M. Xiong

Thermally developing forced convection in a porous medium: parallel plate channel with walls at uniform temperature, with axial conduction and viscous dissipation effects

Abstract A modified Graetz methodology is applied to investigate the thermal development of forced convection in a parallel plate channel filled by a saturated porous medium, with walls held at uniform temperature, and with the effects of axial conduction and viscous dissipation included. The Brinkman model is employed. The analysis leads to expressions for the local Nusselt number, as a function of the dimensionless longitudinal coordinate and other parameters (Darcy number, Peclet number, Brinkman number).

Effect of local thermal non-equilibrium on thermally developing forced convection in a porous medium

Abstract The classical Graetz methodology is applied to investigate the effect of local thermal non-equilibrium on the thermal development of forced convection in a parallel-plate channel filled by a saturated porous medium, with walls held at constant temperature. The Brinkman model is employed. The analysis leads to an expression for the local Nusselt number, as a function of the dimensionless longitudinal coordinate, the Peclet number, the Darcy number, the solid–fluid heat exchange parameter, the solid/fluid thermal conductivity ratio, and the porosity.

Thermally Developing Forced Convection in a Porous Medium: Circular Duct with Walls at Constant Temperature, with Longitudinal Conduction and Viscous Dissipation Effects

A modified Graetz methodology is applied to investigate the thermal development of forced convection in a circular duct filled by a saturated porous medium, with walls held at constant temperature, and with the effects of longitudinal conduction and viscous dissipation included. The Brinkman model is employed. The analysis leads to expressions for the local Nusselt number, as a function of the dimensionless longitudinal coordinate and other parameters (Darcy number, Péclet number, Brinkman number).

EFFECTS OF THERMAL DISPERSION AND TURBULENCE IN FORCED CONVECTION IN A COMPOSITE PARALLEL-PLATE CHANNEL: INVESTIGATION OF CONSTANT WALL HEAT FLUX AND CONSTANT WALL TEMPERATURE CASES

In this article, a composite parallel-plate channel whose central portion is occupied by a clear fluid and whose peripheral portion is occupied by a fluid saturated porous medium, is considered. The flow in the porous region of the channel is assumed to be laminar, governed by the Brinkman-Forchheimer-extended Darcy equation, while the flow in the clear fluid region of the channel is assumed to be turbulent. The validity of this laminar/turbulent assumption is validated by estimating Reynolds numbers in the clear fluid and porous regions of the channel. Although the flow in the porous region remains laminar, it is still fast enough for the quadratic drag (Forchheimer) effects to be important. In this situation, hydrodynamic mixing of the interstitial fluid at the pore scale becomes important and may cause significant thermal dispersion. It is shown that thermal dispersion may result in some counterintuitive effects, such as the increase of the Nusselt number when the width of the clear fluid region in the center of the channel is decreased.

Numerical simulation of the effect of thermal dispersion on forced convection in a circular duct partly filled with a Brinkman‐Forchheimer porous medium

A numerical simulation of the fully developed forced convection in a circular duct partly filled with a fluid saturated porous medium is presented. The Brinkman‐Forchheimer‐extended Darcy equation is used to describe the fluid flow in the porous region. The energy equation for the porous region accounts for the effect of thermal dispersion. The dependence of the Nusselt number on a number of parameters, such as the Reynolds number, the Darcy number, the Forchheimer coefficient, as well as the thickness of the porous region is investigated. The numerical results obtained in this research are in agreement with published experimental data.

Development of an engineering approach to computations of turbulent flows in composite porous/fluid domains

Abstract The purpose of this paper is to develop an engineering approach to computations of turbulent flows in composite domains partly occupied by a clear fluid and partly by a fluid saturated porous medium. Previous research concerning turbulent flows in porous media indicates that the effect of porous media is to dampen turbulence. Therefore, in porous/fluid domains the penetration depth of turbulent eddies into the porous region is expected to be small. The authors suggest assuming that the flow over the whole porous region remains laminar and matching turbulent flow solution in the clear fluid region with the laminar flow solution in the turbulent flow region. Although the flow in the porous region is assumed to be laminar, linear Darcy or Brinkman–Darcy models cannot be utilized to describe momentum transport in the porous region because of large filtration velocity. The momentum transport model in the porous layer utilized in this research is based on the Brinkman–Forchheimer-extended Darcy equation, which allows the accounting for deviation from linearity and also allows a smooth matching of the filtration velocity at the porous/fluid interface. Because of the large filtration velocity in the porous region, the energy equation in the porous region also accounts for the thermal dispersion effects.

Effect of evaporation on thin film deposition in dip coating process

Abstract Evaporation from the free surface is an important phenomenon that occurs during dip coating process. Accounting for evaporation is crucial for correct prediction of film thickness during this process when evaporation rate is large. This paper suggests a method to extend the classical free meniscus theory to account for evaporation from the free surface in a two-component system. The governing equations are solved utilizing a finite difference method. The effects of evaporation on the free surface profile and solute concentration distribution are investigated.

Dependence of microporosity formation on the direction of solidification

Abstract The aim of this paper is to suggest a new approach in the investigation of the effect of gravity on microporosity formation in solidification of binary alloys. Instead of traditional unidirectional solidification from the bottom, which involves solidification against the gravity, we suggest to carry out solidification from the top, which involves solidification along the gravity. Numerical modeling performed in this paper suggests an experimental study that compares the results of these two experiments, which potentially reveals some important data concerning the influence of gravity on microporosity formation and also could be used as a tool for validation of microporosity formation models.

Comparison between Lever and Scheil Rules for Modeling of Microporosity Formation during Solidification

Segregation and microporosity formation are two important physicalphenomena that occur during solidification of binary alloys. The aim ofthis study is to investigate the effect of the model of solute diffusionat the local scale (which means at the local scale of the microscopicrepresentative elemental average volume (REV)) on solute transport andthe microporosity formation during this process. The Scheil rule and thelever rule are used to describe the solute diffusion at the local scale.Results indicate that solute diffusion at the local scale is animportant factor in microporosity formation. Also, microporosityformation slightly reduces inverse segregation because it partiallycompensates for shrinkage. The increase of the external pressure at thefree surface or the decrease of the initial hydrogen concentration inthe molten alloy can be effectively utilized to control microporosityformation.