Presents a study of the flow of a viscous incompressible fluid along a heated vertical plate, taking into account the variation of the viscosity and thermal diffusivity with temperature. The governing conservation equations of mass, momentum and energy are non-dimensionalized by using an appropriate transformation. The resulting system of coupled ordinary differential equations is solved analytically and numerically. Euler's transformation has been used to improve the analytical solution towards the numerical solution. The results show rather good agreement between the analytical and numerical solutions near the plate. It is found that the velocity f' of air or water near the plate increases as the viscosity decreases (the viscosity parameter alpha increases), but an opposite effect is noticed at a certain distance from the plate. It is observed that both the velocity and temperature of air increase as the thermal diffusivity of air increases (the thermal diffusivity parameter beta increases). For water it is found that the temperature theta decreases as the viscosity decreases ( alpha increases). The dimensionless shearing stress at the plate, the heat transfer rate at the plate, the momentum boundary layer thickness delta 1, and the thermal boundary layer thickness delta 2 are estimated for different values of alpha , beta and the Prandtl number sigma .

This paper is concerned with the boundary layer flow of a power law non-Newtonian fluid in the presence of a magnetic field B(x) applied perpendicular to the surface and an electric field E(x) perpendicular to B(x) and the direction of the longitudinal velocity in the boundary layer. Approximate analytical solutions are given, and numerical solutions to the resulting nonlinear ordinary differential equation are presented. Important particular cases like boundary layer flow along a wedge, two-dimensional stagnation point flow, flow over a flat plate and flow in a convergent channel have been studied. The combined effects of the magnetic forces gamma and the flow index n on the velocity profiles, the shear stress on the surface tau w, the displacement thickness delta 1 and the momentum thickness delta 2 are studied. It is found that the velocity of the fluid increases with increase of either gamma or n individually, with the other kept constant. Also, it is established that both analytical and numerical solutions must be used together to solve such problems.

We present simple analytical solutions for the unsteady advection-dispersion equations describing the pollutant concentration C(x, t) in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions x ≤ 0 and x ≥ 0 and the origin at x = 0. The variation of C(x, t) with the time t from t = 0 up to t → ∞ (the steady state case) is taken into account in our study. The special case for which the dispersion coefficient D = 0 is studied in detail. The parameters controlling the pollutant concentration along the river are determined.

No abstract

The flow of a viscous incompressible fluid between two parallel discs which at time t are spaced a distance H(1- alpha t)1/2 apart and are rotating with angular velocities proportional to (1- alpha t)-1 has been studied. Account is taken of the heat transfer between the two discs. The governing Navier-Stokes equation and energy equation are transformed to a set of ordinary differential equations. Approximate and exact solutions to these equations giving temperature distribution are obtained in the case where the upper disc is isothermal and the lower disc is either isothermal or subject to a constant heat flux beta . It is found that the temperature of the fluid increases with the decrease of both the Prandtl number Pr and the parameter beta individually, keeping the other constant. It is established that the rotation of the two discs has a very small effect on the temperature of the fluid and the heat transfer process, while the rapid normal motion of the upper disc (R2>or=1) has a dominant effect on the temperature of the fluid and the heat transfer process. The results show rather good agreement between the approximate and exact solutions.