Interstitial Heat Transfer Coefficient Research Articles

Effects of Channel Flow Blockage on Metal Foam Heat Transfer

Abstract High porosity aluminum foams have the potential to dissipate large heat flux in a channel flow configuration due to their large surface area-to-volume ratio and the ability to enhance mixing due to flow tortuosity. It is well documented that the interstitial heat transfer coefficient has a power law dependence on the flow velocity at the pore-scale. For asymmetrical heating (single wall), a flow blockage concept is proposed with an aim to locally enhance flow speed near the heated wall. To this end, experimental and numerical investigation is carried out on a high porosity (95%) aluminum foam (10 pores per inch) with flow blockages, both upstream and downstream of the metal foam placed in a square channel. The opening was provided closer to the heated wall, where flow blockage was varied from 0% to 87%. With air as working fluid, experiments were conducted for channel Reynolds number varying from 3000 to 13,000. It was found that all flow blockages resulted in enhanced heat transfer over no-blockage case, however, at a high pressure drop penalty. An upstream flow blockage of 70% was found to have the highest thermal-hydraulic performance among other flow blockages (including 0% blockage).

Heat transfer model for moving packed-bed particle-to-sCO2 heat exchangers integrated with metal foams

Particle-to-supercritical carbon dioxide (sCO2) heat exchangers (HXs) play a vital role in coupling heat transfer fluid (HTF) from high-temperature thermal receivers to power cycle working fluids (WF). Heat transfer enhancement is essential for adopting particle-based moving packed-bed heat exchangers (MPBHXs) in next-generation thermal energy storage (TES) systems, as MPBHXs usually exhibit low particle bed-to-wall heat transfer coefficients. High-porosity metal foams have shown their effectiveness in heat transfer enhancement. This work presents a continuum heat transfer model to demonstrate the heat transfer enhancement in MPBHXs when the particle bed channel is filled with high porosity metal foams compared to open channel MPBHXs. The presence of metal foams increases the effective thermal conductivity in the particle channel and enhances the interstitial heat transfer coefficient between the moving particle bed and the stationary metal foams. The present model considers coupled two-dimensional (2D) heat transfer in the particle channel with metal foams and 1D heat transfer in the sCO2 channel and the dividing wall. The temperature profiles for the particle bed, metal foam, dividing wall, and sCO2 stream, as well as the local heat flux profiles between those, are studied in detail for various foam porosities, from which the particle bed-to-wall heat transfer coefficient, overall heat transfer coefficient, and total heat transfer rate for the MPBHX are determined. The effects of major MPBHX design and operating parameters on the particle bed-to-wall heat transfer coefficient and overall heat exchange capacity are thoroughly examined; thus, the MPBHX performance improvement with metal foams is quantified for each case. The present heat transfer model can provide valuable insights into the metal-foam MPBHX design and optimization, scale-up, and operating parameters selection.

Numerical Model for Heat Transfer in Layered Soil with Local Thermal Nonequilibrium

A numerical model, called HT2, is presented for one-dimensional heat transfer in saturated incompressible layered soil with steady fluid flow, effective porosity, and possible local thermal nonequilibrium (LTNE) between solid and fluid phases. The model uses a series-parallel approach and accounts for advection, conduction, linear and nonlinear thermal dispersion, and interstitial heat transfer. The key to HT2 is the definition of separate columns for the solid matrix (SM) and mobile pore fluid (MPF). The SM column includes the solid phase and immobile pore fluid and consists of fixed elements. The MPF column consists of moving elements and uses Lagrangian element-tracking to follow the fluid motion, which reduces numerical dispersion and simplifies heat transfer within the column to that of dispersive flux between contiguous elements. The model uses an interstitial heat transfer coefficient to calculate kinetic heat transfer between SM and MPF elements. The development of HT2 is first presented, followed by verification checks and a limited parametric study. Numerical simulations indicate that larger particle size and higher fluid discharge velocity yields greater local temperature disequilibrium between solid and fluid phases during heat transfer through saturated soil.

Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review

Local thermal equilibrium (LTE) is a frequently-employed hypothesis when analysing convection heat transfer in porous media. However, investigation of the non-equilibrium phenomenon exhibits that such hypothesis is typically not true for many circumstances such as rapid cooling or heating, and in industrial applications involving immediate transient thermal response, leading to a lack of local thermal equilibrium (LTE). Therefore, for the sake of appropriately conduct the technological process, it has become necessary to examine the validity of the LTE assumption before deciding which energy model should be used. Indeed, the legitimacy of the LTE hypothesis has been widely investigated in different applications and different modes of heat transfer, and many criteria have been developed. This paper summarises the studies that investigated this hypothesis in forced, free, and mixed convection, and presents the appropriate circumstances that can make the LTE hypothesis to be valid. For example, in forced convection, the literature shows that this hypothesis is valid for lower Darcy number, lower Reynolds number, lower Prandtl number, and/or lower solid phase thermal conductivity; however, it becomes invalid for higher effective fluid thermal conductivity and/or lower interstitial heat transfer coefficient.

Pore-scale numerical simulation of convection heat transfer in high porosity open-cell metal foam under rotating conditions

High porosity open-cell metal foam can be used in rotating machinery to improve its performances. The interstitial heat transfer coefficient is a key parameter to describe heat transfer in porous media under local thermal non-equilibrium conditions. A pore-scale numerical simulation is performed to obtain the interstitial heat transfer coefficient between air and high porosity open-cell metal foam under rotating conditions in this study. To this end, the convective heat transfer in a radially rotating channel filled with Weaire-Phelan foam cell is investigated numerically. The interstitial heat transfer coefficients are calculated at different Reynolds numbers, Rotation numbers, foam porosities and locations. And the correlation for porous-fluid interstitial heat transfer Nusselt number is established. The results show that the increasing of Reynolds and Rotation number will gradually increase the interstitial heat transfer Nusselt number. The location also has a positive effect on the interstitial heat transfer coefficient. However, the interstitial heat transfer Nusselt number gradually decreases with the increase of porosity. The established correlation can predict the interstitial heat transfer Nusselt number with a deviation within 10% at the studied ranges of the corresponding parameters. It can also be applied to the cases for larger location, larger channel size and larger Rotation number.

Flow and Thermal Transport Through Unit Cell Topologies of Cubic and Octahedron Families

Advancements in Additive Manufacturing (AM) routes have opened several opportunities for manufacturing complex porous structures which could not have been manufactured by the conventional foaming process that essentially results in unit cells represented as Tetrakaidecahedron (TKD) shape. The regular open-cell lattices belonging to the cubic and octahedron family of structures provide wide spectrum of porosity, pore-density, permeability and surface area-to-volume ratios. These complex cell topologies can potentially be manufactured additively, making the realization of above-mentioned properties possible. For efficient heat exchanger designs, the reticulated structures made from these unit cells are expected to have higher permeability, porosity, effective thermal conductivity and interstitial heat transfer coefficient. A detailed understanding of local flow and heat transport characteristics is necessary to design unit cells with such properties. To this end, four different metal foam unit cell topologies have been investigated in the present study, viz. Tetrakaidecahedron (TKD), Cube, FD-Cube and Octet. The Cube and FD-Cube unit cell topologies investigated in the present study belong to the cubic family, where the fibers are present only along the edges and face of the unit cell volume. The TKD and Octet configurations belong to the octahedron class of lattices, where complex connectivity exists within the unit cell volume. To allow for direct comparison between these three unit cells, circular fibers are chosen, which is different from the general TKD cells (tricuspid cross-sections). The porosity was fixed 0.986 which dictated the fiber dimensions of respective unit cells, with Octet fibers being thinnest. Direct simulations have been carried out with periodic boundary conditions on unit cell faces which were parallel to the flow. Such configurations when reticulated in three dimensions are representative of porous structures which are single-cell thick in the streamwise direction. These foam shapes have been proven to be very efficient as they do not allow the thermal boundary layer development. Flow and heat transfer results obtained for above boundary conditions have also been compared with the periodic boundary condition on all the faces.The direct simulation results include pressure drop per unit length and volumetric Nusselt number (corresponding to constant heat flux and constant wall temperature boundary conditions on fibers). Flow stagnation on fibers was the main contributor for both, pressure drop increase, and interstitial heat transfer enhancement. TKD unit cell had higher flow losses and thermal performance than FD-Cube. Octet (octahedron family) configuration had the highest flow losses as well as Nusselt number compared to all other unit cell topologies, because of the large surface area offered for flow stagnation.

Heat generating porous matrix effects on Brownian motion of nanofluid

PurposeThe purpose of this study is to indicate the effect of mounting heat generating porous matrix in a close cavity on the Brownian term of CuO-water nanofluid and its impact on improving the Nusselt number.Design/methodology/approachBecause of the presence of heat source in porous matrix, couple of energy equations is solved for porous matrix and nanofluid separately. Thermal conductivity and viscosity of nanofluid were assumed to be consisting of a static component and a Brownian component that were functions of volume fraction of the nanofluid and temperature. To explain the effect of the Brownian term on the flow and heat fields, different parameters such as heat conduction ratio, interstitial heat transfer coefficient, Rayleigh number, concentration of nanoparticles and porous material porosity were investigated and compared to those of the non-Brownian solution.FindingsThe Brownian term caused the cooling of porous matrix because of rising thermal conductivity. Mounting the porous material into cavity changes the temperature distribution and increases Brownian term effect and heat transfer functionality of the nanofluid. Besides, the effect of the Brownian term was seen to be greatest at low Rayleigh number, low-porosity and small thermal conductivity of the porous matrix. It is noteworthy that because of decrement of thermal conduction in high porosities, the impact of Brownian term drops severely making it possible to obtain reliable results even in the case of neglecting Brownian term in these porosities.Originality/valueThe effect of mounting the porous matrix with internal heat generation was investigated on the improvement of variable properties of nanofluid.

Direct Simulation of Interstitial Heat Transfer Coefficient Between Paraffin and High Porosity Open-Cell Metal Foam

The interstitial heat transfer coefficient (IHTC) is a key parameter in the two-energy equation model usually employed to investigate the thermal performance of high porosity open-cell metal foam/paraffin composite phase change material. Due to the existence of weak convection of liquid paraffin through metal foam during phase change process, the IHTC should be carefully determined for a low Reynolds number range (Re = 0–1), which however has been rarely addressed in the literature. In this paper, a direct simulation at foam pore scale is carried out to determine the IHTC between paraffin and metal foam at Re = 0–1. For this purpose, the cell structures reflecting realistic metal foams are first constructed based on the three-dimensional (3D) Weaire–Phelan foam cell to serve as the representative elementary volume (REV) of metal foam for direct simulation. Then, by solving the Navier–Stokes equations and energy equation for the REV, the influences of Reynolds number (Re), Prandtl number (Pr), foam porosity (ε), and pore density (PPI) on the dimensionless IHTC, i.e., the Nusselt number Nuv, are investigated. According to the numerical results, a correlation of Nuv at Re = 0–1 is proposed for metal foam/paraffin composite material, which covers both diffusion-dominated interstitial heat transfer region (Re ≤ 0.1) and convection-dominated interstitial heat transfer region (0.1 < Re ≤ 1). Finally, the applicability of this correlation in the two-energy equation model for solid–liquid phase change of paraffin in metal foam is validated by comparing the model predicted melting front with that of experimental observations made in this study. It is found that the IHTC correlation proposed in this study can be used in the two-energy equation model for well predicting the phase change process of paraffin in metal foam.

Determination of the stress jump coefficient, the interstitial heat transfer coefficient and the interface heat transfer coefficient in a porous composite system

In this work, the microscopic and macroscopic models of the porous composite system are established to study the stress jump coefficient, the interstitial heat transfer coefficient and the interface heat transfer coefficient under the local thermal non-equilibrium condition. The influences of the free fluid layer thickness, the flow types (including the Poiseuille flow, the Couette flow and the free boundary flow), the porosity and the pore diameter on the stress jump coefficient, the Biot number and the interface Biot number are discussed. In addition, an innovative method is presented to calculate the interstitial heat transfer coefficient inside the porous medium when the phenomenon of heat flux bifurcation occurs.

Transient investigation of mini-channel regenerative heat exchangers: Combined experimental and CFD approach

This paper presents a combined approach based on experiment and CFD as an alternative to single-blow method to investigate heat transfer and flow friction of three mini-channel regenerative heat exchangers (MCRHX), having channel hydraulic diameters of 1.5, 1 and 0.5mm. Experiments were conducted to measure pressure drop and the transient thermal responses at the inlet and outlet of each MCRHX. The thermal response predicted from CFD, based on transient conjugated heat transfer simulations, was iteratively solved until it matched the experimental data within an acceptable deviation. The results showed that 0.5mm MCRHX had the highest interstitial heat transfer coefficient due to the increased specific surface area. However, the penalty is the increased pressure drop. Moreover, Nusselt number and friction factor correlations were obtained for each configuration to correlate mini-channel heat transfer characteristics.

多孔質体内熱流動のモデリングの進展

Recent advances in mathematical modeling of heat and fluid flow in porous media were discussed starting from an introduction of volume averaging theory and leading to various engineering applications. Mathematical interpretations of tortuosity, thermal dispersion and interstitial heat transfer are provided with their models based on solvable volume averaged quantities. A useful concept “effective porosity” was introduced to account for the tortuosity. Moreover, an inverse relationship between the interstitial heat transfer coefficient and thermal dispersion coefficient was explained, which enables us to estimate the thermal dispersion simply by measuring the interstitial heat transfer using a single blow method. Engineering applications based on the local space sharing concept will be discussed ranging from bioheat transfer to ion transport through a membrane.

Numerical modeling of heat transfer in open-cell micro-foam with phase change material

The heat transfer behavior of micro-foam impregnated with phase change material (PCM) was investigated. Both microscopic and macroscopic modeling approaches were considered. An open-cell PCM/micro-foam structure under constant heat flux was modeled using an ideal micro-foam structure based on a cubic unit cell with spherical micro-pores arranged in a BCC lattice. Results from direct numerical simulations (DNS) which take into account the intricate foam geometry were compared with those from one- and two-temperature volume-averaged simulations. The enthalpy-porosity method was used for phase change and conjugated heat transfer was applied at the PCM/micro-foam interface. The DNS simulations provided insight into the complicated heat transfer and a three-dimensional PCM melting front and temperature distribution was observed. Along with serving as a benchmark for the less computationally expensive volume average methods, the DNS results were also used to extract thermo-physical parameters such as effective thermal conductivity and interstitial heat transfer coefficients. These coefficients were subsequently used in the volume averaged simulations. The choice of the effective thermal conductivity of the PCM/micro-foam structure was found to be crucial in matching the temperature profile and liquid PCM volume fraction results from volume averaged simulations and DNS. Effective thermal conductivity values based on the nonlinear Progelhoff model with power factor derived from DNS were found to provide an improvement over the more widely used value based on the arithmetic mean.

Numerical investigation of convective heat transfer in a plane channel filled with metal foam under local thermal non-equilibrium

The present work consists on convective heat transfer modeling in a plate heat exchanger filled with metal foam under local thermal non-equilibrium (LTNE). The metal foam was inserted to fill completely the studied channel, which is crossed by a fluid. The modified Brinkman-Forchheimer extended Darcy model is used in the porous layer, while the macroscopic two-energy equation model is used for the thermal field. The channel walls are maintained at a constant temperature and the velocity at the inlet is supposed uniform. A dimensionless formulation is developed to perform a parametric study in terms of certain dimensionless variables, and solved by the finite volume method (FVM). The results include the effect of the interstitial heat transfer coefficient and the solid to fluid thermal conductivity of different type of metal foams. The results were used to estimate the influence of the convective and conductive contributions using open-celled metal foams with high porosity. It has been shown that such supports can bring a significant enhancement for the heat transfer.

New models for heat flux splitting at the boundary of a porous medium: three energy equations for nanofluid flow under local thermal nonequilibrium conditions

One of the challenging points in the simulation of a nanofluid flowing through a porous medium is modeling the surface heat flux in the presence of nanoparticles and internal solid matrix. The question is how much energy is absorbed by the solid phase, fluid phase, and particles at the surface of imposing heat flux? To reach a suitable answer, a local thermal nonequilibrium approach (including three energy equations) is presented in this paper and three heat flux models are proposed for the first time. The proposed models are compared and analyzed. The effects of interstitial heat transfer coefficients on the heat transfer in a porous channel are completely studied. The fluid temperature distributions and heat transfer rate obtained by homogenous and nonhomogenous approaches (for the proposed models) are completely studied and compared. The results show that the nonhomogeneous approach experiences larger Nusselt number than the homogeneous one for all the recommended heat flux models.

An Accurate Experimental Determination of Interstitial Heat Transfer Coefficients of Ceramic Foams Using the Single Blow Method

An exhaustive experimental investigation has been carried out for accurate determination of interstitial heat transfer coefficients of ceramic foams in forced convective flows. The single-blow method was used, in which, the fluid temperature varies with time and convective heat transfer becomes time-dependent. The method results in a transient and conjugate heat transfer phenomena between the foam and fluid. These transient temperature data are then compared with the theoretical results to obtain the corresponding interstitial heat transfer coefficients between the fluid and foam solid surface. The interstitial coefficients thus determined are compared against available sets of experimental data, so as to ex- amine the consistency among the reported experimental data.

The Effective Pore Diameter of a Three-Dimensional Numerical Model for Estimating Heat and Fluid Flow Characteristics in Metal Foams

A three-dimensional numerical model is proposed to determine heat and fluid flow characteristics in metal foams. A series of full three-dimensional numerical calculations was performed to reveal complex three-dimensional ve- locity, pressure and temperature fields within three-dimensional porous structures of the metal foams. These numerical re- sults are processed to obtain the macroscopic characteristics such as the permeability, inertia, dispersion and interstitial heat transfer coefficients. An effective pore diameter concept has been proposed to correlate the resulting heat and fluid flow characteristics with available empirical correlations. In this study, we shall conduct a numerical study on heat and fluid flow in metal foam using a three-dimensional nu- merical model of periodical structure. In order to capture irregularities in real foams, quantities calculated at specific flow angles are ensemble-averaged over the flow angle. A rational way to evaluate the effective pore diameter, which is used as the characteristic length of present three-dimensional numerical model, is proposed. Permeability, Forchheimer coefficient, thermal dispersion and volumetric heat transfer coefficient are determined by spatially averaging micro- scopic numerical results. The validity of the present numeri- cal model and the effective pore diameter are examined by comparing the numerical results with available empirical correlations. Furthermore, an interesting relationship be- tween the thermal dispersion conductivity and the volumet- ric heat transfer coefficient is elucidated.

Air forced convection through metal foams: Experimental results and modeling

Metal foams are a class of cellular structured materials with open cells randomly oriented and mostly homogeneous in size and shape. In the last decade, several authors have discussed the interesting heat transfer capabilities of these materials as enhanced surfaces for air conditioning, refrigeration, and electronic cooling applications. This paper experimentally characterizes twenty-one aluminum and copper foam samples with different number of pores per linear inch (PPI), which vary between 5 and 40 and with porosity ranging between 0.896 and 0.956; samples of different heights (20 and 40mm) have been studied. The most important parameters both geometrical (porosity, pore density, and foam core height) and operative (air mass flow rate, imposed heat flux) affecting the heat transfer and fluid flow behavior of these enhanced surfaces are analyzed and discussed. The results are presented with reference to different performance parameters: overall and interstitial heat transfer coefficients, foam finned surface efficiency, normalized mean wall temperature, pumping power per area density, and pressure gradient. From the experimental measurements two correlations for the heat transfer coefficient and pressure drop calculations have been developed, validated and here proposed. These models can be successfully used to optimize different foam heat exchangers for any given application.

Experimental analysis of forced convective heat transfer in novel structured packed beds of particles

Followed by the numerical study of Yang et al. (2010), the macroscopic hydrodynamic and heat transfer characteristics in some novel structured packed beds are experimentally studied in this paper, where the packings of ellipsoidal or non-uniform spherical particles are investigated for the first time with experiments and some important results are obtained. For present experiments, the interstitial heat transfer coefficient in the packed bed is determined using an inverse method of transient single-blow technique. The effects of packing form and particle shape are carefully investigated and the experimental and numerical results (Yang et al., 2010) are also compared in detail. Firstly, it is discovered that, the computational method reported by Yang et al. (2010) might be appropriate for heat transfer predictions in structured packings, while it might underestimate the friction factors, especially when the porosity is relatively low. Secondly, it is found that, the traditional Ergun's and Wakao's equations might overpredict the friction factors and Nusselt numbers for the structured packings, respectively, and some experimental modified correlations are obtained. Furthermore, it is also revealed that, both the effects of packing form and particle shape are significant to the macroscopic hydrodynamic and heat transfer characteristics in structured packed beds. With proper selection of packing form, such as simple cubic packing (SC) and particle shape, such as ellipsoidal particle, the pressure drops in the structured packed beds can be greatly reduced and the overall heat transfer performances will be improved. These experimental results would be reliable and useful for the optimum design in industry applications.

Sensitivity analysis of the numerical study on the thermal performance of a packed-bed molten salt thermocline thermal storage system

In this paper, a comprehensive transient, two-dimensional, two-phase model for heat transfer and fluid dynamics within the packed-bed molten salt thermocline thermal storage system is presented. After model validation, the developed model is used to investigate the general thermal behavior of a discharging process of the pack-bed thermocline system and evaluate the interstitial heat transfer coefficient, the effective thermal conductivity and effect of the thermal conductivity of solid fillers. The results show that the thermocline region is moving upward with slight expansion during the discharging process. With the use of two insulation layers, a uniform cross-sectional temperature distribution is well achieved. The use of different correlations for the interstitial heat transfer coefficient or the effective thermal conductivity from the literature leads to negligible difference in the predicted thermal performance. It is also found that decreasing the heat transfer rate between fluid and solid fillers, or increasing the thermal conductivity of solid fillers, results in an increase in the thermocline thickness which finally decreases the effective discharging time and the effective discharging efficiency.

Effects of thermal dispersion on heat transfer in cross-flow tubular heat exchangers

Effects of thermal dispersion on heat transfer and temperature field within cross-flow tubular heat exchangers are investigated both analytically and numerically, exploiting the volume averaging theory in porous media. Thermal dispersion caused by fluid mixing due to the presence of the obstacles plays an important role in enhancing heat transfer. Therefore, it must be taken into account for accurate estimations of the exit temperature and total heat transfer rate. It is shown that the thermal dispersion coefficient is inversely proportional to the interstitial heat transfer coefficient. The present analysis reveals that conventional estimations without consideration of the thermal dispersion result in errors in the fluid temperature development and underestimation of the total heat transfer rate.