Investigation of a Confined Laminar Impinging Jet on a Plate with a Porous Layer Using the Preconditioned Density-Based Algorithm

The preconditioned density-based algorithm and two-domain approach were used to investigate the fluid flow and heat transfer characteristics of a confined laminar impinging jet on a plate covered with porous layer. In the porous zone, the momentum equations were formulated by the Darcy-Brinkman-Forchheimer model; the thermal nonequilibrium model was adopted for the energy equation. At the porous/fluid interface, the applicability and influence of different hydrodynamic and thermal interfacial conditions were analyzed for the problem. The governing equations were solved by the preconditioned density-based finite-volume method, with preconditioning matrix for equations of porous domain adopted, aiming to eliminate the equation stiffness of porous seepage flows. The effects of Reynolds number, porosity, Darcy number, thermal conductivity ratio, Biot number, and porous layer thickness on the flow pattern and local heat transfer performance were studied. Results indicate that the Reynolds number and porosity don't strongly influence the flow pattern of porous channel, while the Darcy number and porous layer thickness have obvious influence on the flow pattern. The heat transfer performance are greatly influenced by the parameters studied.     

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 porous rib arrangement on heat transfer and entropy generation of nanofluid flow in an annulus using a two-phase mixture model

The effect of porous rib arrays on the heat transfer and entropy generation of laminar nanofluid flow inside annuli is studied numerically, using a two-phase mixture model for nanofluid flow simulation. Porous media, nanoparticles, and vortex formation are simultaneously affecting the characteristics of the system. Results showed that the permeability and height of porous ribs have significant effects on the thermal performance of system. Vortex zones also affect the trend of variation of entropy and performance numbers, and local optimums exist for these two parameters. The role of nanofluid in heat transfer enhancement in recirculating zones is more significant for higher volume fractions.     

Numerical Investigation of Laminar-Plate Transpiration Cooling by the Preconditioned Density-Based Algorithm

The preconditioned density-based algorithm and two-domain approach were used to investigate the laminar-plate transpiration cooling process. In the porous zone, the momentum equations were formulated by the Darcy-Brinkman-Forchheimer model; and the local thermal equilibrium model (LTE) was adopted for the energy equation. At the porous/fluid interface, the stress-continuity interfacial condition was utilized. The effects of coolant injection rate, Reynolds number, pressure gradient of mainstream, and thermal conductivity ratio on the transpiration cooling performance were studied. Results indicate that the thickness of the coolant boundary layer on the protected surface has a significant effect on the transpiration cooling effect. Under the current conditions, the transpiration cooling performance would be enhanced with increasing coolant injection rate, but would be weakened with increasing Re. The adverse pressure gradient of mainstream would improve the transpiration cooling performance.     

Numerical simulation of turbulent fluid flow and heat transfer characteristics in heat exchangers fitted with porous media

Numerical simulations have been carried out to investigate the turbulent heat transfer enhancement in the pipe filled with porous media. Two-dimensional axisymmetric numerical simulations using the k–? turbulent model is used to calculate the fluid flow and heat transfer characteristics in a pipe filled with porous media. The parameters studied include the Reynolds number (Re = 5000–15,000), the Darcy number (Da = 10^?1–10^?6), and the porous radius ratio (e = 0.0–1.0). The numerical results show that the flow field can be adjusted and the thickness of boundary layer can be decreased by the inserted porous medium so that the heat transfer can be enhanced in the pipe. The local distributions of the Nusselt number along the flow direction increase with the increase of the Reynolds number and thickness of the porous layer, but increase with the decreasing Darcy number. For a porous radius ratio less than about 0.6, the effect of the Darcy number on the pressure drop is not that significant. The optimum porous radius ratio is around 0.8 for the range of the parameters investigated, which can be used to enhance heat transfer in heat exchangers.     

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.     

Thermal analysis of a 2-D heat recovery system using porous media including lattice Boltzmann simulation of fluid flow

The present work deals with the fluid flow simulation and thermal analysis of a two-dimensional heat recovery system using porous media. A basic high-temperature flow system is considered in which a high-temperature non-radiating gas flows through a random porous matrix. The porous medium, in addition to its convective heat exchange with the gas, may absorb, emit and scatter thermal radiation. It is desirable to have large amount of radiative heat flux from the porous segment in the upstream direction (towards the thermal system). The lattice Boltzmann method (LBM) is used to simulate fluid flow in the porous medium. The gas and solid phases are considered in non-local thermal equilibrium, and separate energy equations are applied to these phases. Convection, conduction and radiation heat transfers take place simultaneously in solid phase, but in the gas flow, heat transfer occurs by conduction and convection. In order to analyze the thermal characteristics of the heat recovery system, volume-averaged velocities through the porous matrix obtained by LBM are used in the gas energy equation and then the coupled energy equations for gas and porous medium are numerically solved using finite difference method. For computing of radiative heat flux in the porous medium, discrete ordinates method is used to solve the radiative transfer equation. Finally the effect of various parameters on the performance of porous heat recovery system is studied.     

Augmentation of heat transfer from a solid cylinder wrapped with a porous layer

In the present study, the heat transfer from a porous wrapped solid cylinder is considered. The heated cylinder is placed horizontally and is subjected to a uniform cross-flow. The aim is to investigate the heat transfer augmentation through the inclusion of a porous wrapper. The porous layer is of foam material with high porosity and thermal conductivity. The mixed convection is studied for different values of flow parameters such as Reynolds number (based on radius of solid cylinder and stream velocity), Grashof number, permeability and thermal conductivity of the porous material. The optimal value of porous layer thickness for heat transfer augmentation and its dependence on other properties of the porous foam is obtained. The flow field is analyzed through a single domain approach in which the porous layer is considered as a pseudo-fluid and the composite region as a continuum. A pressure correction based iterative algorithm is used for computation. Our results show that a thin porous wrapper of high thermal conductivity can enhance the rate of heat transfer substantially. Periodic vortex shedding is observed from the porous shrouded solid cylinder for high values of Reynolds number. The frequency of oscillation due to vortex shedding is dampened due to the presence of the porous coating. Beyond a critical value of the porous layer thickness, the average rate of heat transfer approaches asymptotically the value corresponding to the case where the heated cylinder is embedded in an unbounded porous medium.     

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.     

Laminar heat transfer in a moving porous bed reactor simulated with a macroscopic two-energy equation model

This work investigates the influence of physical properties on heat transfer between the solid and fluid phases in a porous reactor, in which both the permeable bed and the working fluid move in the same direction with respect to fixed bounding walls. For simulating laminar flow and heat transfer, a two-energy equation model is applied in addition to a mechanical model. Transport equations are discretized using the control-volume method and the system of algebraic equations is relaxed via the SIMPLE algorithm. The effects of Reynolds number, solid-to-fluid velocity ratio, permeability, porosity, ratio of solid-to-fluid thermal capacity and ratio of solid-to-fluid thermal conductivity on flow and heat transport are analyzed. The laminar model is validated by means of an analytical solution. Results for concurrent laminar flow indicate that, when the speed of the solid approaches that of the fluid, the strong axial convection of the solid, as well as the reduction of the relative velocity, cause an increase in the axial length needed for thermal equilibrium between phases to occur. Longer thermal developing lengths are also found for higher permeabilities and higher porosities. For higher solid-to-fluid thermal capacities and higher solid-to-fluid thermal conductivity ratios, the temperature of the solid phase shows less axial variation regardless of its velocity in relation to the fluid phase.     

Numerical and experimental study of forced convection in graphite foams of different configurations

Forced convection heat transfer in a channel with different configurations of graphite foams is experimentally and numerically studied in this paper. The physical properties of graphite foams such as the porosity, pore diameter, density, permeability and Forchheimer coefficient are determined experimentally. The local temperatures at the surface of the heat source and the pressure drops across different configurations of graphite foams are measured. In the numerical simulations, the Navier–Stokes and Brinkman–Forchheimer equations are used to model the fluid flow in the open and porous regions, respectively. The local thermal non-equilibrium model is adopted in the energy equations to evaluate the solid and fluid temperatures. Comparisons are made between the experimental and simulation results. The results showed that the solid block foam has the best heat transfer performance at the expense of high pressure drop. However, the proposed configurations can achieve relatively good enhancement of heat transfer at moderate pressure drop.     

Interfacial heat transfer coefficient for non-equilibrium convective transport in porous media

The literature has documented proposals for macroscopic energy equation modeling for porous media considering the local thermal equilibrium hypothesis and laminar flow. In addition, two-energy equation models have been proposed for conduction and laminar convection in packed beds. With the aim of contributing to new developments, this work treats turbulent heat transport modeling in porous media under the local thermal non-equilibrium assumption. Macroscopic time-average equations for continuity, momentum and energy are presented based on the recently established double decomposition concept (spatial deviations and temporal fluctuations of flow properties). Interfacial heat transfer coefficients are numerically determined for an infinite medium over which the fully developed flow condition prevails. The numerical technique employed for discretizing the governing equations is the control volume method. Preliminary laminar flow results for the macroscopic heat transfer coefficient, between the fluid and solid phase in a periodic cell, are presented.     

Developing fluid flow and heat transfer in a channel partially filled with porous medium

A three-dimensional computational model is developed to analyze fluid flow in a channel partially filled with porous medium. In order to understand the developing fluid flow and heat transfer mechanisms inside the channel partially filled with porous medium, the conventional Navier–Stokes equations for gas channel, and volume-averaged Navier–Stokes equations for porous medium layer are adopted individually in this study. Conservation of mass, momentum and energy equations are solved numerically in a coupled gas and porous media domain along a channel using the vorticity–velocity method with power law scheme. Detailed development of axial velocity, secondary flow and temperature field at various axial positions in the entrance region are presented. The friction factor and Nusselt number are presented as a function of axial position, and the effects of the size of porous media inside the channel partially filled with porous medium are also analyzed in the present study.     

Momentum boundary layer and its influence on the convective heat transfer in porous media

Convective heat transfer in a channel filled with a porous medium has been analyzed in this paper. The flow field is analyzed considering both the inertia and solid boundary effects and the thickness of the momentum boundary layer is found as a function of the Darcy and the Reynolds number. The two-equation model is applied for the heat transfer analysis and theoretical solutions are obtained for both fluid and solid phase temperature fields. The Nusselt number is obtained in terms of the relevant physical parameters, such as the Biot number for the internal heat exchange, the ratio of effective conductivities between the fluid and solid phases, and the thickness of the momentum boundary layer. The results indicate that the influence of the velocity profile is characterized within two regimes according to the two parameters, the Biot number and the conductivity ratio between the phases. The decrease in the heat transfer due to the momentum boundary layer is 15% at most within a practical range of the pertinent parameters.     

Modeling of unsteady and steady fluid flow,heat transfer and dispersion in porous media using unit cell scale

A unit cell scale computation of laminar steady and unsteady fluid flow and heat transfer is presented for a spatially periodic array of square rods representing two-dimensional isotropic or anisotropic porous media. In the model, a unit cell is taken as a representative elementary control volume and uniform heat flux boundary conditions are imposed on the solid–fluid interface. The governing equations are discretized by means of the finite volume approach; boundaries between adjacent cells are taken to be spatially periodic. Computations obtained using the SIMPLER algorithm, are made by varying the macroscopic flow direction from 0° to 90° relative to the unit cell, and varying the Reynolds number over the range 1–10³ spanning the Darcian and the inertial flow regimes to construct a database of local flow and heat transfer resistances in terms of permeabilities, inertial coefficients, Nusselt numbers, and thermal dispersion coefficients. The resulting database is utilized in a system scale analysis of a serpentine heat exchanger, where these directional terms from the microscale analysis provide closure to the porous-continuum model.     

Enhancement of Heat Transfer with Porous/Solid Insert for Laminar Flow of a Participating Gas in a 3-D Square Duct

In recent years, porous or solid insert has been used in a duct for enhancing heat transfer in high temperature thermal equipment, where both convective and radiative heat transfer play a major role. In the present work, the study of heat transfer enhancement is carried out for flow through a square duct with a porous or a solid insert. Most of the analyses are carried out for a porous insert. The hydrodynamically developing flow field is solved using the Navier–Stokes equation and the Darcy–Brinkman model is considered for solving the flow in the porous region. The radiative heat transfer is included in the analysis by coupling the radiative transfer equation to the energy equation. The fluid considered is CO₂ with temperature dependent thermophysical properties. Both the fluid and the porous medium are considered as gray participating medium. The increase in heat transfer is analyzed by comparing the bulk mean temperature, Nusselt number, and radiative heat flux for different porous size and orientation, Reyonlds number, and Darcy number.     

Laminar conjugate mixed convection in a vertical channel with heat generating components

Conjugate mixed convection arising from protruding heat generating ribs attached to substrates (printed circuit boards) forming channel walls is numerically studied. The substrates with ribs form a series of vertical parallel plate channels. Assuming identical disposition and heat generation of the ribs on each board, a channel with periodic boundary conditions in the transverse direction is considered for analysis. The governing equations are discretised using a control volume approach on a staggered mesh and a pressure correction method is employed for the pressure–velocity coupling. The solid regions are considered as fluid regions with infinite viscosity and the thermal coupling between the solid and fluid regions is taken into account by the harmonic thermal conductivity method. Parametric studies are performed by varying the heat generation based Grashof number in the range 10⁴–10⁷ and the fan velocity based Reynolds number in the range 0–1500, with air as the working medium. Results are obtained for the velocity and temperature distributions, natural convection induced mass flow rate through the channel, the maximum temperatures in the heat sources and the local Nusselt numbers. The natural convection induced mass flow rate in mixed convection is correlated in terms of the Grashof and Reynolds numbers. In pure natural convection the induced mass flow rate varies as 0.44 power of Grashof number. The maximum dimensionless temperature is correlated in terms of pure natural convection and forced convection inlet velocity asymptotes. For the parameter values considered, the heat transferred to the working fluid via substrate heat conduction is found to account for 41–47% of the heat removal from the ribs.     

Numerical simulation of fluid flow and convection heat transfer in sintered porous plate channels

Fluid flow and convective heat transfer of water in sintered bronze porous plate channels was investigated numerically. The numerical simulations assumed a simple cubic structure formed by uniformly sized particles with small contact areas and a finite-thickness wall subject to a constant heat flux at the surface which mirrors the experimental setup. The permeability and inertia coefficient were calculated numerically according to the modified Darcy’s model. The numerical calculation results are in agreement with well-known correlation results. The calculated local heat transfer coefficients on the plate channel surface, which agreed well with the experimental data, increased with mass flow rate and decreased slightly along the axial direction. The convection heat transfer coefficients between the solid particles and the fluid and the volumetric heat transfer coefficients in the porous media predicted by the numerical results increase with mass flow rate and decrease with increasing particle diameter. The numerical results also illustrate the temperature difference between the solid particles and the fluid which indicates the local thermal non-equilibrium in porous media.     

Convection and evaporation of microlayer underneath bubbles under microgravity

The multidimensional heat transfer and fluid flow in the microlayer region below a vapor bubble formed during boiling in microgravity are investigated by numerically solving the Navier–Stokes equations with the energy equation. The flow is driven by Marangoni flow due to the surface tension gradient along the bubble surface that results from the temperature gradient. The model also includes condensation and evaporation at the bubble surface. The flow field and heat transfer are calculated for microlayer thicknesses from 0.01 mm to 10 mm to investigate the effect of microlayer thickness. The results show that the velocities are small and have only a small effect on the temperature distribution as compared to the solution for pure conduction in the liquid. Natural convection is shown to have a negligible effect on heat transfer. For less than ideal evaporative heat transfer at the bubble interface, Marangoni convection caused the heat transfer to increase several percent. The flow in the microlayer is shown to agree with the lubrication analogy only for thin, relatively flat interfaces. © 2000 Scripta Technica, Heat Trans Asian Res, 30(1): 1–10, 2001     

Influence of conjugate heat transfer on the minimization of entropy generation for forced convective flow through parallel plate channel filled with porous material

A fluid–solid conjugate heat transfer model is developed to analyze the characteristics of entropy generation for forced convective steady hydrodynamically fully developed laminar flow of a Newtonian fluid through a parallel plate channel filled with porous material by modulating the following parameters: substrate thickness, the ratio of thermal conductivity of wall to fluid, Biot number, the axial temperature gradient in the fluid, and Peclet number. The exteriors of both the walls are subjected to the thermal boundary conditions of the third kind. The mass and Brinkman momentum conservation equations in the fluidic domain and the coupled energy conservation in both the solid and fluidic domain are solved analytically using the local thermodynamic equilibrium model, so as to derive closed-form expressions for the velocity in the fluid and the temperature both in the fluid and solid walls in terms of relevant parameters. Suitable combinations of influencing factors, namely the geometric parameters of the system, fluid, flow, and substrate properties are identified for which global entropy generation rate is minimized. The findings may be helpful in the design of thermal systems frequently used in diverse engineering applications having heat transfer in the solid wall being a crucial parameter.