H. Bararnia

Homotopy perturbation method for nonlinear MHD Jeffery-Hamel problem

The article solves the Jeffery-Hamel flow using the homotopy perturbation method, an explicit analytical solution is obtained, and the effect of external magnetic field is studied. Comparison of the obtained result with the numerical one reveals validity of the used method.

Homotopy perturbation method for motion of a spherical solid particle in plane couette fluid flow

Hes homotopy perturbation method is applied to obtain exact analytical solutions for the motion of a spherical particle in a plane couette flow. It is demonstrated that the applied analytical method is very straightforward in comparison with existing techniques. Furthermore, it is decidedly effectual in terms of accuracy and rapid convergence. The formulation of the problem is presented in the text as well as the analytical and numerical procedures. The current results can be used in different areas of particulate flows.

Application of homotopy analysis method to solve MHD Jeffery-Hamel flows in non-parallel walls

The MHD Jeffery-Hamel flows in non-parallel walls are investigated analytically for strongly nonlinear ordinary differential equations using homotopy analysis method (HAM). Results for velocity profiles in divergent and convergent channels are presented for various values of Hartmann and Reynolds numbers. The convergence of the obtained series solutions is explicitly studied and a proper discussion is given for the obtained results. Comparison between HAM and numerical solutions showed excellent agreement.

Solution of the Falkner-Skan wedge flow by HPM-Pade' method

In this paper, the temperature and velocity fields associated with the Falkner-Skan boundary-layer problem have been studied. The nonlinear boundary-layer equations are solved analytically by homotopy Perturbation method (HPM) employing Pade technique. Analytical results for the temperature and velocity of the flow are presented through graphs and tables for various values of the wedge angle and Prandtl number. It is seen that the current results in comparison with the numerical ones are in excellent agreement and the HPM-Pade solution provides a convenient way to control and adjust the convergence region of a system of nonlinear boundary-layer problems.

The Influence of Uniform Suction/Injection on Heat Transfer of MHD Hiemenz Flow in Porous Media

The steady two-dimensional laminar forced magneto-hydrodynamic (MHD) Hiemenz flow against a flat plate with variable wall temperature in a porous medium is analyzed. The transformed nonlinear boundary-layer equations are solved analytically by homotopy analysis method (HAM). Results for the velocity and temperature profiles are presented for various values of Prandtl number Pr , the Hartmann number ( M ), exponent of wall temperature ( λ ), the permeability parameter ( Ω ), and suction and injection parameter ( fw ). Increments in fw , M , and Ω increase the velocities profiles but decrease the temperature profiles. Contrarily, the increment in the Pr decreases the velocity profiles and increases the temperature profiles. The convergence of the obtained series solutions is explicitly studied and a proper discussion is given for the obtained results. Comparison between the HAM and numerical solutions showed excellent agreement.

Numerical Investigation of Laminar Mixed Convection in a Cubic Cavity by MRT-LBM: Effects of the Sliding Direction

Laminar mixed convection in a cubic cavity is studied numerically using the multi-relaxation-time (MRT) lattice Boltzmann method (LBM). The sidewalls of the cavity are thermally adiabatic, while the fixed bottom and top moving walls are maintained at uniform temperatures. Simulations are performed for various values of Richardson number (Ri), sliding angle (θ), and Reynolds number (Re). It is revealed that the Nusselt number increases for different values of Reynolds number as the moving lid angle enhances. In addition, the distribution of the local Nusselt number on the bottom wall follows the direction of the moving lid.

Synthesizing Pickering Nanoemulsions by Vapor Condensation

Nanoparticle-stabilized (Pickering) emulsions are widely used in applications such as cosmetics, drug delivery, membranes, and material synthesis. However, formulating Pickering nanoemulsions remains a significant challenge. Herein, we show that Pickering nanoemulsions can be obtained in a single step even at very low nanoparticle loadings (0.2 wt %) by condensing water vapor on a nanoparticle-infused subcooled oil that spreads on water. Droplet nuclei spontaneously submerge within the oil after nucleating at the oil-air interface, resulting in the suppression of droplet growth by diffusion, and subsequently coalesce to larger sizes until their growth is curtailed by nanoparticle adsorption. The average nanoemulsion size is governed by the competition between nanoparticle adsorption kinetics and droplet growth dynamics, which are in turn a function of nanoparticle size, concentration, and condensation time. Controlling such factors can lead to the formation of highly monodisperse nanoemulsions. Emulsion formation via condensation is a fast, scalable, energy-efficient process that can be adapted for a wide variety of emulsion-based applications in biology, chemistry, and materials science.

Boundary Layer Flows in Porous Media with Lateral Mass Flux

Solutions for free convection boundary layers on a heated vertical plate with lateral mass flux embedded in a saturated porous medium are presented using the Homotopy Analysis Method and Shooting Numerical Method. Homotopy Analysis Method yields an analytic solution in the form of a rapidly convergent infinite series with easily computable terms and contains the auxiliary parameter , which provides a simple way to adjust and control the convergence region of solution series. By suitable choice of the auxiliary parameter , reasonable solutions can be obtained for large modulus. Also, the Shooting Method is used as a numerical method for solution of the problem. The obtained solutions are compared together and admit a remarkable accuracy.