Universal equations of unsteady two-dimensional MHD boundary layer whose temperature varies with time

Abstract

This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD) boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC ). Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation

MHD and Slip Effect on Two-immiscible Third Grade Fluid on Thin Film Flow over a Vertical Moving Belt

“…From Eqs. (21) and (22), the boundary and interface conditions are u (1) 0 (0) = α − Λ (1) ⎛ ⎝ du (1) 0 dx + 2β (1) (︃ du (1)…”

“…To solve Eqs. (19) and (20) along with boundary and interface conditions given in Eqs. (54) and (55) respectively, we apply Adomian Decomposion Method (ADM).…”

“…Double-diffusive MHD convection is significant for material solidification processes [14] and fluid flow over a flat surface or stretching sheet in the presence of a magnetic field finds applications in manufacturing processes such as the cooling of the metallic plate, rolling, purification of molten metals, extrusion of polymers, wire and fiber coating, hydro-magnetic lubrication [15][16][17][18]. Extensive research is presented in MHD control of flow and heat transfer in the boundary layer [19][20][21][22], enhanced plasma ignition [23], and combustion modeling [24]. The analysis of the flow on an inclined porous plate [25] has become the basis of several scientific and engineering applications.…”

Free Convective Flow of Electrically Conducting and Viscous Immiscible Fluid Flow in a Vertical Channel in the Presence of First‐Order Chemical Reaction

“…Many exciting innovations were put forth in the areas of MHD propulsion by Davidson [4], remote energy deposition for drag reduction was studied by Tsinober [5], plasma actuators, radiation-driven hypersonic wind tunnel. MHD control of flow and heat transfer in the boundary layer was studied by many authors such as Boricic and colleagues [6], Obrovic and colleagues [7], Xu and colleagues [8], and Nikodijevic and colleagues [9], enhanced plasma ignition was studied by Kessel and colleagues [10].…”

Mhd flow and heat transfer of two immiscible fluids with induced magnetic field effects

“…Partial differential equations governing the flow and heat transfer and magnetic field conservation are transformed to ordinary differential equations and solved exactly in both fluid regions, under physically appropriate boundary and interface conditions. Extensive research is present in MHD control of flow and heat transfer in the boundary layer [11][12][13][14], enhanced plasma ignition [15], and combustion modeling [16]. The analytical results for various values of the Hartmann number, the angle of magnetic field inclination, loading parameter and the ratio of plates' velocities are presented graphically to show their effect on the flow and heat transfer characteristics.…”