Convection flow over a uniform-flux vertical surface with variable viscosity

A regular perturbation analysis is presented for natural convection flow over an uniform flux vertical surface with temperature dependent viscosity. Numerical calculations are presented forP _r=6.7 which show that the first-order correction to the local temperature difference and to the local skin-fraction are negative whereas it is positive for the local Nusselt number. The effects of variable viscosity on the temperature, velocity profiles, the local temperature difference, the local Nusselt number and the local skin fraction are discussed.     

Effects of rotation on Rayleigh-Taylor instabilities of an accelerating,compressible, perfectly conducting plane layer

The stability of a plane-stratified slab of perfectly conducting, rotating, compressible, inviscid plasma accelerated by a magnetic field is considered. Exact solutions for the growth rates of the unstable modes are determined for a -law gas when the undisturbed equilibrium is an isothermal atmosphere of semi-infinite extent with no frozen-in field. It is shown that the rotation has no effect on the region of unstable modes which has wavelengths long compared with the atmospheric scale height. On the other side, the growth rates in the presence of rotation are less than those in the absence of rotation for unstable modes.     

A class of semi-analytical solutions for a rotating toroidal plasma

In this paper, the problem of stationary MHD flow for a rotating toroidal plasma is investigated by assuming that the entropy is a surface quantity. Then, the system of ideal MHD equations is reduced to a single second-order elliptic partial differential equation known as the modified Grad-Shafranov (or Maschke-Perrin) equation. Under the assumption that both the function,P _s andf ² are quadratic polynomials of the flux function, a class of semi-analytical solutions is obtained for a plasma contained in a perfectly conducting toroidal boundary with a rectangular cross section. The flux function, poloidal current and the generalized pressure are obtained and discussed for relevant values of the parameters.     

Impact of rehabilitation of Assiut barrage, Nile River, on groundwater rise in urban areas

To make optimum use of the most vital natural resource of Egypt, the River Nile water, a number of regulating structures (in the form of dams and barrages) for control and diversion of the river flow have been constructed in this river since the start of the 20th century. One of these barrages is the Assiut barrage which will require considerable repairs in the near future. The design of the rehabilitation of the barrage includes a headpond with water levels maintained at a level approximately 0.60 m higher than the highest water level in the headpond of the present barrage. This development will cause an increase of the seepage flow from the river towards the adjacent agricultural lands, Assiut Town and villages. The increased head pond level might cause a rise of the groundwater levels and impedance of drainage outflows. The drainage conditions may therefore be adversely affected in the so-called impacted areas which comprise floodplains on both sides of the Nile for about 70 km upstream of the future barrage. A rise in the groundwater table, particularly when high river levels impede drainage, may result in waterlogging and secondary salinization of the soil profile in agricultural areas and increase of groundwater into cellars beneath buildings in the urban areas. In addition, a rise in the groundwater table could have negative impact on existing sanitation facilities, in particular in the areas which are served with septic tanks. The impacts of increasing the headpond level were assessed using a three-dimensional groundwater model. The mechanisms of interactions between the Nile River and the underlying Quaternary aquifer system as they affect the recharge/discharge processes are comprehensively outlined. The model has been calibrated for steady state and transient conditions against historical data from observation wells. The mitigation measures for the groundwater rise in the urban areas have been tested using the calibrated mode.     

Analytical solutions for some nonlinear two-dimensional magnetostatic equilibria

By use of the Painlevé analysis approach, a set of analytical solutions of the nonlinear magnetostatic equations is generated from known solutions. The relevance of these results for solar flares and solar active phenomena are discussed.     

Rotating perfect fluids in general relativity

The field equations and the equation of motion for perfect fluids in axially-symmetric-cylindrical coordinates are presented. For rigidly rotating perfect fluid with constant pressure, exact solutions are obtained in symmetric case and axially-symmetric case as well.     

Rotating ideal magnetohydrodynamic flow in General relativity

The field equations and the equation of motion for stationary, axisymmetric, rotating ideal magnetohydrodynamic flow are presented. Exact solutions are obtained for rigid rotation, for vanishing and nonvanishing Lorentz force.     

Analytical solutions of the rayleigh flow problem for a highly rarefied gas of a homogeneous system of charged particles

The Rayleigh flow problem for a highly rarefied gas of a homogeneous system of charged particles is investigated in the framework of kinetic theory of gases. The moments method with two-sided distribution function is used to solve the adopted BGK kinetic model. Approximate analytic solutions are obtained by a resort to Laplace's transform and the small parameter method. The dynamical and electromagnetic behaviour of the gas is examined.     

Two-dimensional magnetohydrodynamic equilibria

For the two-dimensional MHD equilibria, the system of ideal MHD equations is reduced to a single nonlinear equation of the magnetic potential as a Sh—Gordon equation. A set of analytical solutions is presented which are adequate for describing parallel filaments of a diffused magnetized plasma suspended horizontally in equilibrium in a uniform gravitational field.