Analysis of fluid flow and heat transfer in a channel with staggered porous blocks

Fluid flow and heat transfer characteristics in a channel with staggered porous blocks were numerically studied in this paper. The Navier–Stokes and Brinkman–Forchheimer equations were used to model the fluid flow in the open and porous regions, respectively. Coupling of the pressure and velocity fields was resolved using the SIMPLER algorithm. The local thermal equilibrium model was adopted in the energy equation to evaluate the solid and fluid temperatures. The effect of Darcy number, Reynolds number, porous block height and width on the velocity field were studied. In addition, the effects of the above parameters as well as the thermal conductivity ratio between the porous blocks and the fluid on the local heat transfer were analyzed. The pressure drops across the channel for different cases were discussed. The results show that the flow behavior and its associated local heat transfer are sensitive to the variation of the above parameters. It is predicted by the present study that an increase in the thermal conductivity ratio between the porous blocks and the fluid results in significant enhancement of heat transfer at the locations of the porous blocks.     

Numerical investigation of pressure drop reduction without surrendering heat transfer enhancement in partially porous channel

The present study is to investigate the numerical simulation of steady laminar forced convection in a partially porous channel, with four dissimilar porous-blocks, attached to the strip heat sources at the bottom wall. The analysis is based on the Navier–Stokes equation in the fluid field, the Darcy–Brinkman–Forchheimer flow model in the porous field, and the energy equations for two thermal fields. The effects of variations of different parameters such as porous blocks Darcy numbers, arrangements of dissimilar blocks, Forchheimer coefficient, Reynolds number, thermal conductivity and Prandtl number are investigated and the velocity and temperature fields are presented and discussed. In the dissimilar partially porous channel, it is found that when the blocks sorted from the lowest to the highest Da in the flow direction, the total heat transfer enhancement is almost the same as in the similar porous channel (Nu/Nu_sim = 92%), while the total pressure drop is considerably lower (P/P_sim = 28%). In addition, reverse arrangement of porous blocks is suggested to prepare more uniform temperature gradient in all heat sources.     

Mass transfer of viscous gas flow over porous stretching/shrinking sheet in the presence of slip and mass transpiration

The effect of the mass transpiration parameter on the viscous gas flow past a porous stretching/shrinking sheet in the presence of Navier's slip is investigated, and also, the mass transfer characteristics are examined. The physical flow problem executes the Navier–Stokes and the mass equation, which forms the system of nonlinear partial differential equations. These are transformed via similarity variables into a system of ordinary differential equations. The slip flow model of the total mass transfer on the moving sheet is modeled by introducing gas slip velocity. The total mass transfer on the moving sheet is modeled by inducing slip models of first and second order. Further, the suction which induces the slip velocity as opposed to the surface movement is examined. The mass suction-induced slip forces the adjacent gases to flow in the reverse direction to sheet movement. Thus, the solution space expands with the slip-induced suction and sheet movement. In the mass injection case, the induced slip increases the effect of the fluid flow for sheet movement. Upon all previous flow models, the present investigation is significant due as it investigates the mass transfer of viscous gasses flow past a porous medium in the presence of slip and mass transpiration.     

Chemical reacting transport phenomena in a PEM fuel cell

A three-dimensional mathematical model for the PEM fuel cell including gas channel has been developed to simulate fuel cell performance. A set of conservation equations and species concentration equations are solved numerically in a coupled gas channel and porous media domain using the vorticity-velocity method with power law scheme. Detailed development of axial velocity and secondary flow fields are presented at various axial locations. Polarization curves are demonstrated by solving the equations for electrochemical reactions and the membrane phase potential. Compared with experimental data from published literatures, numerical results of this model agree closely with experimental results.     

Unsteady natural convection from a horizontal annulus filled with a porous medium

The unsteady natural convection flow from a horizontal cylindrical annulus filled with a non-Darcy porous medium has been studied. The unsteadiness in the problem arises due to the impulsive change in the wall temperature of the outer cylinder. The Navier–Stokes equations along with the energy equation governing the unsteady natural convection flow have been solved by the finite-volume method. The effect of time variation on the heat transfer is more pronounced only in a small time interval immediately after the start of the impulsive motion and the steady state is reached after certain time. The results show that the annulus completely filled with a porous medium has the best insulating effectiveness. Convection in the horizontal annulus is confined mostly at top and bottom regions. Hence, only these regions should be insulated. In case of annulus partially filled with a porous material, insulating the region near the outer cylinder is more effective than insulating the region near the inner cylinder. The effect of Darcy number on the heat transfer is more pronounced than that of the Grashof number.     

Stratified Poiseuille gas flows in horizontal channels

The present short communication shows an exact solution of the Navier–Stokes equations in the case of a channel filled with gas and with temperature contrast between the boundaries. This exact solution is then compared with the result of a numerical simulation made using a numerical code widely used in fire safety engineering. It shows the ability of the code to reproduce this highly stratified flow. Nusselt numbers are then estimated.     

Pulsating hydromagnetic flow of Casson fluid in a vertical channel filled with non-Darcian porous medium

This paper analyzes the Joule heating, Dufour number, and Soret number effects on hydromagnetic pulsatile flow of a Casson fluid in a vertical channel filled with a non-Darcian porous medium. The governing partial differential equations (PDEs) of the Casson fluid flow are transformed to ordinary differential equations (ODEs) using perturbation technique and solved by employing shooting method with Runge–Kutta (R–K) fourth-order technique using MATHEMATICA function NDSolve. The influence of Forchheimer number, Casson fluid parameter, Dufour number, radiation parameter, and Soret number on flow variables has been studied and the numerical results obtained are presented. The results reveal that the velocity rises with the rise of Darcy number, whereas it decreases for a given rise in the Forchheimer number. Furthermore, the temperature distribution enhances by increasing the Dufour number.     

A note on heat transfer to MHD oscillatory flow in an asymmetric wavy channel

This note deals with the MHD oscillatory flow of an optically thin fluid in an asymmetric wavy channel filled with porous medium. Based on some simplifying assumptions, the governing momentum and energy equations are solved and analytical solutions for fluid velocity, temperature distribution, Nusselt number and skin friction are constructed. The effects of radiation parameter, Peclet number, Hartmann number, porous medium shape factor and geometric parameters on flow and heat transfer characteristics have been examined in detail.     

Numerical Investigation of Nanofluid Mixed‐Convection Flow in the Entrance Region of a Vertical Channel Partially Filled with Porous Medium

In this article, transient two‐dimensional mixed convection of nanofluids in the entrance region of a vertical channel has been studied carefully. The geometry under consideration consisted of a parallel‐plate channel partly filled with a porous medium with a constant wall temperature. In the free flow region, the two‐dimensional flow field has been governed by the Navier–Stokes equations. The general formulation of the momentum equations accounting for the inertial and the viscous effects in the presence of a porous medium has been used. Viscous dissipation effects have also been incorporated in the thermal energy equation. Effects of Brownian diffusion and thermophoresis have also been included for nanoparticles in the nanofluid. The governing equations have been given in terms of the stream function‐vorticity formulation and have been non‐dimensionalized and then solved numerically subject to appropriate boundary conditions. The characteristics of the flow and temperature fields have been presented in the terms of mixed‐convection parameter (GR), Brinkman number (Br), Darcy number (Da), Lewis number (Le), and other important parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 607–627, 2014; Published online 21 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21099     

Model of a porous regenerator used for magnetic refrigeration at room temperature

A transient three-dimensional model of a porous regenerator operating at room temperature is presented. The solid magnetic material and the regeneration fluid are modeled separately. The fluid flows through interstitial channels formed by a regular matrix of solid particles. The velocity, pressure and temperature fields are obtained from the simultaneous solution of the Navier–Stokes and energy equations with variable properties in the solid and the Boussinesq approximation for the fluid. The magnetocaloric effect (MCE) is taken into account by the inclusion of a source term in the energy equation for the magnetic solid. Special numerical schemes are used to avoid unrealistic computation time and memory requirements. Typical velocity fields and transient temperature profiles are presented.     

Numerical study on the formation of Taylor bubbles in capillary tubes

Numerical simulations have been carried out for the transient formation of Taylor bubbles in a nozzle/tube co-flow arrangement by solving the unsteady, incompressible Navier–Stokes equations. A level set method was used to track the two-phase interface. The calculated bubble size, shape, liquid film thickness, bubble length, drift velocity, pressure drop and flow fields of Taylor flow agree well with the literature data. For a given nozzle/tube configuration, the formation of Taylor bubbles is found to be mainly dependent on the relative magnitude of gas and liquid superficial velocity. However, even under the same liquid and gas superficial velocities, the change of nozzle geometry alone can drastically change the size of Taylor bubbles and the pressure drop behavior inside a given capillary. This indicates that the widely used flow pattern map presented in terms of liquid and gas superficial velocities is not unique.     

Flow simulation in an electrostatic precipitator of a thermal power plant

The performance of electrostatic precipitator (ESP) is significantly affected by its complex flow distribution arising as a result of its complex inside geometry. In the present study the gas flow through an ESP used at a local thermal power plant is modeled numerically using computational fluid dynamics (CFD) technique to gain an insight into the flow behavior inside the ESP. CFD code FLUENT is used to carry out the computations. Numerical calculations for the gas flow are carried out by solving the Reynolds-averaged Navier–Stokes equations coupled with the k–ε turbulence model equations. The results of the simulation are discussed and compared with on-site measured data supplied by the power plant. The predicted results show a reasonable agreement with the measured data. The model developed is a novel tool for the thermal power plant to predict the effect of possible modifications made to the ESP design on the flow pattern.     

Heat,mass, and crystal growth of GaN in the ammonothermal process: A numerical study

ABSTRACT

This paper presents a computational model for the ammonothermal gallium nitride (GaN) crystal growth process, including fluid flow, heat transfer, dissolution and crystallization rates, GaN metastable phase transport, and crystal interface advancement. The presented article solves the Navier–Stokes equations along with the Brickman–Darcy–Forchheimer extensions for nutrient porous medium and Boussinesq approximation for free convection. Piecewise Linear Interface Calculation (PLIC) method is adopted to construct and advance the crystal interface. Simulations, in particular, were performed for a common research autoclave with a retrograde ammonothermal system. Special attention is given to the regions close to the crystal interface.     

Three‐dimensional multiphase flow model to study channel flow dynamics of PEM fuel cells

A three‐dimensional multiphase flow model has been developed to study dynamics of a water droplet on the surface of the channel of proton exchange membrane fuel cell. Results are presented based on solving full Navier–Stokes equations for Newtonian liquids. The volume‐of‐fluid method is used to numerically determine the deformation of free surfaces. Water droplet and channel fluid properties determine whether the droplet deforms and remain stationary or disintegrate. We have shown the dependency of the water flooding to the flow rate and pressure drop in the channel has been introduced as a tool to determine water flooding in the channel. Copyright © 2010 John Wiley & Sons, Ltd.     

Characterization of Exhaust Sensors Through Modeling of Multi-Component Gas Transport and Reaction

Transport and reaction of gas mixtures in porous media are common phenomena in many chemical engineering applications. One common method of modeling the transport processes is to notionally substitute a uniform bundle of tortuous capillaries for the irregular porous structure. Then, accurate equations of motion for the gas flow and diffusion inside these small-sized capillaries can be used. This advantage comes at the cost of two additional parameters that enter into the equations, the tortuosity factor and the equivalent capillary diameter. In this work, an existing model for transient transport of multi-component gas mixtures is expanded to comprise heterogeneous fluid domains and chemical reaction. It can be applied to fluid domains that partially or completely enclose porous regions. The potential of the present model is demonstrated by simulating the electrochemically induced and transport-limited signal formation inside an exhaust gas sensor.     

Turbulent flow in a channel occupied by a porous layer considering the stress jump at the interface

For hybrid media, involving both a porous structure and a clear flow region, difficulties arise due to the proper mathematical treatment given at the interface. The literature proposes a jump condition in which shear stresses on both sides of the interface are not of the same value. This paper presents numerical solutions for such hybrid medium, considering here a channel partially filled with a porous layer through which fluid flows in turbulent regime. One unique set of transport equations is applied to both regions. Effects of Reynolds number, porosity, permeability and jump coefficient on mean and turbulence fields are investigated. Results indicate that depending on the value of the stress jump parameters, a substantially different structure for the turbulent field is obtained.     

Microchannel heat transfer and dispersion of nanoparticles in slip flow regime with constant heat flux

If the hydrodynamic diameter of a channel is comparable with the mean free path of the gas molecules moving inside the channel, the fluid can no longer be considered to be in thermodynamic equilibrium and a variety of non-continuum or rarefaction effects can occur. To avoid enormous complexity and extensive numerical cost encountered in modeling of nonlinear Boltzmann equations, the Navier–Stokes equations can be solved considering the concepts of slip flow regime and applying slip velocity boundary conditions at the solid walls.     

Enhancement of forced-convection cooling of multiple heated blocks in a channel using porous covers

A numerical study was carried out for enhanced heat transfer from multiple heated blocks in a channel by porous covers. The flow field is governed by the Navier–Stokes equation in the fluid region, the Darcy–Brinkman–Forchheimer equation in the porous region, and the thermal field by the energy equation. Solution of the coupled governing equations is obtained using a stream function-vorticity analysis. This study details the effects of variations in the Darcy number, Reynolds number, inertial parameter, and two pertinent geometric parameters, to illustrate important fundamental and practical results. The results show that the recirculation caused by porous-covering block will significantly enhance the heat transfer rate on both top and right faces of second and subsequent blocks.     

Natural convection in divided trapezoidal cavities filled with fluid saturated porous media

A numerical work was performed to determine the heat transfer and fluid flow due to buoyancy forces in divided trapezoidal enclosures filled with fluid saturated porous media. In the present investigation, bottom wall was non-uniformly heated while two vertical walls were insulated and the top wall was maintained at constant cold temperature. The divider had constant thermal conductivity. Flow patterns and temperature distribution were obtained by solving numerically the governing equations, using Darcy's law. Results are presented for different values of the governing parameters, such as Rayleigh number for a porous medium, location of the partition, thickness of the partition and thermal conductivity ratio between solid and fluid media. It was observed that the conduction mode of heat transfer became dominant inside the cavity for higher thickness of the partition, low Rayleigh numbers, and low thermal conductivity ratio.     

Forced Convection Analysis of Discrete Heated Porous Convergent Channel

This study investigates numerically forced convection heat transfer and flow analyses of a passive heat exchanger for nonporous and partially filled porous channels with varying exit height (1, 0.5, and 0.25). Four discrete heat sources with uniform heat flux are simulated on the channel bottom wall. The partially filled porous channels are tested at two different porous block heights (0.5 and 1). The flow field and thermal analyses inside the channels are investigated across a wide range of Reynolds and Darcy numbers for Prandtl number of 0.71. The results reveal that the porous block and the exit height affect substantially the flow and heat transfer characteristics inside the tested channels. The Nusselt number is enhanced by 20–40% for the partially filled porous convergent channel (exit height = 0.25 and porous block height = 1) compared to the nonporous channel. Consequently, the heat exchanger size can be reduced by 37.5%. Moreover, the overall heat transfer performance parameter is enhanced with further increase in Darcy number at low Reynolds number. As a result, compact heat exchangers that provide superior heat transfer coefficients lead to development of macro- and microelectronic devices.