A Mathematical Modeling of 3D Cubical Geometry Hypothetical Reservoir under the Effect of Nanoparticles Flow Rate,Porosity,and Relative Permeability

This study aims to formulate a steady-state mathematical model for a three-dimensional permeable enclosure(cavity)to determine the oil extraction rate using three distinct nanoparticles,SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3),in unconventional oil reservoirs.The simulation is conducted for different parameters of volume fractions,porosities,and mass flow rates to determine the optimal oil recovery.The impact of nanoparticles on relative permeability(kr)and water is also investigated.The simulation process utilizes the finite volume ANSYS Fluent.The study results showed that when the mass flow rate at the inlet is low,oil recovery goes up.In addition,they indicated that silicon nanoparticles are better at getting oil out of the ground(i.e.,oil reservoir)than Al_(2)O_(3)and Fe_(2)O_(3).Most oil can be extracted from SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3)at a rate of 97.8%,96.5%,and 88%,respectively.

Boundary Layer on a Moving Wall with Suction and Injection

We investigate the boundary-layer flow on a moving permeable plate parallel to a moving stream. The governing equations are solved numerically by a finite-difference method. Dual solutions are found to exist when the plate and the free stream move in the opposite directions.

Boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretching vertical surface with prescribed skin friction

The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were considered.The governing partial differential equations were transformed into a system of ordinary differential equations,which were then solved numerically using the shooting method.Results for the stretching velocity,the local Nusselt number,the temperature,and the velocity profiles are presented for various values of the mixed convection parameter λ and material parameter K when the Prandtl number is equal to 1.Both assisting（heated plate） and opposing（cooled plate） flow regions are considered.It is found that dual solutions exist for both assisting and opposing flows.

Similarity solutions for the mixed convection flow over a vertical plate with thermal radiation

The steady laminar boundary layer flow adjacent to a vertical plate with prescribed surface temperature immersed in an incompressible viscous fluid,where the effect of thermal radiation was taken into consideration,was investigated.The governing partial differential equations were transformed into a system of ordinary differential equations using similarity transformation,before being solved numerically by the shooting method.Both assisting and opposing buoyant flows were considered.It is found that dual solutions exist for both cases. Moreover,numerical results show that the heat transfer rate at the surface decreases in the presence of the radiation effect.

MHD Flow Towards a Permeable Surface with Prescribed Wall Heat Flux

The steady magnetohydrodynamic （MHD） mixed convection flow towards a vertical permeable surface with prescribed heat flux is investigated. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for the assisting flow, besides the solutions usually reported in the literature for the opposing flow.

Magnetohydrodynamic flow over a moving plate in a parallel stream with an induced magnetic field

A viscous boundary layer flow of an electrically-conducting fluid over a moving flat plate in a parallel stream with a constant magnetic field applied outside the boundary layer parallel to the plate was investigated. The goveming system of partial differential equations was transformed to ordinary differential equations using a similarity transformation. The similarity equations were then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results of the skin friction coefficient, velocity profiles, and the induced magnetic field profiles were obtained for some values of the moving parameter, magnetic parameter, and reciprocal magnetic Prandtl number. The results indicate that dual solutions exist when the plate and the fluid move in the opposite directions up to a critical value of the moving parameter, whose value depends on the value of the magnetic parameter.

Boundary Layer Stagnation-Point Slip Flow and Heat Transfer towards a Shrinking/Stretching Cylinder over a Permeable Surface

In this paper, the boundary layer stagnation-point slip flow and heat transfer towards a shrinking/stretching cylinder over a permeable surface is considered. The governing equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into self-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the velocity slip parameter (α), the thermal slip parameter (β), the curvature parameter (γ) and the velocity ratio parameter (c/a). The physical quantities of interest are the skin friction coefficient and the local Nusselt number measured by f’’(0) and –θ’(0), respectively. The numerical results show that the velocity slip parameter α increases the heat transfer rate at the surface, while the thermal slip parameter β decreases it. On the other hand, increasing the velocity slip parameter α causes the decrease in the flow velocity. Further, it is found that the solutions for a shrinking cylinder (c/ac/a>0) case. Finally, it is also found that the values of f’’(0) and –θ’(0) increase as the curvature parameter γ increases.

Mixed convection boundary layer flow pasta vertical cone embedded in a porous medium subjected to a convective boundary condition

In the present analysis,we study the steady mixed convection boundary layer flowpast a vertical cone embedded in a porous medium subjected to a convective boundarycondition.The governing partial differential equations are reduced to the coupled nonlinearordinary differential equations using a similarity transformation before being solved numeri-cally by a shooting method.Both assisting and opposing flows are considered.The influence ofthe convective heat transfer parameter is analysed and discussed through graphs.Dualsolutions are found to exist for the case of opposing flow.