Local Thermal Non-equilibrium Model Research Articles

Thermal management of fuel-cell stacks using air flow in open-cell metal foam

A new numerical and experimental work investigating the cooling potential of open-cell aluminum foam (using airflow) for fuel cell stacks is described. A model for metal-foam cooling design based on a commercial 500-W proton exchange membrane fuel cell (PEM) stack was simulated and tested experimentally. The new design of the current investigation replaces the existing liquid-cooling channels with compressed aluminum foam having a porosity of 60%. The study considered symmetric and asymmetric heated foam channels subjected to constant heat flux of 1.56 W/cm2, and cooled by airflow at hydraulic-diameter Reynolds numbers in the range 87–657. In the simulations, the thermal energy equations were solved invoking the local thermal non-equilibrium model, which is a more realistic treatment for airflow in metal foam. Local temperatures in the stack, local and length-averaged Nusselt numbers, and friction factors were determined numerically and experimentally. Good agreement between the simulation and experiment was obtained for the local temperatures. The local Nusselt number slightly decreased with distance along the cooling channel, and the length-averaged Nusselt number increased with Reynolds number. As for the friction factors predicted by simulation and obtained experimentally, there was an average difference of about 18.3%. This difference has been attributed to the poor correlation used by the CFD package for pressure drop in metal foam. The new cooling system could remove the 500 W of waste heat of the stack, and would keep the stack within the safe range of operating temperature: 60–90̊ °C.

Natural convection inside nanofluid superposed wavy porous layers using LTNE model

This work describes the natural convection and thermodynamic irreversibility of alumina-water nanofluid filled inside a layered cavity. The local thermal non-equilibrium (LTNE) approach is taken into consideration. The cavity bed is considered as a wavy hot plate of a very thin thickness, while its roof is thermally insulated. The heat is dissipated from the cold vertical walls. A porous layer fills the cavity's lower half and is assumed to obey the Darcy-Forchheimer model. The finite-element method is adopted to compile the numerical results. The relevant parameters assessed in this paper are the Darcy number, waviness of the hot bottom wall, porosity, volume fraction of alumina nanoparticles and the modified ratio of thermal conductivity. The obtained numerical results show that the LTNE condition expands as the Darcy number augments, while a quasi-local thermal equilibrium is attained with a higher modified ratio of thermal conductivity. The waviness of the hot wall raises the Nusselt number of both the fluid and the solid phases but produces more entropy. It is quoted that the augmentations in the fluid and solid phases of the Nusselt numbers and the increase in the maximum entropy production are 42.25%, 69% and 55.5%, respectively.

Effects of gradient porous metal foam on the melting performance and energy storage of composite phase change materials subjected to an internal heater: A numerical study and PIV experimental validation

This work aims to explore the effects of gradient porous metal foam on the 3D melting heat transfer as well as the heat storage performance of a latent heat thermal energy storage (LHTES) unit inside an internal heated cubic cavity. A modified structure of metal foam with gradient porosity of three stratification layers is proposed to optimize the melting characteristic of the composite phase change materials. The enthalpy-porosity method is adopted to model melting process, and the Darcy-Forchheimer law and local thermal non-equilibrium model are assumed for metal foam. The numerical code of proposed model is in good consistency with the experimental results of particle image velocimetry (PIV) visualization. The effects of porosity gradient with equal and non-equal stratification heights, as well as pore per inch (PPI) on the melting performance, heat transfer and heat storage are investigated. The results indicate that the competitive relation between the conduction and convection induced by the gradient porosity influences the heat transfer and energy storage. The energy storage of negative gradient is greater than that of positive gradient, but the average rate of energy storage of the former is lower than that of the latter. In the middle melting stage, the total average Nusselt number increases with larger porosity gradient for positive cases and decreases for negative cases. With the increase of the stratification height of middle layer, the heat transfer efficiency of positive cases weakens, while it is enhanced for negative cases. Moreover, the increase of PPI can reinforce the conduction effect and improve the average rate of energy storage of the LHTES unit for both positive and negative cases.

Optimization of SMR process for syngas production through a solar-assisted thermo-chemical reactor with a multi-layered porous core

A two-dimensional steady-state axisymmetric model is developed to analyze the performance of a thermo-chemical porous reactor used for syngas and subsequently hydrogen generation through the steam methane reforming (SMR) process. The finite volume method coupled with kinetics thermo-chemical reaction and local thermal non-equilibrium (LTNE) model with modified P1 approximation is employed to obtain the temperature distribution for both the fluid and porous zones. First, the effects of inlet mass flow rate, inlet steam to methane ratio, porosity, number of pores per inch (PPI), permeability, and reactor length on reactor performance are scrutinized. Next, to optimize the performance of the reactor, an artificial neural network (ANN) is developed to obtain the maximum hydrogen generation rate concerning the effective parameters. Finally, a two-layer porous foam is utilized as the catalyst zone to further improve the performance. Results show that increasing inlet flow rate leads to temperature decline and causes an incomplete reaction. Also, increasing porosity enhances heat absorption at the inlet and decreases radiative heat transfer through the porous foam. At a specified condition (ṁ= 0.25 kg.h−1, XCH4/XH2O = 1/3, and PPI = 10), increasing the porosity from 0.6 to 0.8 has increased hydrogen production by 27 %, while by a further increase of porosity to 0.9, hydrogen production decreased by 3 %. Results indicate up to 164 % increment in the performance of the optimal case compared to the base case. Furthermore, employing the two-layer porous foam with different PPIs could further increase hydrogen production, up to 20 %, and reduced the pressure drop.

Heat Transfer Characteristics of Mixed Convective Magnetohydrodynamic Counter-current Two-Phase Flow in Rotating Inclined Microporous Channel With Slip Velocity and Asymmetric Thermal Boundary Conditions Using LTNE Model

Abstract The heat transfer characteristics of a mixed convective two-phase flow in an inclined rotating microporous channel kept in a transverse magnetic field are investigated numerically. The counterflow arrangement is assumed within the channel. Slip velocity and asymmetric thermal boundary conditions are assumed. The governing energy equation involves the local thermal non-equilibrium (LTNE) between the two phases. The LTNE implications of the control parameters on the flow field variables and the average Nusselt number, Nu, are highlighted, and pertinent observations are documented. When confined to a few specific cases, the current results are consistent with previous research work. The effect of inclination angle on fluid velocity is determined by the wall temperature difference ratio. According to the findings, for certain values of the wall temperature differential ratio, the velocity increases with the angle; however, it takes on a dual character for other values. The Nusselt number (Nu) is expected to increase with the Biot number, Hartmann number, and rotation parameter, while Nu decreases as the Knudsen number increases. The results also show that as the wall temperature ratio increases, the Nu converges to a common minimum value. This research combines computational fluid dynamics (CFD) simulation and artificial neural network (ANN) analysis. The database was generated from the validated CFD model covering a range of control parameters arising in the system. The multilayer perceptron (MLP) networks were trained using this CFD data set to predict Nu. It is observed that the predicted data given by the ANN model is in good accordance with the estimated values of Nu. The average relative error in Nu's prediction is found to be ±2%.

Effects of foam structure on thermochemical characteristics of porous-filled solar reactor

The foam-structured reactor is one which has hitherto been regarded as of great potential for industrial applications in the field of solar thermochemistry. The utilization mode of ceramic foam has, generally, a significant impact on energy conversion and storage efficiency. This study establishes a numerical model, coupled with computational fluid dynamics and dry reforming of methane reaction kinetics, to find the optimal structural parameters of the ceramic foam. A local thermal non-equilibrium model coupled with the P1 approximation has been developed to address the heat-transfer problems, and the non-Darcy flow effect has been considered to calculate the momentum dissipation in the porous zone. Based on ample simulation examples, the effects of porosity and foam cell size on the reaction temperature, surface heat loss, thermal efficiency, CH4/CO2 conversion, H2/CO yield, carbon deposition, and solar-to-chemical efficiency are illustrated in detail. The results indicate that using the ceramic foam with high porosity and large cell size is able to attain the best thermochemical characteristics, of which the validity can be assured, insofar as the various operating conditions in this study are concerned. Furthermore, as compared to the best single-layer structure, the application of the optimized double-layer foam structure is a more effective solution, which is able to further improve the energy storage efficiency by a remarkable 9.23%.

A Multi‐Phase Heat Transfer Model for Water Infiltration Into Frozen Soil

AbstractIn many regions, water infiltration into frozen soil is a critical process. Frozen soil is known to have a substantially reduced infiltration capacity, resulting in surface water runoff. This surface runoff is often associated with erosive behavior posing a potential natural hazard as it facilitates snow avalanches and debris flow, especially in springtime when rainfall and snowmelt coincide. As infiltration capacity depends on the ice content within the porous soil, thermal and hydraulic processes are strongly coupled. The involved phases during water infiltration into frozen soil are initially not in a local thermal equilibrium as the infiltrated water is warmer than the frozen soil. The duration of the temperature differences is yet to be determined. To adequately describe this thermal state, a local thermal non‐equilibrium (LTNE) model needs to be applied, which accounts for separate phase temperatures and describes the heat transfer between the phases explicitly. While LTNE models are common in more simple setups of saturated porous media flow, in this work, a multi‐phase LTNE model for water infiltration into a partly saturated, frozen soil is presented. All required parameters, such as heat transfer area and heat transfer coefficient are discussed and derived based on a capillary tube model. The theoretical model is implemented into a numerical model and compared to experimental data available from literature. Substantial differences of up to C between phase temperatures during freezing and melting are observed after hours of infiltration and are especially pronounced around the freezing front.

Coupling effect of heat transfer in plate heat exchanger filled with porous media

The forced convection heat transfer characteristics in plate heat exchanger filled with porous media are semi-analytically investigated in this paper. The Darcy-Brinkman model is utilized to describe the fluid flow, and the local thermal non-equilibrium model is employed to establish the energy equations. The solutions of the temperature and velocity distributions are validated in limiting case. The coupling heat transfer characteristics are studied in parallel flow and counter flow under different conditions. The influences of the heat capacity ratio, the Darcy number, the Biot number, the porosity, and the thermal conductivity, on heat transfer are discussed. The results show the coupling effect in plate heat exchanger filled with porous media since the thermal boundary conditions of each channel of the plate heat exchanger are dependent on the flow and heat transfer parameters of both the two channels. The heat capacity ratio is found to have the most important influence on the coupling effect. The coupling effect should be considered when designing the plate heat exchanger filled with porous media.

Numerical assessment of thermal characteristics of metal foams of orderly varied pore density and porosity under different convection regimes

The present study is done to analyze heat transfer and fluid flow in a channel with orderly varied pore density and porosity combination of foam samples. Darcy Forchheimer flow and LTNE thermal models are considered to estimate heat transfer characteristics. Considering the effect of orderly varied combinations of the dual structural properties, forced convection over a range of flow velocities and natural convection phenomenon are studied numerically in the channel housing porous samples. Two limiting solutions for Nusselt number (Nu) i.e., Nun (for natural convection) and Nuf (for forced convection) for Ri→∞ and Ri→0 respectively, as a function of independent variable Richardson number (Ri) with structural properties pore density and porosity are obtained with the help of local thermal non-equilibrium (LTNE) thermal model and Darcy-Forchheimer flow model. Further these asymptotic solutions are blended using technique illustrated in the literature in order to obtain solution for Nusselt number for mixed convection (Num). Correlations for Nusselt number as a function of combination of porosity and pore density are obtained emphasizing on the varied significance of these parameters in different convection regime. The present study not only emphasizes on effect of combination of structural properties of metal foams on heat transfer characteristics, but also illustrates a technique that enables to arrive at suitable correlation for an intermediate phenomenon existing between two other extremes, with zero computational cost. Effect of pore density on heat transfer characteristics at a given porosity, is found to be not much influencing in natural convection dominant regime. However, in mixed and forced convection dominant scenario it is illustrated that, effect of variation in pore density and porosity plays a significant role in expressing distinguishable heat transfer characteristics, along with other well-known independent parameters such as porosity and Reynolds number.

Stability analysis of the thermocline thermal energy storage system during high flow rates for solar process heating applications

The thermal energy storage system is a pivotal system for solar thermal plants for improving reliability. The stability in the thermocline is more significant to clarify and improve the performance of thermal energy storage tank which legitimately shows the quality of the thermocline. In this stability analysis investigation, the modern engineering energy storage material concrete was used as a filler material for high-temperature thermal energy storage applications as a result of the intrinsic properties. A comprehensive laminar and k-ε turbulent flow energy transport model accounts for the heat transfer fluid and filler material with adiabatic and non-adiabatic conditions using LTNE (Local Thermal Non-Equilibrium model). The axial, radial, and diagonal temperature differences were identified which was used to calculate the stability of the thermocline. A thermal energy storage tank size of 1 m height and 0.250 m diameter with a 0.030 m size of filler material packed with an average porosity of 0.3 for the storage capacity of 150 kWh/m3 is used for solar process heating applications considered for the present study. The thermocline stabilities are performed with Reynolds numbers, Re varied from 1 to 3000. It is found that the Re = 1 provides better stability in the axial and radial direction as well as diagonal than other Reynolds number. It is observed that Re = 1 provides superior discharging efficiency for nearly 5.84 hrs which is highly suitable for solar process heating applications and the discharging efficiency consistently drops, when Re increases from 1 to 3000. The wall condition of the tank and velocity of the heat transfer fluid is highly disturbing the thermocline in the radial direction and it creates a ‘spike’ profile in the axial direction. Based on the newly introduced stability scale, the effective length of packing and timing to achieve stability is identified for H/D = 4. From that result, the top and bottom layer of the thermocline tank porosity is also found which is used to decide the porosity of the packed bed distributors. The identified porosity for the top and bottom distributors in the ɛ = 0.3 thermal energy storage tank is less than 0.3 is more suitable for provide the uniform flow in the tank.

Heat and Mass Transfer Analysis in Chemically Reacting Flow of Non-Newtonian Liquid with Local Thermal Non-Equilibrium Conditions: A Comparative Study

In the current paper, we endeavour to execute a numerical analysis in connection with the boundary layer flow induced in a non-Newtonian liquid by a stretching sheet with heat and mass transfer. The effects of chemical reactions and local thermal non-equilibrium (LTNE) conditions are considered in the modelling. The LTNE model is based on energy equations, and provides unique heat transfer for both liquid phases. As a result, different temperature profiles for both the fluid and solid phases are used in this work. The model equation system is reduced by means of appropriate similarity transformations, which are then numerically solved by employing the classical Runge–Kutta (RK) scheme along with the shooting method. The resultant findings are graphed to show the effects of various physical factors on the involved distributions. Outcomes reveal that Jeffrey fluid shows improved velocity for lower values of porosity when compared to Oldroyd-B fluid. However, for higher values of porosity, the velocity of the Jeffery fluid declines faster than that of the Oldroyd-B fluid. Jeffery liquid shows improved fluid phase mass transfer, and decays more slowly than Oldroyd-B liquid for higher values of chemical reaction rate parameter.

Heat transfer analysis of rectangular porous fins in local thermal non-equilibrium model

• Analytical solutions on convective-radiative porous fin in LTNE is accomplished. • Darcy model and Boussinesq approximation are used to simulate the porous medium. • The two energy equations are solved using the Adomian Decomposition Method. • Results are given as temperature profiles and total Nusselt numbers. • Criteria to compare LTNE and LTE hypothesis are given for both scale analysis and ADM. In this study, an analytical solution of a porous fin with natural convection and radiation heat transfer is carried out. For the first time, the analysis is accomplished in Local Thermal Non-Equilibrium (LTNE) model. The investigation is carried out on a porous fin with finite length and adiabatic tip. The Darcy model and Boussinesq approximation for buoyancy effects are used to evaluate the infiltration velocity in the porous medium. Two energy equations are solved using the Adomian Decomposition Method (ADM). The solution is validated with the numerical solution of the finite difference method, and with the asymptotic solution for the Local Thermal Equilibrium (LTE) model. The results are presented in terms of temperature profiles and total average Nusselt numbers. They pointed out the effects of internal and external radiation and convection heat transfer, as well as thermal conductivity ratio and dimensionless thickness. It was found that solid phase temperature profiles decrease as the Biot, Bi , and Rayleigh, Ra *, numbers decrease, whereas the difference between the solid phase and fluid phase temperatures, for assigned Bi , decreases for lower Ra . Thermal conductivity ratio and dimensionless thickness increase engender higher solid phase temperature for assigned Bi and Ra *. The total Nusselt number increases as Ra *, Bi and external radiation increase, whereas it decreases with the thermal conductivity ratio. Criteria to compare LTNE and LTE assumptions are proposed, and they highlight the fact that the minimum Biot number to accept the LTE assumption becomes lower as the Rayleigh number decreases.

Numerical simulation of a novel regenerative heat exchanger with combined sensible–latent heat storage matrix

A new rotary regenerative heat exchanger with combined sensible–latent heat storage matrix was proposed. A local thermal non-equilibrium model with three energy equations for fluid, sensible heat storage material, and latent heat storage material in the porous matrix was developed. Rotary regenerative air preheaters (RAPHs). The RAPHs with combined sensible–latent heat storage matrix (CRAPH), with sensible matrix (SRAPH) and with latent heat storage matrix (LRAPH) were comparatively evaluated according to their thermal and economic performances. The temperature distributions of sensible and latent heat storage materials in the matrix exhibit different characteristics. The latent heat storage material that undergoes a phase change process during charging or discharging can greatly buffer the temperature swings of fluid and sensible heat storage material, especially under lower rotating speed conditions. Even if a small amount of latent heat storage materials were added to the sensible heat storage matrix, the efficiency of RAPH can be greatly improved.

Mixed convection from a heat source in a channel with a porous insert: A numerical analysis based on local thermal non-equilibrium model

Numerical examination was carried out on mixed convection in a horizontal channel containing a single heat source at the bottom wall with a porous insert placed exactly on the heater surface. It was assumed that the porous insert partially fills the channel. The numerical simulations were carried out using the local thermal non-equilibrium (LTNE) condition and the temperature distribution of solid and fluid phases of porous insert were obtained. The impact of height of the porous insert, porosity of the porous insert, material and diameter of the solid particle of the porous insert, buoyancy force, Reynolds number of the flow on the distribution of temperature were investigated and the influence of these parameters over the applicability of the local thermal equilibrium condition (LTE) was also studied. The results indicate that the effect of buoyancy force is considerable and cannot be ignored at low Reynolds number. Applying the LTNE condition, the optimum thickness of porous insert for the improvement in heat transfer with a considerable pressure drop is found to be equal to half the channel height. The porosity of the porous insert, the particle diameter of the solid phase of the porous insert and the thermal conductivity of the solid phase of the porous insert highly affect the applicability of LTE condition.

Effect of rotation on Brinkman-Bénard convection of a Newtonian nanoliquid using local thermal non-equilibrium model

Rayleigh-Bénard-Taylor convection in a Newtonian, nanoliquid-saturated high porous medium using the local thermal non-equilibrium model (LTNE) is studied analytically using the single term Galerkin technique. The Bousinessq approximation is considered to be valid and the exerted centrifugal force due to rotation is taken. A high porosity porous material glass reinforced fiber with porosity 0.88% is considered and hence the Brinkman model is adopted. The rate of rotation is quantified by the Taylor number and the stability of the system is controlled by thermal Rayleigh number. The expression for the critical eigenvalue (Rayleigh number) is obtained for both idealistic and realistic boundary conditions, that is, stress-free, isothermal and rigid-rigid, isothermal boundary conditions. The presumption of LTNE advances the inception of convection and increases the transport of heat in comparison with that of the local thermal equilibrium (LTE) assumption whereas the opposite phenomenon is seen with the effect of rotation. The effect of various non-dimensional parameters on the convection onset and on transport of heat is also investigated. The results of Rayleigh-Bénard-Taylor convection using the LTE assumption are obtained as limiting cases of the present study for infinite values of the ratio of thermal conductivities and the interphase heat transfer coefficient.

Thermal Transport Analysis of Injected Flow through Combined Rib and Metal Foam in Converging Channels with Application in Electronics Hotspot Removal

The development of miniaturized and more powerful electronic devices and microprocessors has resulted in high heat generation and temperature values in these components. That affects the performance, reliability and lifespan of the devices. In addition, more local hot spots are generated in the components that require even more attention to prevent stress failure and fatigue. As such, the employment of advanced electronics cooling systems is very essential to keep the temperature below the safe temperature. In this work, innovative cooling systems are developed and analyzed employing jet impingement technology, high conductive metal foam, rib structured target surfaces, confined non-uniform small-scale channel, and conductive heat spreader plate. The base of the foam-filled cooling channel is subject to a uniform high heat flux value resembling the electronics device to be cooled. For numerical modeling of thermal transport through foam filled region, the local thermal non-equilibrium model in porous media is utilized resulting in two energy equations for solid and fluid phases. For better understanding of flow and thermal characteristics of jet impingement through the combination of metal foam and rib structured surfaces in confined channels, several effective parameters are studied such as slot and circular jet impingements, the shape and orientation of the ribs, impinging jet velocity, applied heat flux and the thickness of conductive heat spreader plate for hotspot removal. The results show that the fully foam filled channel provides a more efficient cooling in comparison with partially foam filled channel. Furthermore, the results indicate the advantage of utilization of ribs at the stagnation region of the impinging jet, for local thermal treatment of hotspots. The perpendicular cuboid ribs placed at the stagnation zone of the coolant jet impingement provide 13% increase in maximum local Nusselt number while the increase in the pressure drop and required pumping power are as small as 4.2%. Doubling the velocity would result in 35.3% increase in the maximum local Nusselt number, 180% increase in the pressure drop and 460.7% increase in the required pumping power. An increase in the thickness of the conductive heat spreader plate increases the base local temperature but improves local temperature uniformity.

Numerical Study of MHD Free Convection in a Packed Bed Square Enclosure Using Local Thermal Non-Equilibrium (LTNE) Model

In the present study, natural convection of fluid in a square packed bed enclosure is investigated numerically using a uniform magnetic field. The geometry model is heated from left-hand side vertical wall and cooled from opposite wall with adiabatic condition at both the top and bottom walls. Normally to this enclosure an electric coil was set to generate a uniform magnetic field. The Brinkman–Forchheimer extended Darcy model was used to solve the momentum equations, while the energy equations for fluid and solid phase were solved using the local thermal non-equilibrium (LTNE) model. Computations are performed for a range of the Darcy number from 10-5 to10-1, the porosity from 0.3 to 0.9, and Hartmann number from 0 to 75. The results showed that both the strength of applied magnetic field and the packed bed characteristics have significant effect on the flow field and heat transfer.

Numerical analysis on the improved thermo-chemical behaviour of hierarchical energy materials as a cascaded thermal accumulator

The present study aims to improve the thermo-chemical conversion behaviours, including reactive transport processes and output performances of an open thermochemical energy storage (TCES) unit. The local thermal non-equilibrium (LTNE) model and the effect of non-uniform porosity are adopted and considered to better elucidate the conversion processes. Cascading the reaction sub-units filled with different thermochemical materials (TCMs), i.e., zeolite, salt hydrate-based composite sorbent, and pure salt of SrBr2·6H2O, to form an integrated storage bed ameliorates the output performance. The numerical results indicate that the maximum temperature difference ranging from 3.5 to 4.9 °C between heat transfer fluid and solid reactants exists during desorption, and the realistic non-uniform porosity facilitates the reactant conversion near the wall compared to the uniform porosity assumption. The cascaded scheme promotes the charging and discharging processes compared to the cases filled with sole TCM, the time required for charging this 10.8 kWh storage model is 16 h. Increasing the charging temperature from 100 °C to 145 °C, the charging time reduced to 6.5 h, saving 59.4%. Boosting the inlet velocity of airflow also accelerates the charging rate. The cascaded storage unit significantly stabilises the output temperature during discharging, warming up the airflow from 20 °C to 35 °C for 24 h with a tiny temperature fluctuation. Airflow with higher relative humidity facilitates hydration but shortens the stable period. Overall power and thermal efficiency of the “thermal accumulator” in charging are 598 W and 92.8%, 164 W and 92.4% in discharging, with a total COP of 0.71. The satisfying performances suggest that the cascaded TCES unit may provide a strategy and reference in the design and promotion of the low-grade energy storage system.

Transient behaviour of heat transfer with complete evaporation process in Porous Channel with localised heating using non-Darcian flow and LTNE model

This study numerically presents the transient behaviour of complete evaporation process inside porous channel. Based on the modified enthalpy formulation under non-Darcy flow and Local Thermal Non-Equilibrium (LTNE) conditions, solutions have been obtained utilizing the finite volume method for various relevant parameters. The results have been validated with the experiments and they show good agreement between them. The results demonstrate that LTNE model should be employed while modelling the transient complete evaporation process in porous media. The non-Darcy effects have considerable influences on the locations of the initiation and termination of the phase change processes as compared to Darcy flow model. Therefore, the behaviours of the two-phase and the superheated vapour zones, when the steady-state solutions is reached, are substantially changed for non-Darcy flow as compared to Darcy model due this assumption provides an additional mechanism for heat transfer that represented by the heat exchange between the solid and fluid phases. It has been observed that the two-phase zone is considerably extended in the axial direction and this zone has not been occupied a large size towards transverse direction due to the axial velocity is noticeably higher than the transverse velocity, caused by reducing the diffusive energy through the two-phase region. The results indicate that non-Darcian effects leads to considerably extend the size of superheated region towards the outlet of the channel, which is not the case for Darcy model. The non-Darican effects become more pronounced for high Reynolds number and heat flux. The influences of varying in Reynolds number, heat flux, porosity, and solid thermal conductivity are substantial near the heated surface, whereas Darcy number has a minor impact on the solution of complete evaporation process. It can be emphasised from the present predictions that the non-Darcy flow along with LTNE condition is indispensable model for the complete evaporation process, especially under high mass flowrate as well heat flux.

Performance evaluation of partially filled high porosity metal foam configurations in a pipe

• Numerical simulation of partially filled metal foams for heat transfer augmentation is studied. • Darcy Forchheimer and Local Thermal Non-Equilibrium models for numerical modeling. • Six different strategies for maximum heat transfer and minimum pressure drop. • 10 to 45 pores per inch and 0.88 and 0.95 porosity are considered. • 30 pores per inch with porosity of 0.92 provides the best performance factor. In this contemporary research, a parametric analysis of partially filled high porosity metallic foams in a horizontal conduit is performed to augment heat transfer with reasonable pressure drop. The investigation includes six different models filled partly with aluminium foam by varying internal diameter of foams from the wall side and external diameter of foam from the core of the tube. The pore density of the foam ranges from 10 to 45 PPI and their porosity varies from 0.90 to 0.95. Flow dynamics are captured using Darcy Extended Forchheimer model for the porous filled region and two-equation turbulence k-ω model employed in clear region of the fluid. The local thermal non-equilibrium assumption is incorporated in porous filled region of the conduit to compute the heat transport characteristics. The results showed that the thermal performance factor of 10 PPI aluminium foam performs close to the 10 PPI expensive copper foam. The performance factor is found to be higher for 30 PPI aluminium foam amongst the PPI’s of the foam considered. However, the performance factor is found to be 2.93, 2.22 and 1.73 for 30PPI, 45 PPI and 20PPI with their porosities of 0.92, 0.90 and 0.90, respectively for the model 1, model 2 and model 3 at lower Reynolds number of 4500 and then it decreases progressively with increasing flow rates of the fluid. The results of average wall temperature, average Nusselt number and Colburn j factor are also evaluated to obtain best possible performance.