Hydromagnetic flow near an oscillating porous limiting surface

Unsteady hydromagnetic flow near a harmonically oscillating limiting surface (e.g., of a star) is considered in presence of a transverse magnetic field. Exact solutions, for a periodic boundary layer without a mean steady flow,are obtained when the magnetic Prandtl number is unity and there is a normal velocity of injection imposed at the wall. The results are also presented for the case when the wall is subjected to a normal velocity of suction instead of injection. It is observed that two distinct boundary (or hydromagnetic boundary) layers exist and tend to coalesce into a single layer when the magnetic field parameter approaches zero. The thicknesses of these boundary layers are significantly affected by the injection/suction velocity and the applied magnetic field.     

Hydromagnetic thermal boundary-layer flow near an oscillating limiting surface

Unsteady hydromagnetic thermal boundary layer flow of an electrically conducting, viscous, incompressible fluid near a harmonically oscillating limiting surface (e.g. in stellar atmospheres) is considered when the viscous dissipation and the Joule heating terms are retained in the energy equation. Exact solution of the problem, with the aid of the Laplace transform technique, is obtained when the magnetic Prandtl number is unity. For the purpose of application and discussion of the results, the variations of the temperature and the rate of heat transfer (expressed in the form of the Nusselt number) are presented for different sets of values of the magnetic parameter for the case of two particular fluids — air and water — when the limiting surface is under the condition of either cooling or heating.     

Unsteady hydromagnetic rotating flow near an oscillating plate

The three-dimensional flow of a viscous incompressible electrically conducting fluid near an infinite plate (or wall) of non-conductor, which is oscillating harmonically in a uniform rotating medium, is studied in the presence of a uniform magnetic field. The impressed uniform magnetic field is perpendicular to the plate and the induced magnetic field is considered. Exact solution of this problem is obtained for the velocity and magnetic fields. Neglecting the induced magnetic field we readily obtain the results of all the previous investigations. The effects of the rotation and the magnetic field are comparable with one another and are discussed for the whole problem. Also, the drag and the lateral stress on the plate are discussed.     

Hydromagnetic free-convection flow near a time-varying accelerated vertical plate

The effect of a uniform transverse magnetic field on the free-convection flow of an electrically conducting fluid past an exponentially accelerated infinite vertical plate is analysed for both cases, when the magnetic lines of force are fixed relative to the fluid and the plate, respectively. The Laplace transform method is used to obtain the expressions for velocity and skin-friction. The effect of a magnetic parameter is to decrease the velocity of water when the magnetic field is fixed to the fluid, while it increases the velocity field when the magnetic lines of force are fixed relative to the plate.     

MHD free-convection flow near a vertical oscillating plate

The unsteady free-convection flow of an electrically-conducting fluid near an oscillating vertical plate of infinite extent, is studied in the presence of a uniform transverse magnetic field. Exact solutions for velocity, temperature and skin friction are obtained with the aid of the Laplace transform method, when the plate is oscillating harmonically in its own plane. The influence of various parameters, entering into the problem, is discussed for the velocity field and skin-friction.     

Hydromagnetic Rayleigh problem for a porous wall in slip flow regime

An analysis of the Rayleigh problem in MHD for a porous wall in a slip flow regime is considered. The normal velocity of suction/injection at the wall is assumed to be time dependent. The solution of the problem is obtained in the form of a power series, in terms of known functions. The variations of the velocity field and the skin friction are shown graphically and are followed by a quantitative discussion.Science Update, The Pioneer, India, 21 July 1995 edition     

Hydromagnetic unsteady flow due to an unsteady plate

The unsteady flow near an infinite flat plate, which is oscillating harmonically in its own plane, is studied in the presence of a magnetic field subjected to suction or injection. The magnetic field is perpendicular to the plate and the flow of viscous incompressible and electrically conducting fluid is regarded as being initially at rest. Exact solutions for velocity and skin-friction are obtained for the magnetic field fixed to the fluid or to the plate.     

Hydromagnetic free-convection laminar flow of an elasto-viscous fluid past an infinite plate

The effect of a transverse magnetic field on unsteady free-convection flow of an electrically conducting elasto-viscous fluid (Walters liquidB') past an impulsively started infinite vertical plate is discussed. The Laplace transform technique is used to obtain the expressions for velocity and shearing stress. The influence of the various parameters, entering in the problem, on the velocity field and shearing stress is extensively discussed.     

Unsteady forced and free convective flow past an infinite vertical porous plate with oscillating wall temperature and constant suction

A study of the two-dimensional unsteady flow of a viscous, incompressible fluid past an infinite vertical plate has been carried out under the following conditions: (1) constant suction at the plate, (2) wall temperature oscillating about a constant non-zero mean, and (3) constant free-stream. Approximate solutions to coupled non-linear equations governing the flow have been carried out for the transient velocity, the transient temperature, the amplitude and phase of the skin friction, and the rate of heat transfer. The velocity, temperature and amplitude are shown graphically whereas the numerical values of the phases are given in a table. It has been observed that the amplitude of the skin friction decreases with increasing (frequency) but increases with increasingG (Grashof number), while the amplitude of the rat of heat transfer increases with increasing .     

Hydromagnetic shock structure in high temperature hypersonic flow

The paper studies the structure of a hydromagnetic shock wave, which is so strong that down-stream of the shock the gas radiates thermally. However, in the study the general differential approximation for radiation is invoked and solution is compared with that in an earlier paper for an optically thick gas.     

Free convection effects on the flow past an infinite vertical oscillating plate

The motion of a semi-infinite incompressible viscous fluid, caused by the oscillation of a plane vertical plate, has been studied, taking into account the presence of free convection currents. Closed form solutions to the velocity, temperature and the penetration distance through which the leading edge effect propagates have been derived on neglecting the transient part. Velocity profiles are shown forGr>0 (Grashof number) (cooling of the plate by the free convection currents),Gr<0 (heating of the plate) on graph. Also the penetration distance has been shown on graphs for different values ofP, the Prandtl number. It has been observed that for t=3/2, greater cooling of the plate may cause the flow to become unstable. Also, the penetration distance is not found to be affected by the frequency of the oscillating vertical plate.     

Rarefied gas flow near an asymmetric plane stagnation point

The probability of pulsars and supernovae being found close to each other on the celestial sphere by chance is calculated. It is found that this corresponds to the number of pulsars found close to supernovae in recent investigations. Thus, we conclude that, given also the inaccuracy of distances involved, the apparent spatial coincidence of pulsars and supernovae does not generally imply generic associations.     

Hydromagnetic free convection effects on the oscillatory flow past an impulsively started porous limiting surface: I

Unsteady two-dimensional free convection flow of an electrically conducting, viscous, incompressible fluid, past an infinite vertical porous limiting surface in the presence of a transverse magnetic field is studied, when the limiting surface is moved impulsively with a constant velocity, either in the direction of the flow or in the opposite direction. The magnetic Reynolds number of the flow is not taken to be small enough so that the induced magnetic field is not negligible. The obtained results, for the mean steady flow phenomena, are discussed with the aid of graphs and tables for different values of the dimensionless parameters entering into the problem.     

Hydromagnetic stability of a stratified parallel flow varying in two directions

The stability of a stratified parallel flow varying in two directions of an incompressible conducting fluid permeated by a uniform aligned magnetic field is investigated. Complex wave speed of an unstable mode lies in the upper half of a semi-circle whose diameter decreases with increasing magnetic field. It is also found that a strong enough magnetic field can completely stabilize flows with unstable density stratification.     

Hydromagnetic flow past a continuously moving semi-infinite plate for large suction

The similarity solution for hydromagnetic flow of an incompressible viscous electrically conducting fluid past a continuously moving semi-infinite porous plate in the presence of a magnetic field has been obtained for the case of small magnetic Reynolds number. The perturbation method has been used to solve the similarity equations at large suction. The resulting equations have been solved by analytical method. The effect of the magnetic parameter is to increase the skin-friction coefficient while it has no significant effect on the Nusselt number.     

Hydromagnetic ekman layer on convective heat generating fluid in slip flow regime

In this analysis, the velocity and temperature distributions on free convective heat generating rarefied gas in a rotating frame of reference are analysed for the case when a strong magnetic field is imposed in a plane which makes an angle with the normal to the plate. The effects of Hall currentm, heat source parameter and rarefaction have been discussed graphically followed by a discussion.     

Hydromagnetic planetary waves in vertically sheared zonal flow and transverse magnetic field

Hydromagnetic planetary waves propagating through a zonal flow and a transverse magnetic field both of which are sheared in the vertical direction are studied. It is found that the effect of the transverse magnetic field is to make planetary waves, which characteristically propagate westwards, propagate eastwards in both westerly and easterly zonal flows. It is also shown that at a critical level the rays are guided by the zonal flow only and that the waves are either attenuated or escalated by an exponential factor as they cross a critical level.     

Unsteady MHD flow of a viscoelastic fluid past an infinite porous plate with oscillating temperature

The unsteady flow of an electrically conducting fluid past an infinite plate with constant suction is investigated in the presence of an external magnetic field and buoyancy forces. The temperature of the plate is assumed to oscillate in time about a constant mean and the flow is considered to be free of convection. For the method of solution, we have employed a small parameter approach when this small parameter is a non-dimensional quantity which is related to the viscoelastic constant of the fluid. Analytical expressions are obtained for the temperature distribution and the velocity profile of the fluid. These analytical results clearly show that the velocity profile is strongly damped when the magnetic field is more intense. This means that the applied magnetic field causes the fluid to move slower as compared with the non-magnetic case.     

Free molecular flow of rarefied gas over an oscillating plate under a periodic external force

The free molecular flow over an infinite oscillating plane wall under external periodic force is considered. The Boltzmann equation is solved by using moments method with two-stream distribution functions. The boundary condition is obtained by assuming that the reflection of the particles from the solid surface takes place with complete energy accommodation. An analytical form for the velocity (X) and shear stress (Y) at any point is obtained. The results show that the amplitude of both the velocity change (X ₁) and the shear stress change (Y ₁) due to the periodic external force at the boundary (y=0) is an increasing function of time (t).