We rigorously justify the infinite Prandtl number model of convection as the limit of the Boussinesq approximation to the Rayleigh-Bénard convection as the Prandtl number approaches infinity. This is a singular limit problem involving an initial layer.

Rapid mixing of liquids is important for most microfluidic applications. However, mixing is slow in conventional micromixers, because, in the absence of turbulence, mixing here occurs by molecular diffusion. Recent experiments show that mixing can be enhanced by generating transient flow resulting in chaotic advection. While these are planar microchannels, here we show that three-dimensional or...

Micromixers with floor-grooved microfluidic channels have been successfully demonstrated in experiment. In this work, we numerically simulated the mixing within the devices and used the obtained concentration versus channel length profiles to quantitatively characterize the process. It was found that the concentration at any given cross-section location of the microfluidic channel periodically ...

This article describes the impact of slip conditions on nanofluid flow through a stretching sheet. Nanofluids are very helpful to enhance the convective heat transfer in a boundary layer flow. Prandtl number also play a major role in controlling the thermal and momentum boundary layers. For this purpose, we have considered a model for effective Prandtl number which is borrowed by means of exper...

Achieving the fast mixing requirements posed by the chemical, biological, and life science community for confined microchannel flows remains an engineering challenge. The viscous and surface tension forces that dominate conventional micro-flows undermine fast, efficient mixing. By increasing the collisional velocity of reagent droplets, inertia can be exploited to increase mixing rates. This pa...

This paper presents and discusses the numerical simulations of transient laminar natural convection cooling of high Prandtl number fluids in cubical cavities, in which the six walls of the cavity are subjected to a step change in temperature. The effect of the fluid Prandtl number on the heat transfer coefficient is studied for three different fluids (Golden Syrup, Glycerin and Glycerin-water s...

A three-dimensional, steady, laminar shear-layer flow spatially developing under a boundary-layer approximation with mixing, chemical reaction, and imposed normal strain is analyzed. The creates counterflow that stretches the vorticity in spanwise direction. equations are reduced to two-dimensional form for three velocity components. non-reactive reactive cases of governing solved numerically, ...

We develop a multi-length scale (multi-fractal) theory for the effect of rock heterogeneity on the growth of the mixing layer of the flow of a passive tracer through porous media. The multi-fractal exponent of the size of the mixing layer is determined analytically from the statistical properties of a random velocity (permeability) field. The anomalous diffusion of the mixing layer can occur bo...

The unsteady free convection flow with thermal radiation past a vertical plate with Newtonian heating has been studied. The governing equations have been solved numerically by the implicit finite difference method of CrankNicolson's type. The variations of the fluid velocity and temperature are presented graphically. It is found that the fluid velocity decreases near the plate and it incre...