C. L. Goudas

Free convection and mass transfer effects on the hydro-magnetic oscillatory flow past an infinite vertical porous plate

Two-dimensional unsteady free convection and mass transfer, flow of an incompressible viscous dissipative and electrically conducting fluid, past an infinite, vertical porous plate, is considered, when the flow, is subjected in the action of uniform transverse magnetic field. The magnetic Reynolds number is taken to be small enough so that the induced magnetic field is negligible. The solution of the problem is obtained in the form of power series of Eckert numberE, which is very small for incompressible fluids. Analytical expressions for the velocity field and temperature field are given, as well as for the skin friction and the rate of heat transfer for the case of the mean steady flow and for the unsteady one. The influence of the magnetic parameter,M, modified Grashof numberGc, Schmidt numberSc and frequency ω, on the flow field, is discussed with the help of graphs, when the plate is being cooled, by the free convection currents (Gr,E>0), or heated (Gr,E<0). A comparative study with hydrodynamic case (M=0) and the hydromagnetic one (M≠0) is also made whenever necessary.

Effects of mass transfer on the free convective flow in the Stokes' problem for an infinite vertical limiting surface

An exact analysis of the mass transfer effects on the free convection flow of an incompressible viscous fluid past an impulsively started infinite vertical (wall) limiting surface (Stokess or Rayleighs problem) has been carried out. Expressions for the velocity, temperature, species concentration and skin friction are obtained by using the Laplace transform technique. The velocity field and the skin friction are shown graphically for air (P=0.71) and mercury (P=0.025). The effects ofG (Grashof number),Gc (the modified Grashof number) andSc (Schmidt number) are considered qualitatively during the course of discussion.

Hydromagnetic free convection effects on the stokes problem for an infinite vertical plate

Abstract The extension of the problem of Stokes (also called Rayleighs problem) to magnetohydrodynamic for the flow past an infinite, non-conducting and non-magnetic, vertical plate, is studied. The plate is assumed to move after receiving an initial impulse. The magnetic Reynolds number is taken small enough so that the induced magnetic field is negligible. Expressions, in closed form for the velocity and the skin friction are obtained by applying the Laplace transform technique and the results obtained for various values of the parameters G (Grashof number) and M (Magnetic parameter) are given in graphical form. The paper is concluded with a discussion of the results obtained.

New types of motion in Strmer's problem

Application of boundary value techniques in the case of an electron performing relativistic motions within a magnetic dipole such as that of the Earth supplemented by a scanning process by means of which the entire phase space of the problem can be investigated, six new types of periodic motion have been discovered and computed. The stability of these motions is investigated and their direct bearing on formation and shape of the Van Allen zones of the Earth is discussed.

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.

A grid search for three-dimensional motions and three new types of such motions

A grid search method aimed at locating ‘all’ doubly symmetric orbits of the three-dimensional restricted problems of one, two, etc. revolutions is developed and applied numerically on the CDC-3300 computer. Three new types of orbits have thus been located and a second order ‘predictorcorrector’ method is applied in order to determine a certain number of members of the families of which the ‘located’ orbits are members. The stability of these members is also discussed.

Hydromagnetic flow near an oscillating wall

The flow of a viscous incompressible and electrically conducting fluid produced by harmonically oscillating wall of infinite extent in presence of a transverse magnetic field is considered. Exact solutions for velocity, induced magnetic field, electrical current density and skin-friction are obtained when the magnetic Prandtl number is unity. It is shown that the velocity has a phase lag with respect to the oscillations of the wall. This phase lag is found to be significantly affected by the applied magnetic field.

Unsteady hydromagnetic thermal boundary layer flow

Unsteady hydromagnetic thermal boundary layer flow past a non-conducting infinite porous wall in presence of a transverse magnetic field is considered. The magnetic Reynolds number of the flow is taken to be small enough so that the induced magnetic field is negligible. It is assumed that the normal velocity of suction/injection at the wall varies att−/12. Solution of the problem, in the form of power series, is obtained for two cases:(I)When the wall temperature is the same as that of the free-stream, and(II)When the difference in the temperatures of the wall and that of the free-stream varies as some power of time. The variations of the skin-friction, the temperature and the rate of heat transfer are shown graphically followed by a quantitative discussion.

Free convection effects on the unsteady laminar boundary-layer flow past a porous limiting surface with uniform suction in stellar atmospheres

Unsteady two-dimensional free convection flow of a viscous fluid (e.g., of a stellar atmosphere) past a porous limiting surface (e.g., of a star) through which suction with uniform velocity occurs is considered when the free-stream velocity and the temperature of the limiting surface are arbitrary functions of time. General solution of the equations governing the flow is obtained in closed form with the help of two-sided Laplace transform technique under the assumption that there exists a mean steady flow to which is superimposed the unsteady flow. Further, in order to demonstrate the applications of the results of the general theory, four particular cases have been considered by prescribing physically acceptable different time-dependent forms to the temperature of the limiting surface and to the free-stream velocity. The results thus obtained for these four cases are discussed quantitatively.

PLANAR ORBITS THROUGH SECOND VARIATIONS

The development and application of a ‘predictor-corrector’ method for the computation of families of periodic motions as well as of singular periodic solutions from which ‘branchings’ or change in the stability character occur, based on the use of second order variations is presented. Numerical results obtained by means of this method are also given. It is found that this algorithm consumes somewhat less computer time in determining orbits-members of a family of periodic orbits, while it represents a unique tool for the determination of ‘branchings’ of various orders, as well as of the precise members of each family at which the orbits change from unstable to stable and viceversa.