Analysis of thermally stratified radiative flow of Sutterby fluid with mixed convection

In this attempt, we investigate the mixed convection in Sutterby fluid flow based on boundary layer approximation. Heat transport analysis is composed of stratification and thermal radiative phenomena. The system of non-linear PDEs is transformed into coupled ODEs. Convergent series approximations are evaluated via homotopic technique. Influence of various pertinent parameters is sketched and graphically analyzed. It is found that horizontal velocity increments for higher mixed convection parameter. The radiation parameter has a similar relation with temperature whereas the stratification parameter shows opposite behavior for temperature field.

Grad-Shafranov reconstruction of the in-plane magnetic field potential in the X-point vicinity: boundary-layer approximation

<p>The problem of steady symmetrical two-dimensional magnetic reconnection is addressed in terms of the EMHD approximation. In the immediate vicinity of the X-point, this approach has been proven to be an appropriate frame for the reconstruction problem, expressed, particularly, by the Poisson equation for the magnetic potential <em>A</em>, where the right-hand side contains the out-of-plane electron current density with reversed sign. With boundary conditions fixed at some curve (the satellite trajectory), and assuming the right-hand side to be a function of <em>A</em>, one arrives at an ill-posed problem for the Grad-Shafranov equation. The further simplification of the problem may be achieved by using the boundary layer approximation, since magnetic configuration in reconnection region is highly stretched. The benchmark reconstruction of PIC-simulation data, using four numerical techniques, has shown that the main contribution for inaccuracy arises from replacing the Poisson equation by the Grad-Shafranov one. A boundary layer approximation, in turn, does not affect the accuracy significantly; in some cases this approach can appear even the most appropriate. </p>

Convection Heat Transfer on a Vertical Surface in Porous Media

Free convection on a vertical surface with Newtonian heating of the form proposed by Merkin (1994) in the fluid-filled porous medium is considered on the basis of the full equations of a viscous liquid. Using dimensional analysis a set of criteria that define the characteristics of flow and heat transfer was derived. Asymptotic analysis of the full equations allowed us to determine the region of applicability of the boundary layer approximation, which was used in the previous studies of this problem. Darcy parameter influence was studied; the composite numerical and analytical solution for stream function and temperature was derived.