Unsteady Magnetohydrodynamic Boundary Layer Flow Research Articles

Delineating impacts of non-uniform wall temperature and concentration on time-dependent radiation-convection of Casson fluid under magnetic field and chemical reaction

Purpose In various kinds of materials processes, heat and mass transfer control in nuclear phenomena, constructing buildings, turbines and electronic circuits, etc., there are numerous problems that cannot be enlightened by uniform wall temperature. To explore such physical phenomena researchers incorporate non-uniform or ramped temperature conditions at the boundary, the purpose of this paper is to achieve the closed-form solution of a time-dependent magnetohydrodynamic (MHD) boundary layer flow with heat and mass transfer of an electrically conducting non-Newtonian Casson fluid toward an infinite vertical plate subject to the ramped temperature and concentration (RTC). The consequences of chemical reaction in the mass equation and thermal radiation in the energy equation are encompassed in this analysis. The flow regime manifests with pertinent physical impacts of the magnetic field, thermal radiation, chemical reaction and heat generation/absorption. A first-order chemical reaction that is proportional to the concentration itself directly is assumed. The Rosseland approximation is adopted to describe the radiative heat flux in the energy equation. Design/methodology/approach The problem is formulated in terms of partial differential equations with the appropriate physical initial and boundary conditions. To make the governing equations dimensionless, some suitable non-dimensional variables are introduced. The resulting non-dimensional equations are solved analytically by applying the Laplace transform method. The mathematical expressions for skin friction, Nusselt number and Sherwood number are calculated and expressed in closed form. Impacts of various associated physical parameters on the pertinent flow quantities, namely, velocity, temperature and concentration profiles, skin friction, Nusselt number and Sherwood number, are demonstrated and analyzed via graphs and tables. Findings Graphical analysis reveals that the boundary layer flow and heat and mass transfer attributes are significantly varied for the embedded physical parameters in the case of constant temperature and concentration (CTC) as compared to RTC. It is worthy to note that the fluid velocity is high with CTC and lower for RTC. Also, the fluid velocity declines with the augmentation of the magnetic parameter. Moreover, growth in thermal radiation leads to a declination in the temperature profile. Practical implications The proposed model has relevance in numerous engineering and technical procedures including industries related to polymers, area of chemical productions, nuclear energy, electronics and aerodynamics. Encouraged by such applications, the present work is undertaken. Originality/value Literature review unveils that sundry studies have been carried out in the presence of uniform wall temperature. Few studies have been conducted by considering non-uniform or ramped wall temperature and concentration. The authors are focused on an analytical investigation of an unsteady MHD boundary layer flow with heat and mass transfer of non-Newtonian Casson fluid past a moving plate subject to the RTC at the plate. Based on the authors’ knowledge, the present study has, so far, not appeared in scientific communications. Obtained analytical solutions are verified by considering particular cases of the published works.

Impact of slip effects on unsteady Sisko nanoliquid heat and mass transfer characteristics over stretching sheet filled with gold nanoparticles

AbstractWe have presented a comparison between steady and unsteady magnetohydrodynamic boundary layer flow, heat transfer features of Au–kerosene‐based nanoliquid over a stretching surface by taking variable viscosity, variable thermal conductivity, and slip boundary conditions in this study. Appropriate similarity translations are engaged to reduce nonlinear partial differential equations into a set of ordinary differential equations. These equations along with boundary conditions are elucidated numerically by finite‐element technique. Influence of several pertinent parameters on velocity, temperature, and concentration scatterings, in addition to that, the values of Nusselt number, skin‐friction coefficient, and Sherwood number are scrutinized in detail and the outcomes are exhibited through plots and tables. It is perceived that the values of Nusselt number, skin‐friction coefficient, and Sherwood number intensify in both steady–unsteady cases as the values of volume fraction parameter rise.

Effect of Prandtl number on leading edge accretion and ablation: A numerical study of unsteady boundary layer flow over a flat plate

AbstractAn efficient numerical method, namely, the Runge‐Kutta fourth order integration scheme with shooting technique is employed to give a suitable solution for the unsteady magnetohydrodynamic boundary layer flow of viscous incompressible fluid with accretion or ablation effects over a flat plate under the influence of homogenous first order chemical reaction. When compared to the other numerical techniques such as perturbation methods, this approach provides the accurate numerical results valid uniformly for all nondimensional time. The unsteady behavior of chemically reacting magnetohydrodynamic boundary layer flow is investigated by analyzing the nature of buoyancy and magnetic parameters in the momentum equation. Also, results are extended to the energy and concentration equations by considering the viscous dissipation, Joule heating and chemical reaction effects. With the help of suitable similarity transformations, the highly nonlinear, coupled, time‐dependent partial differential equations are reduced to ordinary differential equations. Furthermore, the numerical solutions in terms of velocity, temperature and concentration profiles within the boundary layer are presented for the various values of control parameters. Also, the impact of physical parameters on the flow, heat and mass transfer characteristics are examined thoroughly. The present investigation reports that, the increasing magnetic parameter increases the temperature field and decreases the velocity field. Also, Eckert number enhance the thermal field whereas, the chemical reaction parameter decays the concentration field. Before concluding the considered problem, present results are validated with the previous results and are found to be in good agreement.

Unsteady MHD boundary layer flow of tangent hyperbolic two-phase nanofluid of moving stretched porous wedge

PurposeThe purpose of this paper is to address the thermo-physical impacts of unsteady magneto-hydrodynamic (MHD) boundary layer flow of non-Newtonian tangent hyperbolic nanofluid past a moving stretching wedge. To delineate the nanofluid, the boundary conditions for normal fluxes of the nanoparticle volume fraction are chosen to be vanish.Design/methodology/approachThe local similarity transformation is implemented to reformulate the governing PDEs into coupled non-linear ODEs of higher order. Then, numerical solution is obtained for the simplified governing equations with the aid of finite difference technique.FindingsNumerical calculations point out that pressure gradient parameter leads to improve all skin friction coefficient, rate of heat transfer and absolute value of rate of nanoparticle concentration. As well as, lager values of Weissenberg number tend to upgrade the skin friction coefficient, while power law index and velocity ratio parameter reduce the skin friction coefficient. Again, the horizontal velocity component enhances with upgrading power law index, unsteadiness parameter, velocity ratio parameter and Darcy number and it reduces with rising values of Weissenberg number.Originality/valueA numerical treatment of unsteady MHD boundary layer flow of tangent hyperbolic nanofluid past a moving stretched wedge is obtained. The problem is original.

Unsteady MHD boundary layer flow and heat transfer over the stretching sheets submerged in a moving fluid with Ohmic heating and frictional heating

Abstract This paper is devoted to the analysis of the unsteady magnetohydrodynamic (MHD) boundary layer flow and heat transfer on a permeable stretching sheet embedded in a moving incompressible viscous fluid. The combined effects of Ohmic heating, thermal radiation, frictional heating and internal heat absorption/generation are taken into account. The governing time dependent nonlinear boundary layer equations are converted into a systemof nonlinear ordinary differential equations by similarity transformations. Some analytical results that give the characteristics of the velocity field in the boundary layer are presented and proved. The governing equations are then solved by using the shooting technique along with the fourth order Runge-Kutta method. The analytical properties proved in this paper are consistent with those obtained by the numerical method. Furthermore, the effects of the various parameters on the velocity and temperature fields are presented graphically and discussed in detail.

Unsteady Magnetohydrodynamic Boundary Layer Flow near the Stagnation Point towards a Shrinking Surface

The unsteady two-dimensional, laminar flow of a viscous, incompressible, electrically conducting fluid towards a shrinking surface in the presence of a uniform transverse magnetic field is studied. Taking suitable similarity variables, the governing boundary layer equations are transformed to ordinary differential equations and solved numerically by a perturbation technique for a small magnetic parameter. The effects of various parameters such as unsteadiness parameter, velocity parameter, magnetic parameter, Prandtl number and Eckert number for velocity and temperature distributions along with local Skin friction coefficient and local Nusselt number have been discussed in detail through numerical and graphical representations.

Unsteady plane MHD boundary layer flow of a fluid of variable electrical conductivity

This paper is devoted to the analysis of unsteady plane laminar magnetohydrodynamic (MHD) boundary layer flow of incompressible and variable electrical conductivity fluid. The present magnetic field is homogenous and perpendicular to the body surface. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in induction-less approximation. Free stream velocity is an arbitrary differentiable function. Fluid electrical conductivity is decreasing function of velocity ratio. In order to solve the described problem multiparametric (generalized similarity) method is used and so-called universal equations are obtained. Obtained universal equations are solved numerically in appropriate approximation and a part of obtained results is given in the form of figures and corresponding conclusions.