An analytical solution for free convection flow of an electrically conducting fluid in a vertical micro-porous-channel, in the existence of transversely applied magnetic-field and nonlinear Boussinesq approximation is carried out in this article. The governing equations representing stated objective are obtained and solved analytically using method of undetermiend coefficients and direct integration. Pictorial and tabularlar representions of solutions obtained are carried out, so as to ascertain the role of various governing parameters entering flow formation. During the course of numerical simulation of results, it is found that the volumetric flow rate increases with increase in Couette flow parameter, asymmetric heating parameter and suction/injection parameter but decreases with increase in nonlinear Boussinesq approximation parameter.

The study considers the case of the unequal diffusion coefficients of reactant $A$ (bulk fluid) and reactant $B$ (catalyst at the wall) with the dispersion of both nanoparticles and gyrotactic microorganisms of Erying-Powell fluid flow over a surface with non-uniform thickness in the presence of variable fluid properties and stratification. The numerical solution of the transformed governing equations is obtained by using the Runge-Kutta method and shooting techniques. The outcome of this study is that the increasing values of temperature-dependent thermal conductivity parameter lead to the augmentation of the kinetic energy which thereafter causes a significant enhancement of the fluid temperature.

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This study investigates heat absorption on free convection flow past a vertical porous pipe with mass transfer. The governing equations are the continuity, momentum, energy and diffusion equations. The equations in dimensionless form were transformed into ordinary differential equations (ODEs) and solved analytically using perturbation method. Approximate solutions for the velocity, temperature and concentration were determined. Results are presented graphically showing the effects of various parameters on the fluid flow. It is observed that the velocity becomes higher when thermal Grashof number and sustentions paramètre are increased. Also, increase in magnetic parameter, Schmidt number and Prandtl number lead to fall in the velocity of the fluid. The temperature of the fluid rises also with increase in heat generation but reduces for increased values of Prandtl number. Consequently, the concentration boundary layer decreases with increasing values of Schmidt number. Furthermore, increase in suction/injection has a retarding and accelerating effect on the velocity, temperature and concentration of the fluid respectively.

The study investigates the interaction of free convective flow with thermal radiation and variable pressure on natural convective heat and mass transfer fluid flow in porous medium. Solutions for time dependent energy, concentration and momentum equations were obtained by the perturbation series method after transforming into ordinary differential equations. The effect of various flow parameters such as: suction/injection ( δ) radiation (R ) magnetic field (M ) heat source (S ) chemical reaction ( Rc) on the skin friction, rate of heat transfer, velocity, temperature, and concentration profile influencing the physical situation were discussed with the aid of line graphs. Keywords: Thermal Radiation, Variable pressure, Perturbation, Natural Convection