Using porous inserts to enhance heat transfer in laminar fully-developed flows

The objective of this work is to investigate if it is possible to use porous inserts to enhance heat transfer in rectangular channels. A mathematical model that includes inertia and viscous effects is used to determined the velocity profile in the porous region. For the fluid region, momentum transfer is modeled using the Navier-Stokes equation. These equations and the energy equations are solved numerically via a finite-difference method. Heat transfer between the channel walls and the fluid is determined as a function of Darcy number, inertia parameter, ratio of the fluid and porous medium thermal conductivities, and the porous insert thickness. It is shown that heat transfer could be enhanced by placing a porous insert in the channel. Moreover, for some conditions heat transfer is maximized by using a porous insert thinner than the channel height while a porous insert that completely fills the channel is needed for other conditions.     

Simulation of laminar flow and convective heat transfer in conduits filled with porous media using Lattice Boltzmann Method

In the present work, laminar flow and convective heat transfer between two parallel plates of a conduit were simulated using Lattice Boltzmann Method (LBM). The conduit core was filled with a porous medium fully and partially. The effect of porous medium was considered by introducing the porosity into the equilibrium distribution. Viscous and inertia flow resistance effects of porous medium were incorporated in the form of force terms in the Boltzmann's equation. To simulate the temperature field, a simplified thermal lattice BGK model with doubled population method was employed. Comparing the results of the present study to the analytical solutions, a reasonable agreement was observed. The effects of various parameters like Darcy number, porous medium thickness, etc. on the conduit thermal performance were investigated. It was found that all these parameters had significant influence on thermal performance of the channel in certain conditions.     

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.     

Transient and non-Darcian effects on natural convection flow in a vertical channel partially filled with porous medium: Analysis with Forchheimer–Brinkman extended Darcy model

The present study addresses the transient as well as non-Darcian effects on laminar natural convection flow in a vertical channel partially filled with porous medium. Forchheimer–Brinkman extended Darcy model is assumed to simulate momentum transfer within the porous medium. Two regions are coupled by equating the velocity and shear stress in the case of momentum equation while matching of the temperature and heat flux is taken for thermal energy equation. Approximate solutions are obtained using perturbation technique. Variations in velocity field with Darcy number, Grashof number, kinematic viscosity ratio, distance of interface and variations in temperature distribution with thermal conductivity ratio, distance of interface are obtained and depicted graphically. The skin-friction and rate of heat transfer at the channel walls are also derived and the numerical values for various physical parameters are tabulated.     

Flow control with electrode bank arrangements by electrohydrodynamics force for heat transfer enhancement in a porous medium

Active flow control with electrohydrodynamics (EHD) force in the channel flow has been numerically investigated for enhancing heat transfer. This study focuses on the effect of electrode bank arrangements and the number of electrodes on corona wind and fluid flow for heat transfer onto a porous medium. Aligned and staggered configurations of electrode banks are compared. The numerical results show that electric field intensity depends on electrical voltage and the number of electrodes. Shear flow is increased with larger numbers of electrodes and in the aligned configuration, resulting in the enhancement of vortex strength. The swirling flow from staggered configurations spread wider than that of aligned configurations, but the aligned configuration produced more turbulence. In addition, the temperature distribution in the channel flow is increased with increasing numbers of electrodes. With the effect of swirling flow, airflow above the porous sample surface is faster leads the heat to more transfer to the porous sample surface. This causes the temperature of porous medium to increase rapidly so the convective heat transfer coefficient on porous medium surface is increased. Finally, the modified case of the numerical results is validated against the experimental results. The experimental flow visualization is based on the incense smoke technique, in order to verify the accuracy of the swirling flow pattern subjected to the electric field. It is shown that the comparison results in both techniques are in good agreement.     

Experimental study of mixed convection heat transfer in a vertical duct filled with metallic porous structures

This paper reports the results of an experimental investigation to examine the potential of a simple and inexpensive porous insert developed specifically for augmenting heat transfer from the heated wall of a vertical duct under forced flow conditions. The porous insert used in the study consists of a stack of metallic perforated plates filled inside the duct. The characteristic features of the porous medium model on the hydrodynamic and heat transfer behavior have been investigated. The porous medium model developed in the present study shows thermo- hydrodynamic performance similar to those seen in metal foams. A correlation has been developed for predicting the Nusselt number from the geometry under consideration. The key novelty in the present work is the development of a new correlation for the Nusselt number that does not require any information from hydrodynamic studies. Over the range of parameters considered, the largest increase in the average Nusselt number of 4.52 times that for clear flow is observed with a porous material of porosity of 0.85.     

Numerical Analysis of Flow and Thermal Performance of Liquid-Cooling Microchannel Heat Sinks with Bifurcation

Single-phase liquid-cooling microchannels have received great attention to remove the gradually increased heat loads of heat sinks. Proper changes of the flow path and/or heat transfer surface can result in much better thermal performance of microchannel heat sinks. In this study, a kind of rectangular straight microchannel heat sink with bifurcation flow arrangement has been designed, and the corresponding laminar flow and heat transfer have been investigated numerically. Four different configurations are considered. The effects of the bifurcation ratio (the initial channel number over the bifurcating channel number) and length ratio (the channel length before bifurcation over the bifurcation channel length) on laminar heat transfer, pressure drop, and thermal resistance are considered and compared with those of the traditional straight microchannel heat sink without bifurcation flow. The overall thermal resistances subjected to inlet Reynolds number and pumping power are compared for the five microchannel heat sinks. Results show that the thermal performance of the microchannel heat sink with bifurcation flow is better than that of the corresponding straight microchannel heat sink. The heat sinks with larger bifurcation ratio and length ratio provide much better thermal performance. It is suggested to employ bifurcation flow path in the liquid-cooling microchannel heat sinks to improve the overall thermal performance by proper design of the bifurcation position and number of channels.     

Thermal convection in a horizontal porous layer with spatially periodic boundary temperatures: small Ra flow

This study considers a small Rayleigh number thermal convection in a fluid-saturated porous medium between two infinite-horizontal walls. The lower and upper walls have sinusoidal temperature distributions with a wave number and a phase difference, and the effect of the parameters on the flow and heat transfer characteristics is investigated. For a given wave number, an out-of-phase configuration yields minimum heat transfer at the walls. Maximum heat transfer occurs at the wave number of 2.286 with an in-phase configuration.     

An experimental and numerical study on heat transfer enhancement for gas heat exchangers fitted with porous media

The present experimental and numerical work investigates the effect of metallic porous materials, inserted in a pipe, on the rate of heat transfer. The pipe is subjected to a constant and uniform heat flux. The effects of porosity, porous material diameter and thermal conductivity as well as Reynolds number on the heat transfer rate and pressure drop are investigated. The results are compared with the clear flow case where no porous material was used. The results obtained lead to the conclusion that higher heat transfer rates can be achieved using porous inserts at the expense of a reasonable pressure drop. Also, it is shown that for an accurate simulation of heat transfer when a porous insert is employed its effective thermal conductivity should be carefully evaluated.     

Effects of a porous medium on forced convection of a reciprocating curved channel

Enhancement of heat transfer rates of a reciprocating curved channel partially installed by a porous medium is investigated numerically. The distribution of heat transfer rates on the heat surface of the reciprocating curved channel is rather non-uniform that easily causes a thermal damage to destroy the channel. A method of using the porous medium to enhance heat transfer rates of the channel is then developed to solve the thermal damage. The arbitrary Lagrangian–Eulerian method is firstly modified for treating a moving boundary problem of the porous medium. Main parameters of Reynolds numbers, porosities, frequencies and amplitudes are examined. The results show that the enhancements of heat transfer rates of most porous medium situations are achieved. However, heat transfer rates of a few porous medium situations are unexpectedly inferior to those of without porous medium situations.     

Heat transfer with laminar forced convection in a porous channel exposed to a thermal asymmetry

The effect of thermal asymmetry on laminar forced convection heat transfer in a plane porous channel with Darcy dissipation has been investigated numerically. The parallel plates making the channel boundaries were kept at constant, but different temperatures. The thermal asymmetry thus imposed on the system, results in an asymmetric temperature field and different heat fluxes across the channel boundaries. Depending on Darcy, Peclét and Reynolds number, the thermal asymmetry may lead to a reversal of the heat flux at a certain position along the flow at least at one of the channel walls. The corresponding Nusselt numbers become zero and might experience discontinuities thereby jumping from infinite positive to infinite negative, or vice versa. This feature is observed not only in the region of thermal development, but also in the fully developed region. In the fully developed region, an analytical expressions for the Nusselt numbers were obtained. From these expressions, analytical equations were deduced for the calculations of the axial positions along the channel where the Nusselt numbers become zero, or experiences discontinuity.     

Forced convection in a channel partly occupied by a bidisperse porous medium: Asymmetric case

This paper presents an analytic investigation of forced convection in parallel-plate channel partly occupied by a bidisperse porous medium and partly by a fluid clear of solid material, the distribution being asymmetrical. The walls of the channel are subject to an uniform heat flux; the flow is assumed to be hydrodynamically and thermally fully developed. The layer of a bidisperse porous medium is attached to one of the channel walls; it is modeled utilizing a two-velocity two-temperature formulation using Darcy’s law. The Beavers–Joseph boundary condition is employed at the bidisperse porous medium/clear fluid interface. The dependences of the Nusselt number on a conductivity ratio, a velocity ratio, a volume fraction, internal heat exchange parameter, and the position of the porous-fluid interface are investigated. Both cases of symmetric and asymmetric heating are investigated, which is specified by the asymmetry heating parameter introduced here. For the case of asymmetric heating, a singular behavior of the Nusselt number is found and explained.     

Experimental investigation of a new thermal energy storage system using thermo‐sensitive magnetic fluid and porous medium

In this paper, a novel thermal energy storage (TES) system based on a thermo‐sensitive magnetic fluid (MF) in a porous medium is proposed to store low‐temperature thermal energy. In order to have a better understanding about the fluid flow and heat‐transfer mechanism in the TES system, four different configurations, using ferrofluid as the basic fluid and either copper foam or porous carbon with different porosity (90 and 100 PPI, respectively) as the packed bed, are investigated experimentally. Furthermore, two thermal performance parameters are evaluated during the heat charging cycle, which are thermal storage velocity and thermal storage capacity of the materials under a range of magnetic field strength. It is shown that heat conduction is the primary heat‐transfer mechanism in copper foam TES system, while magnetic thermal convection of the magnetic fluid is the dominating heat‐transfer mechanism in the porous carbon TES. In practical applications in small‐scale systems, the 90‐PPI copper foam should be selected among the four porous materials because of its cost efficiency, while porous carbon should be used in industrial scale systems because of its sensitivity to magnetic field and cost efficiency.     

Conjugate heat transfer in channels with heat-conducting inclined fins

Conjugate heat transfer in a finned channel with equally spaced fins placed transversely to the flow direction following in-line and staggered arrangements is evaluated. The fins and channel walls are heat-conducting and are fully coupled to a turbulent fluid flow problem. The hydrodynamic and thermal effects of the fin blockage ratio, fin angle, and flow velocity were investigated. The simulations show that the fin arrangement is of paramount importance on the performance of the heat exchanger: the staggered fin configuration provided lower pressure drop and higher heat transfer rate than the in-line fin arrangement for different flow conditions.     

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.     

Discharge improvement of a phase change material-air-based thermal energy storage unit for space heating applications using metal foams in the air sides

This study examines the energy discharge of a phase-changing material (PCM)-based air heat exchanger using a metal foam inside the heat transfer fluid (HTF) channel. Such systems have various potential applications in the heating space and building ecosystem. Thermal energy storage (TES) often utilizes air as the HTF, which limits the heat transfer performance due to the low thermal conductivity. This paper aims to address this drawback via incorporating a metal foam into the HTF channel to enhance the thermal performance between the heat transfer fluid (air) and the PCM, which is considered as the novel side of this study. The combined system is mathematically modeled with an symmetrical, three-dimensional computational fluid dynamics method for various flow rates and inlet temperatures of the HTF with different geometric parameters of the metal foam. This study indicates the advantage of utilizing the porous medium in the air channel. The results show the HTF flow rate has a great influence on the discharging rate. The presence of the porous medium in the system improves the discharging process by 116% compared with a non-porous medium system at the same flow rate. The discharging time decreases by increasing the porosity, and the value of 90% is found as the best porosity value at the flow rate of 0.005 kg/s in this system. The solidification rate is proportional to the pore density because of the surface area impacts of the porous medium, also the pressure-drop and the pumping required are highly affected by the mentioned dependent parameters.     

Experimental investigation of heat transfer in a triple tube heat exchanger with coiled spring inserts

Experiments have been performed to investigate the effect of coiled spring inserts on heat transfer, pressure drop, and performance parameters of a triple tube heat exchanger (TTHX). Three different spring inserts having a pitch of 5, 10, and 15 mm are used and the diameter of the spring wire is taken as 1 mm. The experiments were carried out under a turbulent flow regime, with water as a working medium in parallel and counter flow configurations. The variation in different performance characteristics like heat transfer coefficient, Nusselt number, and effectiveness have been compared at various Reynolds numbers ranging between 4000 and 16,000 in the considered flow patterns. The Nusselt number of TTHX with the lowest pitch spring is found to be higher than that of the plain TTHX by 57.27% at Re = 4000 for the counter flow configuration. Both the thermal performance factor and effectiveness increased as the pitch of the spring insert was decreased. The effectiveness of TTHX with the lowest pitch spring insert is found higher than that of the plain TTHX by 43.84% in the counter flow pattern.     

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.     

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.     

Hot Dates

For this article, an analytical study has been conducted on the flow and energy transfer of unsteady compressible oscillating flow through channels filled with porous medium representing stack in thermoacoustic engines/refrigerators. The flow in the porous material is described by the Darcy momentum equation. Analytical expressions for oscillating velocity, temperature in the porous layer, complex Nusselt number, and energy flux density are obtained after simplifying and solving the governing differential equations with reasonable approximations (such as long wave, short stack, small amplitude oscillation, etc.). The result for heat transfer between the porous medium and the channel wall is expressed as a dimensionless Nusselt number. For the limiting case of nonporous medium, the Nusselt number obtained in the present study matches quantitatively with the expression available in the existing literature. The results reveal that the Nusselt number in oscillating flow is significantly enhanced (almost an order of magnitude) by employing sufficiently large thermal conductivity of porous media in a channel. The system of equations developed in the present study is a helpful tool for thermal engineers to design porous stacks for thermoacoustic devices.