An analysis of the Poiseuille-Couette flow of two immiscible fluids between inclined parallel plates is investigated. One of the fluids is assumed to be electrically conducting while the other fluid and channel walls are assumed to be electrically insulating. The viscous and Ohmic dissipation terms are taken into account in the energy equation. The coupled nonlinear equations are solved both analytically valid for small values of the product of Prandtl number and Eckert number (= ) and numerically valid for all . Solutions for large  reveal a marked change on the flow and rate of heat transfer. The effects of various parameters such as Hartmann number, Grashof number, angle of inclination, ratios of viscosities, widths and thermal conductivities are presented and discussed in detail.

In this paper, the effect of thermal radiation, variable viscosity and variable thermal conductivity on the flow and heat transfer of a thin liquid film over an unsteady stretching sheet is analyzed. The continuity, momentum and energy equations, which are coupled nonlinear partial differential equations, are reduced to a set of two non-linear ordinary differential equations, before being solved numerically. Results for the skin-friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. It is found that increasing the viscosity parameter leads to a rise in the velocity near the surface of the sheet and a fall in the temperature. Furthermore, it is shown that the temperature increases due to an increase in the values of the thermal conductivity parameter and the thermal radiation parameter, while it decreases with an increase of the Prandtl number.

An analysis is performed to the study of the momentum, heat and mass transfer of a viscous fluid-saturated porous medium past an impermeable, non-isothermal stretching sheet with internal heat generation or absorption and chemical reaction. The governing partial differential equations are converted into ordinary differential equations by means of a similarity transformation. Exact solutions of velocity components together with the pressure distribution, which can not be found in the boundary layer theory, are obtained analytically; in addition, the temperature and concentration functions are given in terms of confluent hypergeometric functions. The velocity, temperature (concentration) profiles and thermal characteristics at the sheet for relevant parameters are plotted, tabulated and discussed.

Convective flow and heat transfer in an inclined channel bounded by two rigid plates is studied, where the lower plate is fixed and upper plate is moving with a constant velocity. One of the regions filled with clear viscous fluid and the other region filled with the porous matrix saturated with a viscous fluid different from the fluid in the first region are considered. The coupled nonlinear equations are mainly solved numerically using finite difference method. It is found that the presence of porous matrix in one of the region reduces the velocity and temperature. Both the velocity and temperature profiles enhance as the values of buoyancy parameter GP, height ratio h, Brinkman number Br, density ratio n and thermal expansion ratio b increase but reduce as the values of porous parameter , viscosity ratio  and thermal conductivity ratio  T increase. The Nusselt numbers at upper plate diminish as GP, h and Br increase, whereas they increase as ,  and  T increase. The lower plate Nusselt numbers are reversely affected by the relevant parameters. The effect of  and GP on shear stress profiles are drawn and discussed.

The solutions for flow and heat transfer in a steady laminar boundary layer flow are presented analytically for an electrically conducting viscoelastic fluid, subject to a transverse uniform magnetic field, past a semi-infinite stretching sheet. The temperature profiles and thermal characteristics at the wall are drawn and tabulated for selected parameters with prescribed surface temperature (PST) and prescribed surface heat flux (PHF) conditions. We also give the asymptotic solutions for temperature when the Prandtl number is very large. It is found that the inclusion of Joule heating has a significant influence on the thermal characteristics at the wall and the wall heat transfer strongly depends on the Prandtl number Pr as well as the Eckert number Ec. The heat flow may transfer from the fluid to the wall when Ec is large rather than from wall to the fluid when Ec is small. A physical argument about the thermal characteristics at the wall is proposed.