Abdelraheem M. Aly

MHD FREE CONVECTION FLOW OF A NANOFLUID PAST A VERTICAL PLATE IN THE PRESENCE OF HEAT GENERATION OR ABSORPTION EFFECTS

This work is focused on the numerical solution of steady natural convection boundary-layer flow of a nanofluid consisting of a pure fluid with nanoparticles along a permeable vertical plate in the presence of magnetic field, heat generation or absorption, and suction or injection effects. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing boundary-layer equations of the problem are formulated and transformed into a non-similar form. The obtained equations are then solved numerically by an efficient, iterative, tri-diagonal, implicit finite-difference method. Comparisons with previously published work are performed and are found to be in excellent agreement. Representative results for the longitudinal velocity, temperature, and nanoparticle volume fraction profiles as well as the local heat transfer rates for various values of the physical parameters are displayed in both graphical and tabular forms.

SIMILARITY SOLUTION FOR UNSTEADY HEAT AND MASS TRANSFER FROM A STRETCHING SURFACE EMBEDDED IN A POROUS MEDIUM WITH SUCTION/INJECTION AND CHEMICAL REACTION EFFECTS

An analysis is presented to investigate the effects of chemical reaction on unsteady free convective heat and mass transfer on a stretching surface in a porous medium. The governing partial differential equations have been transformed by a similarity transformation into a system of ordinary differential equations, which are solved numerically using an efficient tri-diagonal implicit finite-difference method. The results obtained show that the flow field is influenced appreciably by the presence of unsteadiness parameter, chemical reaction parameter, permeability parameter, and suction/injection parameter.

A stabilized incompressible SPH method by relaxing the density invariance condition

A stabilized Incompressible Smoothed Particle Hydrodynamics (ISPH) is proposed to simulate free surface flow problems. In the ISPH, pressure is evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection method. Even if the pressure is evaluated implicitly, the unrealistic pressure fluctuations cannot be eliminated. In order to overcome this problem, there are several improvements. One is small compressibility approach, and the other is introduction of two kinds of pressure Poisson equation related to velocity divergence-free and density invariance conditions, respectively. In this paper, a stabilized formulation, which was originally proposed in the framework of Moving Particle Semi-implicit (MPS) method, is applied to ISPH in order to relax the density invariance condition. This formulation leads to a new pressure Poisson equation with a relaxation coefficient, which can be estimated by a preanalysis calculation. The efficiency of the proposed formulation is tested by a couple of numerical examples of dam-breaking problem, and its effects are discussed by using several resolution models with different particle initial distances. Also, the effect of eddy viscosity is briefly discussed in this paper.

Natural Convection in a Non-Darcy Porous Cavity Filled with Cu–Water Nanofluid Using the Characteristic-Based Split Procedure in Finite-Element Method

Natural convection of Cu–water nanofluid in a differentially heated non-Darcy porous cavity was numerically investigated by using the characteristic-based split algorithm in finite element method. Effects of the various thermophysical parameters and the solid volume fraction of nanoparticle on heat transfer and fluid flow in different flow regimes were demonstrated. Although the addition of nanoparticles in the porous medium generally resulted in the higher average Nusselt number in most flow regimes, the average Nusselt number appears to decrease or stay nearly the same with increased solid volume fraction in Darcy flow regime at a high Rayleigh number and low Darcy number.

Modelling of surface tension force for free surface flows in ISPH method

Purpose – The purpose of this paper is to show how a surface tension model and an eddy viscosity based on the Smagorinsky sub‐grid scale model, which belongs to the Large‐Eddy Simulation (LES) theory for turbulent flow, have been introduced into ISPH (Incompressible smoothed particle hydrodynamics) method. In addition, a small modification in the source term of pressure Poisson equation has been introduced as a stabilizer for robust simulations. This stabilization generates a smoothed pressure distribution and keeps the total volume of fluid, and it is analogous to the recent modification in MPS.Design/methodology/approach – The surface tension force in free surface flow is evaluated without a direct modeling of surrounding air for decreasing computational costs. The proposed model was validated by calculating the surface tension force in the free surface interface for a cubic‐droplet under null‐gravity and the milk crown problem with different resolution models. Finally, effects of the eddy viscosity hav...

HEAT AND MASS TRANSFER IN STAGNATION-POINT FLOW OF A POLAR FLUID TOWARDS A STRETCHING SURFACE IN POROUS MEDIA IN THE PRESENCE OF SORET, DUFOUR AND CHEMICAL REACTION EFFECTS

This work is focused on the numerical solution of steady boundary-layer stagnation-point flow of a polar fluid towards a stretching surface embedded in porous media in the presence of the effects of Soret and Dufour numbers and first-order homogeneous chemical reaction. The governing boundary-layer equations of the problem are formulated and transformed into a self-similar form. The obtained equations are solved numerically by an efficient, iterative, tri-diagonal, implicit finite-difference method. Both assisting and opposing flow conditions are considered. Comparisons of the present numerical results with previously published work under limiting cases are performed and found to be in excellent agreement. Representative results for the fluid velocity, angular velocity, temperature, and solute concentration profiles as well as the local heat and mass transfer rates for various values of the physical parameters are displayed in both graphical and tabular forms.

Modelling of Non-Darcy Flows through Porous Media Using Extended Incompressible Smoothed Particle Hydrodynamics

In this article, a novel numerical method is presented for the simulation of non-Darcy flows through porous media by the incompressible smooth particle hydrodynamics (ISPH) method with a predictor-corrector scheme. In the ISPH algorithm, a semi-implicit velocity-correction procedure is used and the pressure is obtained by solving the pressure Poisson equation. The key point for the application to non-Darcy flows is to include porosity and drag forces of the medium (the Darcy term and the Forcheimer term) in the ISPH method. Unsteady lid-driven flow, natural convection in non-Darcy porous cavities, and natural convection at a porous medium–fluid interface are examined separately by our extended ISPH method. The results are presented with flow configurations, isotherms, and average Nusselt numbers for different Darcy numbers from 10−4 to 10−2, porosity values from 0.4 to 0.9, and Reynolds/Rayleigh numbers. The flow pattern and rate of heat transfer inside the cavity are affected by these parameters. The results demonstrate the important effect of the Darcy number on both the heat transfer rate and the flow regime. The results from this investigation are well validated and compare favorably with previously published results.

Three-Dimensional Incompressible Smoothed Particle Hydrodynamics for Simulating Fluid Flows Through Porous Structures

In this paper, a stabilized incompressible smoothed particle hydrodynamics (ISPH) method is presented in three dimensions for simulating fluid flows through porous structures. In the ISPH algorithm, a semi-implicit velocity correction procedure is utilized and the pressure is implicitly evaluated by solving pressure Poisson equation. Evaluated pressure has been improved by relaxing the density invariance condition to formulate a modified pressure Poisson equation. The effect of eddy viscosity by using a sub-particle scale turbulence model is introduced to the entire computational domain. The key point for the application to the non-Darcy flows is to include porosity and drag forces of the medium into ISPH method. Modified density of particles according to their porosity is introduced to satisfy continuity criteria in ISPH method. Tracking free surface with Dirichlet boundary condition is modified for the free surface flows in the porous structure. In this study, different numerical tests for fluid flows through porous structures have been simulated. Also, the results from this investigation are well validated and have favorable comparisons with the experimental results.

Modeling of multi-phase flows and natural convection in a square cavity using an incompressible smoothed particle hydrodynamics

Purpose – Modeling of multi-phase flows for Rayleigh-Taylor instability and natural convection in a square cavity has been investigated using an incompressible smoothed particle hydrodynamics (ISPH) technique. In this technique, incompressibility is enforced by using SPH projection method and a stabilized incompressible SPH method by relaxing the density invariance condition is applied. The paper aims to discuss these issues. Design/methodology/approach – The Rayleigh-Taylor instability is introduced in two and three phases by using ISPH method. The author simulated natural convection in a square/cubic cavity using ISPH method in two and three dimensions. The solutions represented in temperature, vertical velocity and horizontal velocity have been studied with different values of Rayleigh number Ra parameter (103=Ra=105). In addition, characteristic based scheme in Finite Element Method is introduced for modeling the natural convection in a square cavity. Findings – The results for Rayleigh-Taylor instabi...

Analysis of unsteady mixed convection in lid-driven cavity included circular cylinders motion using an incompressible smoothed particle hydrodynamics method

Purpose – The purpose of this paper is to model mixed convection in a square cavity included circular cylinders motion using an incompressible smoothed particle hydrodynamics (ISPH) technique. Design/methodology/approach – The problem is solved numerically by using the ISPH method. Findings – The SPH tool shows robust performance to simulate the rigid body motion in the mixed convective flow with heat transfer, and it may apply easily to complicated problems in 2D and 3D problem without difficulties. Originality/value – The application of the SPH method to mixed convective flow with heat transfer and its potential application easily to complicated 3D problems is original.