Incompressible micropolar fluid flow over a semi-infinite plate

Micropolar fluid flow over a semi-infinite flat plate has been described by using the parabolic co-ordinates and the method of series truncation in order to study the flow for low to large Reynolds numbers. These co-ordinates permit to study the flow regime at the leading edge. Numerical results have been presented for different Reynolds numbers. Results show a reduction in skin friction.

Unsteady flow and heat transfer on a semi-infinite flat plate with an aligned magnetic field

The unsteady laminar boundary layer flow of an electrically conducting fluid past a semi-infinite flat plate with an aligned magnetic field has been studied when at time t > 0 the plate is impulsively moved with a constant velocity which is in the same or opposite direction to that of free stream velocity. The effect of the induced magnetic field has been included in the analysis. The non-linear partial differential equations have been solved numerically using an implicit finite-difference method. The effect of the impulsive motion of the surface is found to be more pronounced on the skin friction but its effect on the x-component of the induced magnetic field and heat transfer is small. Velocity defect occurs near the surface when the plate is impulsively moved in the same direction as that of the free stream velocity. The surface shear stress, x-component of the induced magnetic field on the surface and the surface heat transfer decrease with an increasing magnetic field, but they increase with the reciprocal of the magnetic Prandtl number. However, the effect of the reciprocal of the magnetic Prandtl number is more pronounced on the x-component of the induced magnetic field. (C) 1999 Elsevier Science Ltd. All rights reserved.

Compressible laminar boundary-layer flows of a dusty gas over a semi-infinite flat-plate

The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions : the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a seriesexpansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.

On the natural convection boundary layer adjacent to an inclined flat plate subject to ramp heating

An investigation of the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a temperature boundary condition which follows a ramp function up until some specified time and then remains constant is reported. The development of the flow from start-up to a steadystate has been described based on scaling analyses and verified by numerical simulations. Attention in this study has been given to fluids having a Prandtl number Pr less than unity. The boundary layer flow depends on the comparison of the time at which the ramp heating is completed and the time at which the boundary layer completes its growth. If the ramp time is long compared with the steady state time, the layer reaches a quasi steady mode in which the growth of the layer is governed solely by the thermal balance between convection and conduction. On the other hand, if the ramp is completed before the layer becomes steady; the subsequent growth is governed by the balance between buoyancy and inertia, as for the case of instantaneous heating.

An improved boundary layer scaling with ramp heating on a sloping plate

A scaling analysis for the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a non-instantaneous heating in the form of an imposed wall temperature which increases linearly up to a prescribed steady value over a prescribed time is reported. The development of the boundary layer flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. The analysis reveals that, if the period of temperature growth on the wall is sufficiently long, the boundary layer reaches a quasi-steady mode before the growth of the temperature is completed. In this mode the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the imposed wall temperature growth period is sufficiently short, the boundary layer develops differently, but after the wall temperature growth is completed, the boundary layer develops as though the startup had been instantaneous. The steady state values of the boundary layer for both cases are ultimately the same.

Mixed convection along a vertical flat plate in a non-absorbing medium

Here mixed convection boundary layer flow of a viscous fluid along a heated vertical semi-infinite plate is investigated in a non-absorbing medium. The relationship between convection and thermal radiation is established via boundary condition of second kind on the thermally radiating vertical surface. The governing boundary layer equations are transformed into dimensionless parabolic partial differential equations with the help of appropriate transformations and the resultant system is solved numerically by applying straightforward finite difference method along with Gaussian elimination technique. It is worthy to note that Prandlt number, Pr, is taken to be small (<< 1) which is appropriate for liquid metals. Moreover, the numerical results are demonstrated graphically by showing the effects of important physical parameters, namely, the modified Richardson number (or mixed convection parameter), Ri*, and surface radiation parameter, R, in terms of local skin friction and local Nusselt number coefficients.

Unsteady flow of a dilute suspension in a semi-infinite contracting or expanding pipe

In the present paper an exact similar solution of the Navier-Stokes equation for unsteady flow of a dilute suspension in a semi-infinite contracting or expanding circular pipe is presented. The effects of the Schmidt number (Sc), Reynolds number (|ε|), the volume fraction (α) and the relaxation time (τ) of the particulate phase on the flow characteristics are examined. The presence of the solid particles has been observed to influence the flow behaviour significantly. These solutions are valid down to the state of a completely collapsed pipe, since the nonlinearity is retained fully. The results may help understanding the flow near the heart and certain forced contractions or expansions of valved veins.

Heat transfer with solid liquid phase change initiating at a point in a semi infinite mold

Short-time analytical solutions of temperature and moving boundary in two-dimensional two-phase freezing due to a cold spot are presented in this paper. The melt occupies a semi-infinite region. Although the method of solution is valid for various other types of boundary conditions, the results in this paper are given only for the prescribed flux boundary conditions which could be space and time dependent. The freezing front propagations along the interior of the melt region exhibit well known behaviours but the propagations along the surface are of new type. The freezing front always depends on material parameters. Several interesting results can be obtained as particular cases of the general results.

Unsteady flow of a dilute suspension in a semi-infinite contracting or expanding pipe

In the present paper an exact similar solution of the Navier-Stokes equation for unsteady flow of a dilute suspension in a semi-infinite contracting or expanding circular pipe is presented. The effects of the Schmidt number (Sc), Reynolds number (|ε|), the volume fraction (α) and the relaxation time (τ) of the particulate phase on the flow characteristics are examined. The presence of the solid particles has been observed to influence the flow behaviour significantly. These solutions are valid down to the state of a completely collapsed pipe, since the nonlinearity is retained fully. The results may help understanding the flow near the heart and certain forced contractions or expansions of valved veins.

Surface instability in a semi-infinite plasma in the presence of high frequency fields

The surface instability of a semi-infinite plasma immersed in a high frequency field is investigated. When the natural Langmuir frequency of the surface is nearly equal to the frequency of the high frequency field, the dispersion relation predicts build-up of oscillations with a growth rate comparable with the real part of the frequency. Threshold values above which the instability is possible are derived.

Two-dimensional heat conduction with phase change in a semi-infinite mould

Analytical solution of a 2-dimensional problem of solidification of a superheated liquid in a semi-infinite mould has been studied in this paper. On the boundary, the prescribed temperature is such that the solidification starts simultaneously at all points of the boundary. Results are also given for the 2-dimensional ablation problem. The solution of the heat conduction equation has been obtained in terms of multiple Laplace integrals involving suitable unknown fictitious initial temperatures. These fictitious initial temperatures have interesting physical interpretations. By choosing suitable series expansions for fictitious initial temperatures and moving interface boundary, the unknown quantities can be determined. Solidification thickness has been calculated for short time and effect of parameters on the solidification thickness has been shown with the help of graphs.