Thermal instability in a horizontal layer of nanofluid with vertical AC electric field in a porous medium is investigated. The flux of volume fraction of nanoparticles is taken to be zero on the isothermal boundaries and the eigenvalue problem is solved using the Galerkin method. Darcy model is used for the momentum equation. The model used for nanofluid incorporates the effect of Brownian diffusion and thermophoresis.Linear stability theory based upon normal mode technique is employed to find the expressions for Rayleigh number for stationary and oscillatory convection. Graphs have been plotted to study the effects of Lewis number, modified diffusivity ratio, concentration Rayleigh number, AC electric Rayleigh number and porosity on stationary convection.

Diffusion problems are nonlinear partial differential problems of parabolic type with diffusion coefficient as a function of fluid flow in a porous medium. Usually this coefficient is unknown. In this paper, the one phase flow of fluid in porous medium is modeled and the existence and uniqueness of porous medium problem is proved.

Double-diffusive convection in a micro polar fluid layer heated and soluted from below in the presence of uniform rotation saturating a porous medium is theoretically investigated. An exact solution is obtained for a flat fluid layer contained between two free boundaries. To study the onset of convection, a linear stability analysis theory and normal mode analysis method have been used. For the case of stationary convection, the effect of various parameters like medium permeability, solute gradient, rotation and micro polar parameters (i.e. coupling, spin diffusion, micro polar heat conduction and micro polar solute parameters arising due to coupling between spin and solute fluxes) have been analyzed. The critical thermal Rayleigh numbers for various values of critical wave numbers (found by Newton Raphson method) for the onset of instability are determined numerically and depicted, graphically. The oscillatory modes were introduced due to the presence of the micro polar viscous effects, micro inertia, rotation and stable solute gradient, which were non-existence in their absence. The principle of exchange of stabilities is found to hold true for the micro polar fluid saturating a porous medium heated from below in the absence of micro polar viscous effect, micro inertia, rotation and stable solute gradient. An attempt was also made to obtain sufficient conditions for the nonexistence of overstability.

In this article, two-dimensional laminar-forced convection nanofluids flow over a stretching surface in a porous medium has been studied. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved numerically by the fourth order Runge–Kutta integration scheme featuring a shooting technique. Different models of nanofluid based on different formulas for thermal conductivity and dynamic viscosity are used. Different types of nanoparticles as copper, silver, alumina and titanium Oxide with water and Ethylene glycol as their base fluids has been considered. The influence of significant parameters such as nanoparticle volume fraction, kind of nanofluid, Magnetic parameter and Reynolds number on the flow and heat transfer characteristics is discussed. The influence of significant parameters such as Thermal conductivity parameter, volume fraction of the nanoparticles, Permeability parameter, suction/injection parameter and Velocity ratio parameter on the flow and heat transfer characteristics is discussed. It was found that choosing Titanium oxide as the nanoparticle and Ethylene glycol as base fluid proved to have the highest cooling performance for this problem.

Porous media has interesting features in compared with free flame combustion due to the extended of the lean flammability limits and lower emissions. Advanced new generation of internal combustion (IC) engines are expected to have far better emissions levels both gaseous and particulate matter, at the same time having far lower fuel consumption on a wide range of operating condition. These criteria could be improved having a homogeneous combustion process in an engine. Present work considers simulation of direct fuel injection in an IC engine equipped with a chemically inert porous medium (PM), having cylindrical geometry that is installed in cylinder head to homogenize and stabilize the combustion process.A numerical study of a 3D model, PM engine is carried out using a modified version of the KIVA-3V code.Since there is not any published material for PM-engines in literature, the numerical results for combustion waves propagation within PM are compared with experimental data available in the literature for a lean mixture of air and methane under filtration in packed bed, the accuracy of results are very promising. For PM-engine simulation the methane fuel is injected directly through a hot PM which is mounted in cylinder head. Therefore volumetric combustion occurs as a result within PM and in-cylinder. The effects of injection timing on mixture formation, pressure and temperature distribution in both phases of PM and in cylinder fluid together with combustion emissions such as CO and NO are studied in detail for an important part of the cycle.

A free convective unsteady visco-elastic flow through porous medium of variable permeability bounded by an infinite vertical porous plate with variable suction, constant heat flux under the influence of transverse uniform magnetic field has been investigated in the present study. The permeability of porous medium fluctuates with time about the constant mean. Approximate solutions for mean velocity, transient velocity, mean temperature and transient temperature of non-Newtonian flow and skin friction are obtained. The effects of various parameters such as Pr (Prandtl number), Gr (Grashof number), M (Hartmann number),  w (frequency parameter) and k0 (mean permeability parameter) on the above are depicted, skin friction, amplitude and phase are shown graphically and discussed. Expressions for fluctuating parts of velocity ‘Mr’ and ‘Mi’ are found and plotted graphically, effects of different parameters on them are discussed.