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The homotopy analysis method (HAM) with two auxiliary parameters is employed to examine heat and mass transfer in a steady two-dimensional magneto hydrodynamic viscoelastic fluid flow over a stretching vertical surface by considering Soret and Dufour effects. The two-dimensional boundary-layer governing partial differential equations are derived by considering the Boussinesq approximation. The highly nonlinear ordinary differential forms of momentum, energy, and concentration equations are obtained by similarity transformation. These equations are solved analytically in the presence of buoyancy force. The effects of different involved parameters such as magnetic field parameter, Prandtl number, buoyancy parameter, Soret number, Dufour number, and Lewis number on velocity, temperature, and concentration profiles are plotted and discussed. The effect of the second auxiliary parameter is also illustrated. Results show that the effect of increasing Soret number or decreasing Dufour number tends to decrease the velocity and temperature profiles (increase in Sr cools the fluid and reduces the temperature) while enhancing the concentration distribution.

The applications of nanotechnology in oilfields have attracted the attention of researchers to nanofluid injection as a novel approach for enhanced oil recovery. To better understand the prevailing mechanisms in such new displacement scenarios, micromodel experiments provide powerful tools to visually observe the way that nanoparticles may mobilize the trapped oil. In this work, the effect of silicon oxide nanoparticles on the alteration of wettability of glass micromodels was investigated in both experimental and numerical simulation approaches. The displacement experiments were performed on the original water-wet and imposed oil-wet (after aging in stearic acid/n-heptane solution) glass micromodels. The results of injection of nanofluids into the oil-saturated micromodels were then compared with those of the water injection scenarios. The flooding scenarios in the micromodels were also simulated numerically with the computational fluid dynamics (CFD) method. A good agreement between the experimental and simulation results was observed. An increase of 9% and 13% in the oil recovery was obtained by nanofluid flooding in experimental tests and CFD calculations, respectively.

Describing matrix-fracture interaction is one of the most important factors for modeling natural fractured reservoirs. A common approach for simulation of naturally fractured reservoirs is dual-porosity modeling where the degree of communication between the low-permeability medium (matrix) and high-permeability medium (fracture) is usually determined by a transfer function. Most of the proposed matrix-fracture functions depend on the geometry of the matrix and fractures that are lumped to a factor called shape factor. Unfortunately, there is no unique solution for calculating the shape factor even for symmetric cases. Conducting fine-scale modeling is a tool for calculating the shape factor and validating the current solutions in the literature. In this study, the shape factor is calculated based on the numerical simulation of fine-grid simulations for single-phase flow using finite element method. To the best of the author's knowledge, this is the first study to calculate the shape factors for multidimensional irregular bodies in a systematic approach. Several models were used, and shape factors were calculated for both transient and pseudo-steady-state (PSS) cases, although in some cases they were not clarified and assumptions were not clear. The boundary condition dependency of the shape factor was also investigated, and the obtained results were compared with the results of other studies. Results show that some of the most popular formulas cannot capture the exact physics of matrix-fracture interaction. The obtained results also show that both PSS and transient approaches for describing matrix-fracture transfer lead to constant shape factors that are not unique and depend on the fracture pressure (boundary condition) and how it changes with time.

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An analytical strong method, the homotopy analysis method (HAM), is employed to study the mixed convective heat transfer in an incompressible steady two-dimensional viscoelastic fluid flow over a wedge in the presence of buoyancy effects. The two-dimensional boundary-layer governing partial differential equations (PDEs) are derived by the consideration of Boussinesq approximation. By the use of similarity transformation, we have obtained the ordinary differential nonlinear (ODE) forms of momentum and energy equations. The highly nonlinear forms of momentum and energy equations are solved analytically. The effects of different involved parameters such as viscoelastic parameter, Prandtl number, buoyancy parameter, and the wedge angle parameter, which is related to the exponentmof the external velocity, on velocity and temperature distributions are plotted and discussed. An excellent agreement can be seen between the results and the previously published papers forf′′(0)andθ′(0)in some of the tables and figures of the paper for velocity and temperature profiles for various values of viscoelastic parameter and Prandtl number. The effects of buoyancy parameter on the velocity and temperature distributions are completely illustrated in detail.

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