Effect of Darcy,Reynolds, and Prandtl Numbers on the Performance of Two‐Phase Flow Heat Exchanger Filled with Porous Media

Experimental investigation of two‐phase laminar forced convection in a single porous tube heat exchanger is presented. The effect of Darcy, Reynolds, and Prandtl numbers on the performance of this heat exchanger during the condensation process of carbon dioxide at different test conditions were investigated. Gravel sand with different porosities is used as a porous medium. The flow in the porous medium is modeled using the Brinkman–Forchheimer‐extended Darcy model. Parametric studies are also conducted to evaluate the effects of porosity and Reynolds and Prandtl numbers on the heat transfer coefficient and the friction factor. A dimensionless performance parameter is developed in order to be used in evaluating the porous tube heat exchanger based on both the heat transfer enhancement and the associated pressure drop. The study covers a wide range of inlet pressure (P_in), mass flow rate (), porosity of gravel sand (ε), and Darcy number (Da) which ranged: 34.5 ≤ P_in ≤ 43 bars, 8 * 10^{? 5} ≤ ≤ 16 * 10^{? 5} kg/s, 34.9% ≤ ε ≤ 44.5%, 1.6 * 10^{? 6} ≤ Da ≤ 5 * 10^{? 6}, respectively. The study predicted the combined effect of the Reynolds number, Darcy number, porosity, and Prandtl number on the heat transfer and pressure drop of carbon dioxide during the condensation process in a porous medium. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21117     

Appropriate position of porous insert in a heat exchanger by thermohydraulic analysis

This paper presents numerically an appropriate position of a porous insert to get a better thermohydraulic performance from a porous heat exchanger. The simulation is based on the Darcy‐Brinkman‐Forchheimer model in the porous field. Two‐dimensional continuity, momentum, and energy equations with incompressible, laminar, steady assumptions have been solved using a finite volume approach. The analysis is performed for different values of porous layer thickness, length, and porosity at a fixed value of Reynolds number (Re = 100) and thermal conductivity ratio (Rc = 5). The results showed that there is about a 48% and 13% reduction in pressure drop and Nusselt number, respectively, by decreasing horizontal porous substrate thickness from 1 to 1/2 for δ_v = 1/3 at ε = 0.7. As a result, the pressure drop reduces considerably with a reasonable reduction in heat transfer rate by decreasing horizontal porous substrate thickness from 1 to 1/2.     

Mixed convection on jet impingement cooling of a constant heat flux horizontal porous layer

In the present study, numerical investigation of jet impingement cooling of a constant heat flux horizontal surface immersed in a confined porous channel is performed under mixed convection conditions, and the Darcian and non-Darcian effects are evaluated. The unsteady stream function-vorticity formulation is used to solve the governing equations. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Reynolds number (1 ≤ Re ≤ 1000), modified Grashof number (10 ≤ Gr¹ ≤ 100), half jet width (0.1 ≤ D ≤ 1.0), Darcy number (1 × 10^?6 ≤ Da ≤ 1 × 10^?2), and the distance between the jet and the heated portion (0.1 ≤ H ≤ 1.0). It is found that the average Nusselt number (Nu_avg) increases with increase in either modified Grashof number or jet width for high values of Reynolds number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. The average Nusselt number decreases with the increase in Da for the non-Darcy regime when Re is low whereas Nu_avg increases when Re is high. It is shown that mixed convection mode can cause minimum heat transfer unfavorably due to counteraction of jet flow against buoyancy driven flow. Minimum Nu_avg occurs more obviously at higher values of H. Hence the design of jet impingement cooling through porous medium should be carefully considered in the mixed convection regimes.     

Multiobjective optimization of free convection through a nonuniform cabinet filled with porous media

In the current study, multiobjective optimization and numerical simulation were used to evaluate free convection through a nonuniform cabinet, which has several technical applications, such as cooling techniques, solar air collectors, and heat sinks. The new aspect of the current study is to compute the maximum free convection within an irregular L-shaped cavity filled with porous media using both computational analysis and response surface methodology (RSM). Moreover, the impacts of constant coefficients, such as aspect ratios of the horizontal (AR_h), vertical (AR_v), and Darcy numbers (Da) on the Nusselt number (Nu_ave), Nusselt number maximization (NNM), the temperature of the surface (Ts), and entropy (S) are studied and discussed to evaluate their effect on the thermal performance. The results showed that when Da, AR_h, and AR_v increase, Nu_ave improves while the Ts and S decline and the largest desirability is achieved at AR_h = 0.9, AR_v = 0.9, and Da = 10⁻¹. Additionally, when compared with the subpar design data, the largest gain in NNM was 26.7 times, while the biggest decreases in surface temperature and entropy were 59% and 97%, respectively. As a result, the combination of the numerical simulation and RSM study produces a novel strategy and insightful suggestions for the ideal cooling L-shaped cabinet design.     

Analytical investigation of heat transfer enhancement in a channel partially filled with a porous material under local thermal non-equilibrium condition

Forced convection through a channel partially filled with a porous medium is investigated analytically in the present work. Thermally developed condition is considered and the local thermal non-equilibrium model is utilized to obtain the exact solutions of both fluid and solid temperature fields for flow inside the porous material as well as for flow in the clear region. Nusselt number is obtained in terms of the porous insert thickness (S), porosity (?) as well as pertinent parameters such as thermal conductivity ratio (k), Biot number (Bi), and Darcy number (Da). The values of S by which the temperature difference between the two phases approach to zero, for different values of Bi, k, and Da number are obtained. It is found that three mechanisms affect the Nu number i: clear fluid conduction ii: internal heat exchange in the porous medium iii: channeling effect in the clear flow. The value of S, which yields the highest Nu number is found to vary linearly from 0.8 to 0.97 as the value of Da decreases from 10⁻³ to 10⁻⁷. At the expense of reasonable pressure drop the optimum thickness of porous material in order to enhance the heat transfer rate is found S = 0.8.     

Thermoconvective instability in a horizontal porous cavity saturated with cold water

The onset of convection in a horizontal porous cavity with regard to the density maximum of water at 3.98°C is studied using a linear stability analysis. In the formulation of the problem use is made of the Brinkman-extended Darcy model which is relevant to sparsely packed porous media. A parabolic density-temperature relationship is used to model the effect of density inversion. The perturbation equations are solved with the aid of the Galerkin and finite element methods. The onset of motion is found to be dependent of the aspect ratio A of the cavity, the Darcy number Da, the inversion parameter γ and the hydrodynamic boundary conditions applied on the horizontal walls of the porous layer. The results for a viscous fluid (Da→∞) and the Darcy porous medium (Da→0) emerge from the present analysis as limiting cases. Numerical results for finite amplitude convection, obtained by solving the full governing equations, indicate that subcritical convection is possible when the upper stable layer extends over more than the half depth. Also, the existence of multiple solutions for a given range of governing parameters is demonstrated.     

Forced Convection of Metallic Foam Heat Sink under Laminar Slot Jet Confined by Parallel Wall

This investigation numerically explores the fluid flow and heat transfer characteristics of the metallic foam heat sink under the laminar slot jet confined by a parallel wall. The Prandtl number is 0.7, and the range of Reynolds numbers is 100–500. The parameters of interest in this work are the porosity (?), pore density (PPI), effective solid conductivity (k _s *), jet nozzle width (W), ratio of the porous sink length to the jet nozzle width (L/W), ratio of the jet-to-sink distance to the jet nozzle width (C/W), and ratio of the porous sink height to the jet nozzle width (H/W). The simulation data reveal that the Nusselt number of the system with a metallic porous heat sink was much better than that of the system without a porous sink, for a given volumetric flow rate and value of (C+H)/W. The porous properties (such as ? and k _s *) and the system configurations (such as L/W and H/W) strongly influenced the cooling performance. The effect of the PPI, W, and C/W values on the heat transfer characteristics of the system was negligible. The effect of the fluid flow on the thermal results was examined. Finally, the correlations of the stagnation Nusselt number and the average Nusselt number were also determined using the numerical data for a system with the size of a common multi-chips module.     

Non-Darcian Effects on the Mixed Convection Heat Transfer in a Metallic Porous Block with a Confined Slot Jet

The present numerical investigation addresses non-Darcian effects on the mixed convection heat transfer in a metallic porous block with a confined slot jet. The generalized model of the momentum equation, which is also known as the Forchheimer-Brinkman extended Darcy model, was used in representing the fluid motion inside the porous layer. The local thermal equilibrium condition was assumed to be valid for the range of the thermophysical parameters considered in the present investigation. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used was ascertained by comparing our results with previously published results. Our results revealed that the heat transfer performance of the slot jet was 2.4 times as large as that without the presence of a porous block. In addition, the average Nusselt number was found to increase with a decrease in porosity and an increase in the thermal conductivity ratio. The present results illustrate that the average Nusselt number increases with a decrease in the dimensionless height of the porous layer up to H _porous =  0.05 , after which the Nusselt number decreases.     

Thermal analysis of a metal foam subject to jet impingement

The present study conducted a thermal analysis on a FeCrAlY foam subjected to jet impingement cooling in a horizontal channel. The temperature distribution of the metal foam is captured with infrared thermography imaging camera for different jet velocities (219.5 ≤ Pe ≤ 548.9). Two dimensional numerical studies have been conducted to obtain the temperature contour of the metal foam and compared to the thermographic images. The thermographic images show inconsistencies in temperature variation across the metal foam due to the porosity within the metal foam. The temperature contours of the metal foam obtained numerically are found to be similar to the thermographic images. The top portion of the metal foam directly impinged by the jet of low velocities shows lowest temperature, but the heat near the heated surface is transferred majorly through conduction.     

Entropy generation due to natural convection in discretely heated porous square cavities

Optimization of industrial processes for higher energy efficiency may be effectively carried out based on the thermodynamic approach of entropy generation minimization (EGM). This approach provides the key insights on how the available energy (exergy) is being destroyed during the process and the ways to minimize its destruction. In this study, EGM approach is implemented for the analysis of optimal thermal mixing and temperature uniformity due to natural convection in square cavities filled with porous medium for the material processing applications. Effect of the permeability of the porous medium and the role of distributed heating in enhancing the thermal mixing, temperature uniformity and minimization of entropy generation is analyzed. It is found that at lower Darcy number (Da), the thermal mixing is low and the heat transfer irreversibility dominates the total entropy generation. In contrast, thermal mixing is improved due to enhanced convection at higher Da. Friction irreversibility is found to dominate the total entropy generation for higher Prandtl number (Pr) fluids at higher Da, whereas the heat transfer irreversibility dominates the total entropy generation for lower Pr fluids. Based on EGM analysis, it is established that larger thermal mixing at high Darcy number may not be always recommended as the total entropy production is quite large at high Darcy number. Overall, it is found that the distributed heating methodology with multiple heat sources may be an efficient strategy for the optimal thermal processing of materials.     

Experimental study on the effect of porous medium on performance of a single tube heat exchanger: A CO2 case study

An experimental study on single‐phase laminar forced convection in a single porous tube heat exchanger is presented. Parametric studies are conducted for different inlet pressures, different mass flow rates, and different porosities to evaluate the effects of particle diameter and Reynolds number on the heat transfer and friction factor. The Nusselt number and friction factor are developed for efficient design of a porous heat exchanger based on the present configuration. Heat is transferred to the walls of the heat exchanger by natural convection mode. Gravel sand with different porosities is used as a porous medium during the tests. The flow of carbon dioxide as a working fluid in the porous medium is modeled using the Brinkman–Forchheimer‐extended Darcy model. A dimensionless performance parameter is developed in order to be used in evaluating the porous tube heat exchanger based on both the heat transfer enhancement and the associated pressure drop. The study covers a wide range of inlet pressures (P_i), mass flow rates ( ), porosity of gravel sand (ε), and particle diameters (d_m) which ranged 34.5 ≤ P_i ≤ 43 bars, 8 ?? 10^?5 ≤ ≤ 16 ?? 10^?5 kg/s, 34.9% ≤ ε ≤ 44.5%, 1.25 ≤ d_m ≤ 5.15 mm, respectively. This study revealed that a smaller particle diameter can be used to achieve higher heat transfer enhancement, but a larger particle diameter leads to a more efficient performance based on heat transfer enhancement. The average heat transfer coefficient of carbon dioxide decreases when the porosity increases. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21059     

Evaluation of Turbulence Models in the Prediction of Heat Transfer Due to Slot Jet Impingement on Plane and Concave Surfaces

The performance of several turbulence models in the prediction of convective heat transfer due to slot jet impingement onto flat and concave cylindrical surfaces is evaluated against available experimental data. The candidate models for evaluation are (1) the standard k – ε model, (2) the RNG k – ε model, (3) the realizable k – ε model, (4) the SST k – ω model, and (5) the LRR Reynolds stress transport model. Various near-wall treatments such as equilibrium wall function and two-layer enhanced wall treatment are used in combination with these turbulence models. The computations are performed using the commercial computational fluid dynamics (CFD) code Fluent. From the validation exercises, it is found that when the impingement surface is outside the potential core of the jet, most of the turbulence models predict reasonably accurate thermal data (local Nusselt number variation along the impingement surface). When the impingement surface is within the potential core of the jet, the turbulence models grossly overpredict the Nusselt number in the impingement region, but in the wall jet region the Nusselt number prediction is fairly accurate. Overall, the RNG k – ε model with the enhanced wall treatment and the SST k – ω model predict the Nusselt number distribution better than the other models for the flat plate as well as for the concave surface impingement cases. However, the hydrodynamic data such as the mean velocity profiles are not accurately predicted by the SST k – ω model for the concave surface impingement case, whereas the RNG k – ε model predictions of the velocity profiles agree very well with the experiment. The Reynolds stress model does not show any distinctive advantage over the other eddy viscosity models.     

Non‐Darcy assisted flow along a channel with an open cavity filled with water–TiO2 nanofluid

Numerical investigation on forced (assisted) convection heat transfer in a two‐dimensional horizontal porous channel with an open cavity is studied in this article. A non‐uniform heat flux is considered to be located on the bottom surface of the cavity. The rest of the surfaces are taken to be perfectly insulated. The physical domain is filled with a water‐based nanofluid containing TiO₂ nanoparticles. The fluid enters from the left and exits from the right with initial velocity U_i and temperature T_i. Governing equations are discretized using the penalty finite element method. The simulation is carried out for a wide range of Reynolds number Re (= 10–500) and Darcy number Da (= 10^?5–∞). Results are presented in the form of streamlines, isothermal lines, local and average Nusselt numbers, average temperatures of the fluid, horizontal and vertical velocities at mid‐height of the channel and mean velocity fields for various Re and Da. The enhancement of heat transfer rate is caused by the increasing Re and falling Da. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21046     

Natural convection cooling process from two identical porous-covering electronic components

In the present work, we focus to study numerically the natural convection cooling process from two identical electronic components located on the bottom wall of a two-dimensional cavity. Each electronic component is covered by a porous medium with finite thickness. The conservation equations governing the problem are discretized using the finite volume method and the SIMPLER algorithm is used to handle the nonlinear character of conservation equations. Calculations were carried out for the following control parameters: the porous/fluid thermal conductivity ratio (1 ≤ Rk_P1 ≤ 100), the Darcy and Rayleigh numbers (10⁻¹ ≤ Da ≤ 10⁻⁶, 10³ ≤ Ra ≤ 10⁶), the first porous-cover thickness (0.05 ≤ e₁ ≤ 0.3), and the separation distance between components (0.2 ≤ S ≤ 1) to highlight their influence on the cooling process. The results show that under specific values of the Darcy and Rayleigh numbers and in the limiting case of a high value of the porous/fluid thermal conductivity ratio (Rk_P1 = 100), a decrease in the maximum components temperature, up to 95%, is observed by increasing the porous-cover thickness from 0.05 to 0.3. In addition, by increasing the permeability, the Rayleigh number or the separation distance, an improvement in the cooling process of the two components greater than or equal to 22% is achieved.     

Computational analysis of gas permeability of slip flow through microannulus replete by based-circular Sierpinski porous medium

There are wide applications for flow in a microporous medium. In this study, a computational analysis of airflow through a porous microannulus constructed by circular-based Sierpinski has been performed in a slip flow regime, where several parameters played an important role in the flow characteristics. These parameters are the Knudsen number, the average friction factor, radius ratio, and porosity. The impacts of these parameters on permeability and the gas flow characteristics are examined and analyzed thoroughly. The ranges of the investigated parameters are as follows (0.001 ≤ Kn ≤ 0.1 and the porosity range is 0.75 ≤ ε ≤ 0.95). The results showed that porosity has a significant impact on the velocity distribution and Darcy number. The Knudsen number has also a direct effect on the velocity distribution, while it has a positive logarithmic proportionality with a dimensionless permeability but the radius ratio does have a neglected effect on the Darcy number. Moreover, the effect of the average friction factor has an inverse proportional relationship to the Darcy number.     

Natural convection in metal foams with open cells

This paper presents a combined experimental and numerical study on natural convection in open-celled metal foams. The effective thermal conductivities of steel alloy (FeCrAlY) samples with different relative densities and cell sizes are measured with the guarded-hot-plate method. To examine the natural convection effect, the measurements are conducted under both vacuum and ambient conditions for a range of temperatures. The experimental results show that natural convection is very significant, accounting for up to 50% of the effective foam conductivity obtained at ambient pressure. This has been attributed to the high porosity (ε > 0.9) and inter-connected open cells of the metal foams studied.Morphological parameters characterizing open-celled FeCrAlY foams are subsequently identified and their cross-relationships are built. The non-equilibrium two-equation energy transfer model is employed, and selected calculations show that the non-equilibrium effect between the solid foam skeleton and air is significant. The study indicates that the combined parameter, i.e., the porous medium Rayleigh number, is no longer appropriate to correlate natural convection by itself when the Darcy number is sufficiently large as in the case of natural convection in open-celled metal foams. Good agreement between model predictions and experimental measurements is obtained.     

Analysis of entropy generation during natural convection in porous enclosures with curved surfaces

The natural convection is analyzed via the entropy generation approach in the differentially heated, porous enclosures with curved (concave or convex) vertical walls. The numerical simulations have been carried out for various fluids (Prandtl number: Pr_m?=?0.015, 0.7, and 7.2) at various permeabilities (Darcy numbers: 10^?5?≤?Da_m?≤?10^?2) for a high value of Rayleigh number (Ra_m?=?10⁶). The finite element method is employed to solve the governing equations and that is further used to calculate the entropy generation and average Nusselt number. The detailed spatial distributions of S_θ and S_ψ are analyzed for all the wall curvatures. Overall, the case with the highly concave surfaces (case 3) is the optimal case at low Da_m, whereas the cases with the less convex surfaces (cases 1 and 2) are the most efficient cases at high Da_m.     

Lattice Boltzmann method for nanofluid forced convection heat exchange in a porous channel with multiple heated sources

Abstract

The nanofluid forced convection heat exchange in a porous channel within three heated blocks was numerically investigated using the Nonorthogonal multiple-relaxation time lattice Boltzmann method (MRT-LBM). The effects of various parameters such as nanoparticle volume fraction (?), Darcy number (Da) on heat exchange performance and flow phenomena were analyzed when the Pecklel number (Pe), the Prandtl number (Pr), and porosity (ε) were 25, 5.829 and 0.3, respectively. The outcome showed that the mean Nusselt number (Nu) on the surface of heated sources remarkably improved by adding nanoparticles. Furthermore, the forced convection heat exchange of the fluid flow in the mainstream area and the heat conduction in the liquid retention zone had a conspicuous influence on the heat-transfer properties. It is worth noting that the forced convection heat transfer of the fluid flow dominates heat exchange. The simulation showed that the average surface Nusselt number on the heated blocks and the heat exchange performance declined with the increase of the Darcy number.     

Heat transfer enhancement in rectangular channels with axial ribs or porous foam under through flow and impinging jet conditions

Heat transfer and pressure loss characteristics of a high aspect ratio duct are measured under both, jet impingement and channel flow conditions, respectively. For both cases, roughness elements in consideration are staggered and inline axial ribs. The spacing (P) to height (e) ratios studied are P/e = 2 and P/e = 4; the rib height (e) to channel height (H) ratio is 0.125. Also studied is an aluminum foam roughness with a porosity of 92% and a height to channel height ratio of 0.15. Reynolds numbers considered for the channel flow case (based on the hydraulic diameter) range from 10,000 to 40,000. Reynolds numbers for the jet impingement case (based on the hole diameter) range from 5,000 to 20,000. Tests are performed using the copper plate regional average method. Results show a 50–90% increase in heat transfer due to the use of axial ribs in both, impingement and channel flow cases. The porous foam shows a more significant increase in heat transfer coefficient for both channel flow and impingement cases.