate on increasing rotation parameter K2. Suction accelerates primary flow whereas it retards secondary flow. Injection retards both the primary and secondary flows

Computational study of unsteady couple stress magnetic nanofluid flow from a stretching sheet with ohmic dissipation

To provide a deeper insight of the transport phenomena inherent to the manufacturing of magnetic nano-polymer materials, in the present work a mathematical model is developed for time-dependent hydromagnetic rheological nanopolymer boundary layer flow and heat transfer over a stretching sheet in the presence of a transverse static magnetic field. Joule heating (Ohmic dissipation) and viscous heating effects are included since these phenomena arise frequently in magnetic materials processing. Stokes’ couple stress model is deployed to simulate non-Newtonian micro-structural characteristics. The Tiwari-Das nanoscale model is adopted which permits different nano-particles to be simulated (in this article both copper-water and aluminium oxide-water nanofluids are considered). Similarity transformations are utilized to convert the governing partial differential conservation equations into a system of coupled, nonlinear ordinary differential equations with appropriate wall and free stream boundary conditions. The shooting technique is used to solve the reduced nonlinear coupled ordinary differential boundary value problem via MATLAB symbolic software. Validation with published results from the literature is included for the special cases of non-dissipative and Newtonian nanofluid flows. Fluid velocity and temperature profiles for both Copper and Aluminium Oxide (Al2O3) nanofluids are observed to be enhanced with greater non-Newtonian couple stress parameter and magnetic parameter whereas the opposite trend is computed with greater values of unsteadiness parameter. The boundary layer flow is accelerated with increasing buoyancy parameter, elastic sheet stretching parameter and convection parameter. Temperatures are generally increased with greater couple stress rheological parameter and are consistently higher for the Aluminium oxide nanoparticle case. Temperatures are also boosted with magnetic parameter and exhibit an overshoot near the wall when magnetic parameter exceeds unity (magnetic force exceeds viscous force). A decrease in temperatures is induced with increasing sheet stretching parameter. Increasing Eckert number elevates temperatures considerably. With greater nanoparticle volume fraction both skin friction and Nusselt number are elevated and copper nano-particles achieve higher magnitudes than aluminium oxide

A numerical treatment of unsteady three-dimensional hydromagnetic flow of a Casson fluid with Hall and radiation effects

The study of the unsteady magnetohydrodynamic three-dimensional radiative flow of a viscous incompressible electrically conducting Casson liquid along a stretching surface including the effects of Hall current is presented in this article. The fluid flow model consists of time-dependent partial differential equations which are highly non-linear. Similarity transformations are utilized to obtain ordinary differential equations in similarity form. Further, a numerical approach, namely spectral quasilinearization method (SQLM), is used to solve resulting highly nonlinear ordinary differential equations. A detailed analysis is carried out to study the influences of significant parameters, such as Casson liquid parameter, Hall current parameter, magnetic parameter, unsteadiness parameter, radiative parameter, on the profiles’ of the velocity field and temperature field. The behavior of emerging quantities of engineering interest such as skin friction coefficient and the Nusselt number is also studied. Fluid flow model as presented in the paper finds applications in silicon suspensions, blood flow, polymer engineering, and printing industry. Keywords: Casson fluid, Hall effect, Radiation, Stretching surface, Spectral quasilinearization metho

Newtonian heating effect on unsteady hydromagnetic Casson fluid flow past a flat plate with heat and mass transfer

The influence of Newtonian heating on heat and mass transfer in unsteady hydromagnetic flow of a Casson fluid past a vertical plate in the presence of thermal radiation and chemical reaction is studied. The Casson fluid model is used to distinguish the non-Newtonian fluid behavior. The fluid flow is induced due to periodic oscillations of the plate along its length and a uniform transverse magnetic field is applied in a direction which is normal to the direction of fluid flow. The partial differential equations governing the flow, heat, and mass transfer are transformed to non-dimensional form using suitable non-dimensional variables which are then solved analytically by using Laplace transform technique. The numerical values of the fluid velocity, fluid temperature, and species concentration are depicted graphically whereas the values of skin-friction, Nusselt number, and Sherwood number are presented in tabular form. It is noticed that the fluid velocity and temperature decrease with increasing values of Casson parameter while concentration decreases with increasing values of chemical reaction parameter and Schmidt number. Such a fluid flow model has several industrial and medical applications such as in glass manufacturing, paper production, purification of crude oil and study of blood flow in the cardiovascular system

Unsteady Hydromagnetic Heat and Mass Transfer Flow of a Heat Radiating and Chemically Reactive Fluid Past a Flat Porous Plate with Ramped Wall Temperature

Unsteady hydromagnetic free convective flow of a viscous, incompressible, electrically conducting, and heat radiating fluid past a flat plate with ramped wall temperature and suction/blowing is studied. The governing equations are first subjected to Laplace transformation and then inverted numerically using INVLAP routine of Matlab. The numerical solutions of the fluid properties are presented graphically while the skin friction and heat and mass transfer coefficients are presented in tabular form. The results are verified by a careful comparison with results in the literature for certain parameter values

MHD Stagnation Point Flow of a Nanofluid with Velocity Slip, Non-linear Radiation and Newtonian Heating

AbstractThe flow of a viscous, incompressiable and electrically conducting nanofluid flow over a stretching sheet under the influence of a transverse magnetic field is investigated taking in to account the effect of non-linear thermal radiation, newtonian heating and partial velocity slip. The nanofluid model considered in the paper incorporates the effect of Brownian motion and thermophoresis. The governing equations, in similarity form, are solved using Matlab's in-built boundary value problem solver “bvp4c”. The nanofluid flow model discussed in the present paper has significant applications in fluid engineering devices where the boundary surface is subjected to convecting heating and the temperature difference between the ambient fluid and the surface is large

Regression analysis and features of negative activation energy for MHD nanofluid flow model: A comparative study

This article elucidates the impact of activation energy on magnetohydrodynamic (MHD) stagnation point nanofluid flow over a slippery surface in a porous regime with thermophoretic and Brownian diffusions. Negative activation energy is scarce in practice, but the impact of negative activation energy could not be neglected as it is noticed in chemical processes. The rate of some Arrhenius-compliant reactions is retarded by increasing the temperature and is therefore associated with negative activation energies, such as exothermic binding of urea or water. In some processes, the temperature dependence of the pressure-induced unfolding and the urea-induced unfolding of proteins at ambient pressure give negative activation energies. The present mathematical model is solved with successive linearization method (a spectral technique). A comparison of results is made for negative and positive values of activation energy. Apart from it, the quadratic multiple regression model is discussed briefly and explained with bar diagrams. It is observed that with rise in unsteadiness parameter from 0 to 1 (taking positive activation energy), skin friction and Sherwood number are increased by 9.36% and 19% respectively, and Nusselt number is decreased by 26%. However, for negative activation energy, 9.36% and 112% enhancement is observed in skin friction and Sherwood number, respectively