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.

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.

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 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.