A. S. Gupta

Magnetohydrodynamic stagnation-point flow towards a stretching sheet

Steady two-dimensional stagnation-point flow of an incompressible viscous electrically conducting fluid over a flat deformable sheet is investigated when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. It is shown that the velocity at a point decreases/increases with increase in the magnetic field when the free stream velocity is less/greater than the stretching velocity. Temperature distribution in the flow is obtained when the surface is held at a constant temperature.

Hydromagnetic flow past a porous flat plate with hall effects

SummaryAn investigation is made of the flow of a conducting liquid past an infinite porous flat plate taking Hall effects into account, the liquid being permeated by a transverse magnetic field. It is shown that asymptotic solution for the velocity and magnetic field exists both for suction or blowing at the plate. Further when the magnetic Reynolds number is very small, the flow pattern is remarkably similar to that for a non-conducting flow past a flat plate in a rotating frame.ZusammenfassungUntersucht wird die Strömung einer leitenden Flüssigkeit längs einer unendlich langen, porösen Platte mit einem transversalen Magnetfeld und unter Berücksichtigung des Hall-Effektes. Es wird gezeigt, daß asymptotische Lösungen des Geschwindigkeits- und des Magnetfeldes existieren; im Fall des Absaugens an der Platte, wie auch bei Ausblasen. Für kleine magnetische Reynolds-Zahl ist die Strömung erstaunlich ähnlich der einer nichtleitenden, längs einer Platte rotierenden Flüssigkeit.

Mixed convection of an incompressible viscous fluid in a porous medium past a hot vertical plate

Abstract This paper analyses steady two-dimensional mixed convection of an imcompressible viscous fluid in a porous medium past a hot vertical plate. Assuming Darcy-Brinkman model for the flow in a porous medium, the boundary layer equations are integrated numerically to obtain the non-similar solution for the velocity and temperature distribution for several values of the permeability and viscous dissipation parameters. It is shown that for a fixed value of Prandtl number Pr and dissipation parameter E , the skin-friction at the plate decreases with increase in the permeability parameter K 1 . However for the same value or Pr and E , the heat transfer rate at the plate increases with increasing K 1 . The dimensionlcss velocity and temperature functions in the flow are plotted for several values of E and K 1 with Pr = 0.73. It is also shown that for fixed values of K 1 , and KPr , the skin-friction increases with increase in the dissipation parameter E .

MHD flow and heat transfer at a general three-dimensional stagnation point

The flow characteristics of an incompressible viscous electrically conducting fluid at a three-dimensional stagnation point with arbitary velocity gradients a and b (with a > 0 and ¦b¦ ⩽ a) in two orthogonal directions are determined. A similarity solution of the boundary layer equations for this flow over a surface permeated by a uniform transverse magnetic field is obtained when the surface is subjected to injection. Two types of stagnation point flows are distinguished: (i) nodal point flow when 0 < α ⩽ 1 with α = ba and (ii) saddle point flow with − 1 < α < 0. It is found that for nodal point flow the velocity component v in the boundary layer in the direction of the free stream with velocity gradient b approaches the free stream velocity more slowly than the corresponding velocity component u along the free stream with velocity gradient a. Further velocity at a point in the boundary layer increases with increase in the magnetic parameter M. It is found that at a saddle point for M = 0, a back flow in the v-profile occurs at α = − 0.43. A novel result of the analysis is that with increase in M, the magnitude of α for which the back flow in the v-profile first occurs also increases and for M = 1.258, no back flow occurs at all. Skin-friction components near nodal or saddle points corresponding to the u and v profiles are computed for various values of injection and magnetic parameters. Finally it is shown that increase in blowing results in decrease in the surface heat transfer thus illustrating the salutary effect of blowing in cooling the surface.

Oscillatory entry flow in a plane channel with pulsating walls

Abstract An analysis is made of the unsteady flow of an incompressible viscous fluid in the entrance region of a parallel-sided channel whose walls pulsate in a prescribed manner. The flux of fluid entering the channel oscillates cosinusoidally with time so that there is always an inflow at the entrance. The time-dependent Navier–Stokes equations are solved numerically using the finite difference method. Axial velocity profiles at various distances from the entrance of the channel are found at different instants of time during one period of oscillation of the flux of fluid entering the channel. It is shown that for large values of frequency of pulsation f 0 of the channel walls oscillating sinusoidally with time, back flow occurs near the channel walls at a certain location far downstream from the entrance section at a certain instant of time. It is also found that at a subsequent time there is flow reversal at the same location across the entire cross-section of the channel. For sufficiently small values of f 0 , such back flow does not occur. The effect of variation of the phase difference in the oscillation of entry flux of fluid and the channel wall oscillation on the time intervals in which wall shear stress does not vanish is also determined. No proper entry length could be found when f 0 ≠0.

Flow past an accelerated horizontal plate in a rotating fluid

SummaryA semi-infinite mass of an incompressible viscous fluid bounded by an infinite flat plate is initially rotating with uniform angular velocity Ω about an axis normal to the plate. An analysis is presented for the subsequent flow when the plate started impulsively from rest relative to the rotating fluid moves with uniform acceleration in its own plane. It is found that when Ω≠0, the velocity profiles for varying times are nonsimilar in contrast to the velocity profiles which are similar in the absence of rotation (Ω=0). At a given instant, the velocity component along the direction of motion of the plate decreases with an increase in rotation but the transverse velocity component (induced by the Coriolis force) increases with increasing rotation. Due to the gradual thinning of the boundary layer with rotation, both the skin-friction components along and transverse to the direction of motion of the plate increase with increasing rotation. A study of the asymptotic behavior of the velocity field for large time reveals a novel feature of the flow; it develops inertial oscillations with frequency 2Ω, which grow with time. This behavior has not been reported in the absence of rotation.

Stability of a thin layer of a second-grade fluid on a rotating disk

Abstract An analysis is made of the linear stability of a thin film of a second-grade fluid formed on a disk rotating uniformly about an axis normal to the plane of the disk. The characteristic Ekman number E based on the film thickness is assumed large so that the basic velocity distribution depends only on the co-ordinate normal to the disk. The disturbances are assumed in the form of spiral waves at some distance away from the central region of the film where smooth flow occurs. These waves are assumed periodic in some direction x∗ (which makes an angle β with the direction of the centrifugal force) with no variation perpendicular to the x∗-direction. A linear perturbation analysis of the stability equations for large wavelength (as found in experiments on the corresponding viscous flow problem) shows that the second-grade parameter stabilizes the flow while the cross-viscosity parameter N also exerts a stabilizing influence on the flow for β ≠ nπ, n being an integer. Surface tension is also found to be stabilizing for disturbances of large wave lengths.

Stability of magnetogasdynamic shear flow

SummarySome general results on the stability of a compressible parallel shear flow permeated by an aligned magnetic field are derived. It is shown that the complex wave speed of an unstable wave lies in a semi-circle in the upper half plane with the range of the shear flow as diameter. Further both compressibility and magnetic field are found to be stabilizing. It is also shown that in a flow near a wall, two acoustic waves carry energy away from the wall. A semi-circle theorem for a non-planar compressible shear flow is also deduced.ZusammenfassungEinige allgemeine Aussagen über die Stabilität einer kompressiblen, parallelen Scherströmung in einem Magnetfeld werden hergeleitet. Die komplexe Wellengeschwindigkeit der instabilen Welle liegt in einem Halbkreis in der oberen Halbebene, wobei der Radius durch die Breite der Scherströmung gegeben ist. Sowohl die Kompressibilität, wie das Magnetfeld üben einen stabilisierenden Einfluß aus. Was die Strömung in unmittelbarer Wandnähe angeht, so tragen zwei akustische Wellen Energie von der Wand fort. Abschließend wird ein Halbkreistheorem für nicht ebene kompressible Scherströmungen hergeleitet.

Stability of Taylor–Couette Magnetoconvection With Radial Temperature Gradient and Constant Heat Flux at the Outer Cylinder

An analysis is made of the linear stability of wide-gap hydromagnetic (MHD) dissipative Couette flow of an incompressible electrically conducting fluid between two rotating concentric circular cylinders in the presence of a uniform axial magnetic field. A constant heat flux is applied at the outer cylinder and the inner cylinder is kept at a constant temperature. Both types of boundary conditions viz; perfectly electrically conducting and electrically nonconducting walls are examined. The three cases of μ 0 (co-rotating), and μ=0 (stationary outer cylinder) are considered. Assuming very small magnetic Prandtl number Pm, the wide-gap perturbation equations are derived and solved by a direct numerical procedure. It is found that for given values of the radius ratio η and the heat flux parameter N, the critical Taylor number Tc at the onset of instability increases with increase in Hartmann number Q for both conducting and nonconducting walls thus establishing the stabilizing influence of the magnetic field. Further it is found that insulating walls are more destabilizing than the conducting walls. It is observed that for given values of η and Q, the critical Taylor number Tc decreases with increase in N. The analysis further reveals that for μ=0 and perfectly conducting walls, the critical wave number ac is not a monotonic function of Q but first increases, reaches a maximum and then decreases with further increase in Q. It is also observed that while ac is a monotonic decreasing function of μ for N=0, in the presence of heat flux (N=1), ac has a maximum at a negative value of μ (counter-rotating cylinders).

Thermal instability in a porous medium with random vibrations

SummaryOnset of thermal convection in a layer of saturated porous medium, heated from below, is examined when the layer is subjected to random vibrations. It is shown that when the vibrations are characterized by a white noise process, they hasten the onset of convection. Further, decrease in permeability tends to stabilize the flow field.