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ABSTRACTThe concentration fluctuations in long wavelength limit and thermodynamic properties, i.e. free energy of mixing, heat of mixing, entropy of mixing and activity of the components involved in the Zn-Sn binary liquid alloy at a specified temperature, have been investigated using a familiar formalism in which the combined effect of size ratio, entropic and enthalpic effect is considered. These properties of Zn-Sn liquid alloys at 750 K have been computed by estimating the best fit value of order energy parameter (W) and size ratio () in the entire range of concentration in order to match their experimental and theoretical values. This value of Whas been used to determine the values of Wat different temperatures with the help of temperature derivative of Wwhich are then used for the optimization procedure in order to calculate the corresponding values of excess free energy of mixing, partial excess free energy of mixing and activity of the components involved in the alloy at different temperatures. These parameters have been used to predict the concentration fluctuations in long wavelength limit {Scc(0)} at different temperatures over the entire range of concentration.

A linear optimal controller is designed to implement Variable Series Compensation (VSC) in transmission network of interconnected power systems. The proposed controller is used to dampen inter-area oscillations and enhance power system stability. The effectiveness of the linear optimal controller to properly control such a variable series reactance is demonstrated through mode shapes and digital simulation studies on a two-machine system. The digital simulation studies are conducted using a PSCAD/EMTDC software package. The mode shapes and simulation results show that the controller contributes significantly to the damping of inter-area oscillations and the power stability enhancement.

A new approach to the design of variable series compensators for transmission systems is proposed. The compensators incorporate an optimal minimum time control strategy which will suppress power oscillations following large disturbances and a linear control part suitable for the regulation of power flows during small perturbations. The coordination between these two control functions is based on the magnitudes of the power oscillations. Computer simulation of the proposed scheme shows that it is effective in improving the stability performance of transmission networks.

The role of a variable series compensator in a multimachine infinite-bus system is investigated. The proposed compensator comprises a combination of thyristor-switched capacitors (TSCs) and a thyristor-controlled reactor (TCR). The role of the TSCs is to suppress large power oscillations while that of the TCR is to damp out small power perturbations. A performance index to quantify the overall power imbalance in the system is proposed and is used to formulate the control strategies for the TSCs and TCR. The coordination between the control actions of the TSCs and TCR is established on the basis of the magnitudes of the power oscillations. Computer simulations show that the proposed scheme is effective in suppressing power flow oscillations in transmission networks.

The problem of the steady flow of an electrically conducting viscous fluid through porous walls of a channel in the presence of an applied transverse magnetic field is considered. A solution for the case of small M2/R (where M = Hartmann number, R = suction Reynolds number) with large blowing at the walls has been given by Terrill and Shrestha [3]. Their solution, on differentiating three times, is found to become infinite at the centre of the channel. Physically this means that there must be a viscous layer at the centre of the channel and Terrill and Shrestha are neglecting the shear layer. In this paper the solution given by Terrill and Shrestha is extended by obtaining an extra term of the series of expansion and the method of inner and outer expansion is used to obtain the complete solution which includes the viscous layer. The resulting series solutions are confirmed by numerical results.

The steady laminar flow of a viscous incompressible fluid through a two-dimensional channel, having fluid sucked or injected with different velocities through its uniformly porous parallel walls is considered. A solution for small suction Reynolds number has been given by the authors in a previous paper. The purpose of this paper is to present a solution valid for large Reynolds numbers for the cases of (i) suction at both walls, and (ii) suction at one wall and injection at the other. A technique of matching outer and inner expansions is used to obtain an asymptotic solution for both of these cases. Further a perturbation solution for the case of suction at one wall and injection at the other is obtained by choosing the difference between two wall velocities as the perturbation parameter. Both asymptotic and perturbation solutions are confirmed by exact numerical solutions. As expected, the resulting solutions show the presence of the usual suction boundary layers in both types of flow considered in this paper.

The problem of two-dimensional steady laminar flow of a viscous incompressible and electrically conducting fluid through a channel with two equally porous walls in the presence of a transverse magnetic field has been extended to include all values of Hartmann number and small suction velocity at the walls. Expressions for the velocity components, the pressure and the wall friction in terms of the Hartmann number and the suction Reynolds number are given. It is found that the pressure drop in the major flow direction and the wall friction decrease with the increase in suction and increase with the increase in the strength of the magnetic field.

Abstract: The problem of oscillating free stream flow of an elastico-viscous, incompressible, and electrically conducting fluid along an infinite plate with suction varying periodically with time, is considered in the presence of a transverse magnetic field. The effect of the elasticity of the fluid, the magnetic fluid, and the fluctuation of suction velocity on the velocity and the skin friction is examined.

The two-dimensional steady flow of an incompressible elastico-viscous fluid through a porous channel that has the fluid sucked or injected with different normal velocities V1 and V2 at the walls is considered. For the viscous case Terrill and Shrestha [2] have given a series solution for small suction Reynolds number. In this paper the solution of [2] is extended to include the effect of the elasticity of the fluid. It is found that the elasticity of the fluid comes into effect only when suction or blowing is present. The general expressions for the pressure distribution and the friction coefficient are given and are found to increase as the elastic parameter increases. Finally, the resulting solution is confirmed by numerical results.

The steady laminar flow of an incompressible, viscous, and electrically conducting fluid between two parallel porous plates with equal permeability has been discussed by Terrill and Shrestha [6]. In this paper, using the solution of [6] for the velocity field, the heat transfer problems of (i) uniform wall temperature and (ii) uniform heat flux at wall are solved.

The flow of a viscous incompressible and electrically conducting fluid in a two-dimensional uniformly porous channel, having fluid sucked or injected with a constant velocity through its walls, is considered in the presence of a transverse magnetic field. A solution for small Reynolds number has been given by the authors in a previous paper. A solution valid for large suction Reynolds number and all values of Hartmann number is presented here and the resulting boundary layer is discussed. Also Yuan’s solution for large negativeRis extened to include small values ofM2/R.

The flow of a viscous incompressible and electrically conducting fluid in a two-dimensional uniformly porous channel, having fluid sucked or injected with a constant velocity through its walls, is considered in the presence of a transverse magnetic field. A solution for small Reynolds number has been given by the authors in a previous paper. A solution valid for large suction Reynolds number and all values of Hartmann number is presented here and the resulting boundary layer is discussed. Also Yuan's solution for large negativeR is extened to include small values ofM2/R.

The problem of two-dimensional steady laminar flow of a viscous incompressible and electrically conducting fluid through a channel with two equally porous walls in the presence of a transverse magnetic field has been extended to include all values of Hartmann number and small suction velocity at the walls. Expressions for the velocity components, the pressure and the wall friction in terms of the Hartmann number and the suction Reynolds number are given. It is found that the pressure drop in the major flow direction and the wall friction decrease with the increase in suction and increase with the increase in the strength of the magnetic field.

The flow of a viscous, incompressible, and electrically conducting fluid in a two-dimensional channel with porous walls, through which fluid is uniformly injected or extracted, is considered in the presence of a transverse magnetic field. The problem is reduced to solving a fourth order non-linear differential equation which depends on a suction Reynolds number R and a Hartmann number M. A solution of this equation, valid for large suction Reynolds number and all values of Hartmann number has been given by Terrill and Shrestha (8) without proceeding to obtain outer and inner expansions separately. Further, they have given a solution for small values of M2/R with large negative R. In this paper the technique of outer and inner expansions is used to solve the equation for large values of R (positive and negative) and different values of M. In particular a magnetic-boundary-layer type solution is obtained for large negative R and large M2/R. Further a formal asymptotic solution is obtained for the case of large positive R and an arbitrary value of M. The resulting asymptotic solutions are then confirmed by the numerical solution of the equation.

The steady laminar flow in a two-dimensional channel having porous walls of different permeability through which fluid is uniformly extracted or injected has been investigated by the authors (6) and (7). The authors gave solutions for small suction or blowing and for large suction at one or both walls. In the present paper a series solution for large blowing at both walls is obtained by using the method of inner and outer expansions. The resulting solution is confirmed by numerical results.