Thermal Non-equilibrium Model Research Articles

Exergy Transfer and Irreversibility of Metal Foams Filled in a Vertical Channel

Abstract The aim of this work is to unveil the exergy transfer and overall thermal performance of the metal foams partially filled in varying thicknesses in the vertical channel. The numerical examination performed in this study consists of a heater cum plate assembly which is sited at the core of the vertical channel and the heat transfer from the plates is augmented by placing metal foams with high heat conducting capacities on either side of the channel. The uniqueness of the current investigation is to determine the optimum filling rate in various thicknesses of the channel with respect to overall thermal performance along with exergy transfer. Four different partial filling rates are considered in each thickness of the channel to find the optimum exergy transfer. The integrated Darcy Extended Forchheimer and local thermal non-equilibrium models are used for predicting the flow and heat transfer features via metal foam porous medium. The methodology implemented in this study is affirmed by validating the findings with the literature. The flow and heat transfer, along with exergy and irreversibility parameters are presented and discussed. Results showed that higher working limits permitted by exergy (WLPERe) are obtained for lesser metal foam filling rate as well as for higher metal foam thicknesses for all the cases examined in the study.

Thermal analysis and optimization of metal foam PCM-based heat sink for thermal management of electronic devices

Efficient thermal management in electric devices is highly essential for ensuring the reliability and durability of electronics. This study aims to investigate the thermal performance and optimization of metal foam PCM-based heat sink for thermal management units. Different design parameters, such as PCM types (RT31, RT42, and RT55), metal foam porosities (85%, 90%, and 95%), and metal foam materials, are studied to determine heat sink optimal parameters, considering various critical temperatures: 40 °C, 50 °C, 60 °C and 70 °C. The volume-averaged method is used to simulate the heat transfer, phase change, and fluid flow within the heat sink unit. Heat transfer between PCM and metal foam is established using a thermal non-equilibrium model. The results show that the usage of metal foam is conducive to the thermal performance enhancement of heat sinks. Among the three parameters, PCM types show a considerable effect on thermal performance of heat sinks, e.g., the maximum operation time of heat sinks with RT31 is about 5 times that of heat sinks with RT55 for the critical temperature of 40 °C. Among all the cases, heat sinks using RT31 and aluminum foam perform optimally, which can achieve the optimal design of heat sinks.

Performance Evaluation Based on Exergy Analysis Through Partially Filled Metal Foams in Forced Convection

Abstract The intention of this paper is to present the numerical analysis of thermal performance and exergy transfer through high porosity metal foams filled partially in a horizontal pipe. The heater is embedded in the pipe's circumference and is assigned with known heat input. To enhance heat transfer, aluminum metal foam of pore density 10 with porosity 0.95 is inserted adjacent to the pipe's inner wall. To determine the optimal thickness of metal foam for enhancing its performance thermodynamically, metal foams with five different thicknesses (10, 20, 40, 60, and 80 mm) are examined in this research for a fluid velocity ranging from 0.7 to 7 m/s under forced convection heat transfer condition. The Darcy– Brinkman–Forchheimer and local thermal nonequilibrium (LTNE) models are used for forecasting the flow features and heat transfer through the metal foams, respectively. The numerical methodology implemented in this research is confirmed by comparing the present outcomes with the experimental outcomes accessible in the literature and found a fairly good agreement between them. The thermal performance is assessed in terms of heat transfer enhancement ratio and performance factor, and the thermodynamic performance is evaluated based on exergy analysis. In the exergy analysis, the parameters like mean exergy-based Nusselt number (Nue), merit function (MF), and nondimensional exergy destruction (I*) are considered for the evaluation. The result shows a better performance from partially filled metal foams than from completely filled metal foams.

A comprehensive approach combining gradient porous metal foam and the magnetic field to regulate latent heat storage performance

This study proposes a comprehensive regulation method of gradient porous metal structure combined with the magnetic field to improve the controllability of heat utilization of latent heat thermal energy storage (LHTES) unit. Melting and solidification are considered. The enthalpy porosity method and magnetic force model describe the phase change of phase change material (PCM) and the movement of Fe3O4 nanoparticles under the magnetic field and assume the local thermal non-equilibrium model of metal foam. The numerical model is consistent with the visual experimental results of melting front evolution. The effects of magnetic nanoparticle concentration and gradient porosity on heat transfer and thermal energy change during melting and solidification are numerically studied. The results show that the phase change rate increases with the concentration of nanoparticles. The positive magnetic field further accelerates the phase change and heat energy change. The addition of copper foam considerably shortened the phase change time. The positive magnetic field accelerated the melting and heat energy change rate of PCM in copper foam by 18.2% and 23.1%, but the improvement of solidification was weak. Based on magnetic field promotion, the setting of porosity spacing with different gradients can regulate the phase interface uniformity, total heat energy, and heat energy change rate. Finally, according to different heat utilization scenarios of the LHTES system, this study gives recommended cases to optimize the performance of melting, solidification, and the phase change cycle.

Improving the cooling performance of cylindrical lithium-ion battery using three passive methods in a battery thermal management system

Developing a high-performance battery thermal management system (BTMS) to keep the temperature of lithium-ion battery (LIB) in a suitable range has become of great interest for electric vehicle (EV) applications. Hence, this study has been set out to design a BTMS by utilizing various combination of phase change material (PCM), metal foam, and fins that keeps the battery surface temperature at the lowest level in normal and harsh environmental conditions under discharging with 3C current rate. Considering these three passive methods, four different cases of BTMS have been designed separately. Moreover, the effects of various fin shapes including rectangular, triangular, trapezoidal, I-shape, and wavy fins are studied for the optimum BTMS. The two-equation local non-equilibrium thermal model has been used which is more precise than the traditional thermal equilibrium model in simulating heat transfer between the PCM and metal foam. The numerical results demonstrated that the optimum BTMS, which is the combination of PCM, metal foam, and fins (fourth case), can reduce the battery surface temperature by 3 K. Furthermore, the maximum delay of about 470 s in melting of the PCM has been reported for this case. Additionally, the applied fins in the fourth case are acting as a network of heat sources to spread heat in the middle of the system, and utilized metal foam can create a uniform distribution of heat between LIB and ambient. Analyzing the effect of different fin shapes on the performance of optimum BTMS showed that there are no remarkable changes between the battery surface temperature of various fin shapes and it would be hard to find a suitable shape of fins for all environmental conditions.

Cattaneo–Christov heat flux impacts on MHD radiative natural convection of Al2O3-Cu-H2O hybrid nanofluid in wavy porous containers using LTNE

This paper aims to examine impacts of Cattaneo–Christov heat flux on the magnetohydrodynamic convective transport within irregular containers in the presence of the thermal radiation. Both of the magnetic field and flow domain are slant with the inclination angles Ω and γ, respectively. The worked fluid is consisting of water (H2O) and Al2O3-Cu hybrid nanoparticles. The enclosures are filled with a porous medium, and the local thermal nonequilibrium (LTNE) model between the hybrid nanofluids and the porous elements are considered. Influences of various types of the obstacles are examined, namely, horizontal cold elliptic, vertical elliptic and cross section ellipsis. The solution methodology is depending on the finite volume method with nonorthogonal grids. The major outcomes revealed that the location (0.75, 0.5) is better for the rate of the flow and temperature gradients. The higher values of H* causes that the solid phase temperature has a similar behavior of the fluid phase temperature indicating to the thermal equilibrium state. Also, the fluid-phase average Nusselt number is maximizing by increasing Cattaneo–Christov heat flux factor.

Combined Effect of Temperature Modulation and Rotation on the Onset of Darcy-Bénard Convection in a Porous Layer Using the Local Thermal Nonequilibrium Model

Combined Effect of Temperature Modulation and Rotation on the Onset of Darcy-Bénard Convection in a Porous Layer Using the Local Thermal Nonequilibrium Model

UNSTEADY TRIPLE-DIFFUSIVE CONVECTION EMBEDDED WITH DARCY-BRINKMAN THREE-TEMPERATURE MODEL

The theory of binary nanofluid layer heated and soluted from below under the effect of local thermal non-equilibrium has been investigated by applying the technique of superposition of basic feasible modes with one-term Galerkin residual method. The so-called Darcy-Brinkman model for the top-heavy distribution of nanoparticles has been employed. A three-temperature local thermal non-equilibrium (LTNE) model, assuming one-temperature field for the solid matrix, one for the base fluid, and one for the suspended nanosized particles, is employed, incorporating the effects of Brownian and thermophoretic diffusions. Numerical computations are carried out with the software Mathematica (version 12.0). The novelty of the problem lies in the fact that destabilizing influence of nanoparticles and solute is countered with stabilization due to the presence of Darcy-Brinkman porous medium. Further, it has been observed that the two LTNE parameters namely, Nield parameter for particles and modified solute thermal capacity ratio, have destabilizing effects which are balanced by the other two parameters, viz. Nield parameter for solute and modified thermal capacity ratio for particles. The impact of nanofluid parameters is found to destabilize this top-heavy configuration of nanoparticles. Due to the consideration of Darcy-Brinkman model, Darcy number came into existence, which postpones the onset of instability. Similar is the effect of porosity and modified thermal diffusivity ratios for the particles as well as the solute.

HEAT AND MASS TRANSPORT IN A NANOFLUID LAYER USING A THERMAL NONEQUILIBRIUM MODEL CONFINED WITHIN A HELE-SHAW CELL UNDER THE EFFECT OF GRAVITY MODULATION

The local thermal nonequilibrium (LTNE) condition is the temperature difference between the base fluid and the nanoparticle. In the present research article, linear analysis was done to know about the onset of convection in the system, and a weakly nonlinear stability analysis was done to know about heat and mass transport in the system for both the unsteady and steady case. Here we have taken temperature to be constant and nanoparticle flux to be zero at the upper and lower boundaries of the system. The normal mode technique is used for linear analysis, and the truncated Fourier series method is used for nonlinear analysis; plot streamlines, isotherms, and isohaline are used to visualize the conduction, convection, and steady state. We found that the behavior of Hele-Shaw cell is the same in the case of LTNE and local thermal equilibrium (LTE). The effect of Hele-Shaw number, interphase heat transfer coefficient, modified thermal capacity ratio, thermal diffusivity ratio, amplitude, and frequency of modulation on the onset of convection, heat, and mass transfer are depicted graphically. We found that the effect of LTNE can be seen only for the intermediate values of the interphase heat transfer coefficient, and this region is called the LTNE region. We also discuss the result of thermal Nusselt number, streamlines, and isothermals of fluid and particle phase for steady case and plot the graphs with respect to the Hele-Shaw cell Rayleigh number. Rate of heat transfer for the particle phase is higher than the fluid phase for both the unsteady and steady state. In this research paper we find the result for both LTE and LTNE conditions with unsteady and steady cases, while in the previous study we analyzed only for the LTE condition.

THREE TEMPERATURE MODEL FOR HEAT AND MASS TRANSFER IN NON-NEWTONIAN Cu-EG NANOFLUIDS EMBEDDED WITH PERMEABLE MEDIUM

In the current study, the impacts of local thermal non-equilibrium model and Cu-EG Oldroyd-B nanofluid layer on natural convective heat and mass transfer in a permeable medium are investigated. The transport equations are framed using modified Buongiorno two-phase Darcy model with different temperature profiles for fluid, particle, and porous-matrix phases. The thermophysical properties of the considered nanofluid are calculated using available experimental data. In the current situation, weak, non-linear analysis has been performed to find the Nusselt number and Sherwood number by solving finite amplitude equations using NDSolve in Mathematica 12.0. Influence of different parameters including viscoelastic parameters, LTNE parameters, thermal Rayleigh number, and nanoparticle volume fraction on heat and mass transfer mechanisms are explained graphically. An increase in the Nusselt number with the rising values of volume fraction of nanoparticles is registered and reach its maximum value at φ = 0.05 due to enhanced thermal conductivity. The significant findings for Oldroyd-B nanofluids are that the stress relaxation parameter declines heat transfer while strain retardation parameter promotes it. This study improves the theoretical understanding of heat transfer in porous media and facilitates the use of such theoretical models in practical applications.

Optimization of 10 N Monopropellant High Test Peroxide Thruster for Space Applications

Monopropellant thruster is one of the most propulsion system types developed in the space industry. This system uses a single type of propellant that reacts in porous medium catalytic packed bed to generate thrust in the form of hot gases. The last decade, green propellant hydrogen peroxide (H2O2), also known as High Test Peroxide (HTP), thanks to its low cost and easy to store as liquid, is used as an alternative solution of hydrazine which is very toxic and not environmentally friendly. In the current study, hydrogen peroxide monopropellant thruster is investigated for application in the future satellites. A numerical simulation is performed using the Computational Fluid Dynamics (CFD) software ANSYS Fluent in order to simulate fluid flow of hydrogen peroxide in thruster, and the finite volume method was employed for resolving the governing equation. Species transport model is applied in the single-phase reaction simulation using the Eddy Dissipation model (EDM) for turbulence-chemistry interaction. A mathematical approach based on the local thermal non-equilibrium (LTNE) model is used to describe the heat transfer through solid and fluid phases in the packed bed consisting of identical spherical silver particles. Several simulations performed allowed an optimal design of the injector, catalyst bed length and diameter and nozzle geometry, to achieve a 10N monopropellant thruster with hydrogen peroxide at 87.5% concentration.

Aiming to personalized laser therapy for nevus of Ota: melanin distribution dependent parameter optimization.

Aiming to the personalized laser therapy of nevus of Ota (NO), a local thermal non-equilibrium model was employed to optimize laser wavelength, pulse duration, and energy density under different melanin depth and volume fraction. According to our simulation, the optimal pulse duration is between 15 and 150ns to limit heat transfer inside the hyperplastic melanin, and 50ns is recommended to decrease the energy absorption by normal melanin in epidermis. Correlations of the minimum and the maximum energy densities are proposed with respect to melanin depth and volume fraction for the 755-nm and 1064-nm lasers. For the same NO type, the therapy window of the 755-nm laser is larger than that of 1064-nm. For NO with shallow depth or low volume fraction, the 755-nm laser is recommended to make the treatment more stable owing to its lager therapy window. For deeper depth or higher volume fraction, the 1064-nm laser is recommended to avoid thermal damage of epidermis. Through comparison with clinical data, the optimized laser parameters are proved practicable since high cure rate can be achieved when energy density falls into the range of predicted therapy window. With developing of non-invasive measurement technology of melanin content and distribution, personalized treatment of NO maybe possible in the near future.

Chaotic Cattaneo-LTNE porous convection

The chaotic convection in a porous medium has been studied with a local thermal nonequilibrium (LTNE) model and hyperbolic-type heat transport equation in the solid arising due to Cattaneo heat flux law. The Brinkman-extended Darcy model is considered to describe the flow in a porous medium. A system of autonomous nonlinear ordinary differential equations is derived by using a truncated double Fourier series expansion such that the linear stability theory results are the same as those for the full two-dimensional problem. The stability of equilibrium points of the system is discussed in detail for the governing parameters involved therein. The transition to chaos in different phase planes and the transient behavior of heat transfer are analyzed by solving the model equations numerically using the Runge-Kutta-Fehlberg technique. The effect of increasing scaled solid thermal relaxation time parameter is to speed up the transition to chaos and to decrease the heat transfer.

Modeling and simulation in supersonic three-temperature carbon dioxide turbulent channel flow

This paper pioneers the direct numerical simulation (DNS) and physical analysis in supersonic three-temperature carbon dioxide (CO2) turbulent channel flow. CO2 is a linear and symmetric triatomic molecular, with the thermal non-equilibrium three-temperature effects arising from the interactions among translational, rotational, and vibrational modes at room temperature. Thus, the rotational and vibrational modes of CO2 are addressed. The thermal non-equilibrium effect of CO2 has been modeled in an extended three-temperature kinetic model, with the calibrated translational, rotational, and vibrational relaxation time. To solve the extended kinetic equation accurately and robustly, non-equilibrium high-accuracy gas-kinetic scheme is proposed within the well-established two-stage fourth-order framework. Compared with the one-temperature supersonic turbulent channel flow, supersonic three-temperature CO2 turbulence enlarges the ensemble heat transfer of the wall by approximate 20% and slightly decreases the ensemble frictional force. The ensemble density and temperature fields are greatly affected, and there is little change in Van Driest transformation of streamwise velocity. The thermal non-equilibrium three-temperature effects of CO2 also suppress the peak of normalized root mean square of density and temperature, normalized turbulent intensities and Reynolds stress. The vibrational modes of CO2 behave quite differently with rotational and translational modes. Compared with the vibrational temperature fields, the rotational temperature fields have the higher similarity with translational temperature fields, especially in temperature amplitude. Current thermal non-equilibrium models, high-accuracy DNS and physical analysis in supersonic CO2 turbulent flow can act as the benchmark for the long-term applicability of compressible CO2 turbulence.

Validation of the local thermal equilibrium assumption for free convection boundary layer flow over a horizontal cylinder embedded in an infinite saturated porous medium

This study numerically investigated the validity of the local thermal equilibrium model for free convection over a horizontal cylinder embedded in an infinitely packed bed of spherical particles saturated with Newtonian fluid. The local thermal non-equilibrium and Forchhemimer-Brinkman extended Darcy model were used by considering the boundary-layer theory assumptions and were solved with the implicit Keller box finite difference scheme. The governing parameters considered are the porosity, thermal conductivity ratio, Rayleigh number, Prandtl number, the ratio of cylinder diameter to spherical particle diameter and Biot number. The results showed the two parameters of conductivity ratio and Biot number can significantly affect the other parameters. For low Biot number and conduction coefficient ratio, the local thermal non-equilibrium assumption was inapplicable in almost all cases. Significantly, for high values of the conductivity ratio and Biot number, the assumption that the fluid and solid matrix are isothermal, could be used in almost all cases studied. Furthermore, increasing the amount of Rayleigh number, Porosity and Prandtl increased the temperature difference between the solid and fluid phases. In addition, increasing the ratio of cylinder diameter to particle diameter reduced the temperature difference between the two phases. The average temperature difference between fluid and solid can have the most changes as follows: It can experience 200% growth when the Prandtl number changes from 2 to 7. Also, it can reduce by 33% by increasing the Bio number from 0.01 to 10. In addition, the temperature difference of two phases can be increased by 7 and 0.5 times by increasing the porosity from 0.25 to 0.85 and increasing the ratio of cylinder diameter to particle diameter from 20 to 100, respectively.

Numerical Simulation of Subcooled Boiling in Swing Rectangular Channel based on Non-Equilibrium Thermal Model

Theoretical analysis on the fluid flow in a vertical rectangular channel under swing motion is performed to establish the mathematical model which is based on Eulerian two-fluid framework and non-equilibrium subcooled boiling model. It is analyzed that the flow and heat transfer characteristics and the force of the fluid under the condition of forced flow and swing motion condition. The results show that, for the existence of Coriolis force, the period of acceleration of the fluid is 1/2 of the period of swing angle, and the phase differ. In the rectangular channel, the angle of pressure isoline and horizontal line is sinusoidal likely, which is behind the swing angle phase; Due to the influence of the periodic force field, with the increase of the swing angle, the bubbles in the rectangular channel move to one side, and the wall temperature also increases, which leads to the deterioration of heat transfer; In a swing period, the vapor volume fraction at the outlet and the pressure drop between the inlet and outlet of the rectangular channel fluctuate, and the vapor volume fraction is located at the minimum pressure drop, and the vapor volume fraction at the outlet fluctuates in a trough type.

Numerical Study for Enhancement of Heat Transfer Using Discrete Metal Foam with Varying Thickness and Porosity in Solar Air Heater by LTNE Method

A two-dimensional rectangular domain is considered with a discrete arrangement at equal distances from copper metal foam in a solar air heater (SAH). The local thermal non-equilibrium model is used for the analysis of heat transfer in a single-pass rectangular channel of SAH for different mass flow rates ranging from 0.03 to 0.05 kg/s at 850 W/m2 heat flux. Three different pores per inch (PPI) and porosities of copper metal foam with three different discrete thicknesses at equal distances are studied numerically. This paper evaluates the performance of SAH with 10 PPI 0.8769 porosity, 20 PPI 0.8567 porosity, and 30 PPI 0.92 porosity at 22 mm, 44 mm, and 88 mm thicknesses. The Nusselt number for 22 mm, 44 mm, and 88 mm thicknesses is 157.64%, 183.31%, and 218.60%, respectively, higher than the empty channel. The performance factor for 22 mm thick metal foam is 5.02% and 16.61% higher than for 44 mm and 88 mm thick metal foam, respectively. Hence, it is found that metal foam can be an excellent option for heat transfer enhancement in SAH, if it is designed properly.

Modeling on cryogenic heat exchangers considering variable properties, axial heat conduction and viscous heating

Cryogenic heat exchangers are key components of low temperature refrigerators and determine the ultimate refrigeration performance. Accurate modeling on the cryogenic heat exchangers in sub-Kelvin regime has important theoretical and applied values, yet is still short of study. This study proposes local thermal nonequilibrium models of the heat exchangers in sub-Kelvin regime, including continuous and discrete ones. The effects of the variable properties, axial heat conduction, and viscous heating were investigated. The finite volume method was employed to solve the models numerically; in addition, the temperature and pressure distributions were obtained and analyzed. The proposed models were validated using a comparison of the obtained simulation results with experimental results in the literature. The analysis of the obtained results revealed that: (1) for continuous heat exchangers, the variable Kapitza thermal conductance leads to a large temperature gradient at the entrance. The outlet temperature was negligibly affected by applying different inlet temperature. (2) The axial heat conduction significantly degrades the performance of discrete heat exchangers. The performance was found to be limited by the axial heat conduction when the axial heat conduction parameter was larger than 0.02. (3) For the sintered heat exchanger, both the dimensionless temperature and pressure drop are obviously affected by the geometric impedance when it is greater than 4 × 1014 m−4. Consequently, the proposed mathematical models are useful for the accurate prediction and optimization of cryogenic heat exchangers.

Numerical study on comprehensive performance of flow and heat transfer coupled with ortho-para hydrogen conversion

The energy consumption of hydrogen liquefaction can be effectively reduced by filling the plate-fin heat exchanger with the catalyst to achieve continuous conversion of ortho-para hydrogen while cooling. In this study, a three-dimensional numerical model of heat transfer and flow coupled with ortho-para hydrogen conversion is established, and the simulation results are verified by the experimental data. Both the temperature field and the outlet parahydrogen fraction demonstrate better accuracy of the local thermal non-equilibrium model results compared to the local thermal equilibrium model results, and the thermal non-equilibrium effect is most significant at the inlet of the porous medium, where the temperature difference between the fluid and the solid exceeds 2 K. Furthermore, it is indicated that two typical stages exist in the hot channel: the heat transfer dominates in the inlet section and the ortho-para hydrogen conversion efficiency decreases significantly, even once falling below 30%. In the thermal fully developed section, the catalytic performance is effectively improved along with the decay of velocity, with a 10% improvement compared to the lowest point of performance. Finally, an integrated comprehensive performance evaluation criterion is summarized regarding the overall performance of heat transfer, flow and catalysis, with excellent comprehensive performance being achieved at Reynolds numbers of 170 to 300. This research can provide a reference for the comprehensive performance study of catalyst-filled plate-fin heat exchanger for hydrogen.

The role of a second diffusing component on the Gill–Rees stability problem

The stability of natural convection in a vertical porous layer using a local thermal nonequilibrium model was first studied by Rees (Transp Porous Med 87:459–464, 2011) following the proof of Gill (J Fluid Mech 35:545–547, 1969), called the Gill–Rees stability problem. The aim of the present study is to investigate the implication of an additional solute concentration field on the Gill–Rees problem. The stability eigenvalue problem is solved numerically and some novel results not observed in the studies of double-diffusive natural convection in vertical porous (local thermal equilibrium case) and non-porous layers are disclosed. The possibility of natural convection parallel flow in the basic state becoming unstable due to the addition of an extra diffusing component is established. In some cases, the neutral stability curves of stationary and travelling-wave modes are connected to form a loop within which the flow is unstable indicating the requirement of two thermal Darcy–Rayleigh numbers to specify the stability/instability criteria. Moreover, the change in the mode of instability is recognized in some parametric space. The results for the extreme cases of the scaled interphase heat transfer coefficient are discussed.