Local Thermal Non-equilibrium Condition Research Articles

Numerical simulation of chemical reactive flow of Boger fluid over a sheet with heat source and local thermal non-equilibrium conditions

In this article, the effect of nonlinear heat source on chemical reactive flow of magnetized Boger fluid over a sheet with Marangoni convection and porous medium is explored. In the modelling, local thermal non-equilibrium (LTNE) conditions and heat sources are taken into account. The unique heat transport for both liquid and solid phases is provided by the LTNE model, which is based on thermal equations. As a result, various temperature profiles are used in this work for both the solid and fluid phases. It is essential for streamlining industrial procedures, improving material processing methods, comprehending biological systems like blood flow for medicine delivery, determining the environmental impact of pollutant dispersion, and increasing the effectiveness of oil and gas transportation. This model supports crucial decision-making processes in numerous disciplines by offering insights into the intricate interplay between reactive fluids, heat transmission, and chemical reactions. The appropriate similarity variables are used to compress the model equation system, and the shooting method and the conventional bvp4c solver are then used to solve the system numerically. Optimal homotopy approach is used to achieve residual errors. There are suggested best estimates for auxiliary variables. Results show that for larger values of the solvent fraction parameter, Boger fluid exhibits an enhanced velocity profile and a declining thermal profile of the liquid phase. The concentration and thermal profiles of both the solid and liquid phases are declined and enhanced the velocity of the Boger fluid for higher values of the Marangoni convection parameter.

Solid–liquid phase transition simulated by the lattice Boltzmann model: from pore scale to representative elementary volume scale

Purpose This paper aims to establish a lattice Boltzmann (LB) method for solid-liquid phase transition (SLPT) from the pore scale to the representative elementary volume (REV) scale. By applying this method, detailed information about heat transfer and phase change processes within the pores can be obtained, while also enabling the calculation of larger-scale SLPT problems, such as shell-and-tube phase change heat storage systems. Design/methodology/approach Three-dimensional (3D) pore-scale enthalpy-based LB model is developed. The computational input parameters at the REV scale are derived from calculations at the pore scale, ensuring consistency between the two scales. The approaches to reconstruct the 3D porous structure and determine the REV of metal foam were discussed. The implementation of conjugate heat transfer between the solid matrix and the solid−liquid phase change material (SLPCM) for the proposed model is developed. A simple REV-scale LB model under the local thermal nonequilibrium condition is presented. The method of bridging the gap between the pore-scale and REV-scale enthalpy-based LB models by the REV is given. Findings This coupled method facilitates detailed simulations of flow, heat transfer and phase change within pores. The approach holds promise for multiscale calculations in latent heat storage devices with porous structures. The SLPT of the heat sinks for electronic device thermal control was simulated as a case, demonstrating the efficiency of the present models in designing and optimizing SLPT devices. Originality/value A coupled pore-scale and REV-scale LB method as a numerical tool for investigating phase change in porous materials was developed. This innovative approach allows for the capture of details within pores while addressing computations over a large domain. The LB method for simulating SLPT from the pore scale to the REV scale was given. The proposed method addresses the conjugate heat transfer between the SLPCM and the solid matrix in the enthalpy-based LB model.

Importance of thermophoretic particles deposition in ternary hybrid nanofluid with local thermal non-equilibrium conditions: Hamilton–Crosser and Yamada–Ota models

This article exhibits a brief study of magneto ternary hybrid nanofluid flow with thermophoretic particle deposition and porous medium based on the extended version of model, known as the Yamada-Ota and Hamilton Crosser models. Thermophoretic particle deposition, which is important in both aero-solution and electrical engineering, is one of the most fundamental methods for transferring small particles across a heat gradient. This suggested model's goal is to evaluate how well Hamilton-Crosser and Yamada-Ota, two trihybrid nanofluid models, perform. Advanced heat transfer systems, in particular the creation of effective cooling and heating technologies, may benefit from this research. Researchers can develop more efficient heat exchangers, boost thermal management in electronic devices, and increase energy efficiency in industrial processes by better understanding how thermophoretic particles behave in complicated nanofluid systems under various conditions. By using the required similarity variables, the MATLAB solver bvp4c package handles the system of ODEs acquired from the leading PDEs to arrive at the numerical solution. The relevant parameters' effects on the relevant fields have been graphically explained. The results show that when inter-phase heat transfer parameter value grows, thermal profile and rate of heat transfer decrease of liquid phase. With regard to heat and mass transfer effectiveness, the Yamada-Ota model performs better than the Hamilton Crosser trihybrid nanofluid model.

Effects of local thermal non-equilibrium on hydraulic stimulation efficiency of enhanced geothermal systems

Motivated by hydraulic stimulation of enhanced geothermal systems, the present paper investigates the coupled thermo-hydro-mechanical response of a geothermal well imbedded in a thermoporoelastic medium, subjected to a non-isothermal fluid flux and convective cooling on the borehole surface. Our focus centers on the effect of local thermal non-equilibrium (LTNE) on the temporal-spatial evolution of temperatures, pore pressure, and stresses, where the solid and fluid phases have two distinct temperatures and local heat transfer between the two phases is addressed. We employ integral transform and load decomposition techniques to derive analytical solutions in the Laplace domain. This methodology allows us to disentangle and separate the individual contributions to changes in pore pressure and stresses from fluid injection and convective heat transfer. The results reveal that compared to the classical local thermal equilibrium model, the thermally induced pore pressure is slightly lower under LTNE conditions. The LTNE has a significant influence on the temporal evolution of thermally induced stresses, especially in the vicinity of the wellbore.

Effect of the Aligned Magnetic Field over a Stretching Sheet through Porous Media in Casson Fluid Flow

Researchers in the thermo-fluidic field have dedicated considerable effort to exploring methods for improving heat transfer in diverse thermal systems. Among these methods, incorporating porous mediums into thermal systems stands out as particularly effective. The movement of substances through these porous materials, which encompass both fluid and solid components, can be described by either assuming that both phases are at the same temperature or that they are at different temperatures. The significance of heat and mass flux arises from their association with chemical potential and temperature gradient respectively. These connections hold value within a wide array of fields, including electrical power generation, solar power technology, chemical engineering, petrology and many more. In the present study, aligned magnetic effects have been investigated on local thermal non-equilibrium (LTNE) circumstances on steady, incompressible, laminar flow of a non-Newtonian Casson fluid across a stretching sheet in a porous medium. The LTNE conditions are implemented to generate two distinct temperature profiles for both fluid and solid phases. By choosing appropriate similarity transformations, the governing partial differential equations are transformed into ordinary differential equations for the flow parameters and are solved using numerical method Runge-Kutta-4 with shooting technique. The flow attributes are thoroughly inspected graphically in response to the influence of the developing factors. As aligned magnetic parameter and porosity parameter values increase, heat transmission improves, but velocity decreases. In the flow zone, as values of angle increases, magnetic field intensity increased. The heat flux in both fluid and solid phases decreases as the Dufour number rises. As the Soret number rises, the mass transfer rate falls.

Effects of porous medium filling on thermally developing forced convection in a parallel plate channel

This study obtains the semi-analytical solutions and explores the thermal characteristics of a thermally developing flow in a parallel plate channel, partially filled with a porous medium at the core, while considering local thermal non-equilibrium conditions, and viscous dissipation for the first time. The developing temperature field, for a porous medium filling of volume fraction fixed at 0.9, indicates an increasing difference in temperature between the solid and fluid phases with the axial distance. Besides, heat flux bifurcation starts in the entrance region as more heat diffuses to the solid at the interface, more markedly with a decreasing Darcy number, Da. When the thermal transport is dominated by interstitial heat transfer between solid and fluid in the porous medium, the thermal entrant length is the shortest. An increasing amount of porous medium filling with such quality and an increasing Da tend to shorten the thermal entry length. Nonetheless, as a lower Da porous media convects more heat away from the interface, it expedites the thermal development in cases where interstitial heat transfer in porous medium is poor. With an increasing porous medium fraction, the impact of viscous dissipation on heat transfer magnifies at the entrance region, thereby reducing the effectiveness of porous medium insert.

Three-dimensional non-Darcy free convective heat transfer flow in a bidisperse porous medium within a cubical cavity

Heat transport in porous media, especially in a bidisperse porous matrix, has recently received considerable attention due to its diverse real-life applications in applied science and engineering. In the current study, we employ the Darcy-Brinkman-Forchheimer model and three temperature equations incorporating the local thermal nonequilibrium conditions among the fluid and the porous matrix to examine the three-dimensional free convective heat transfer flow in a bidisperse permeable matrix inside a cubical cavity. The Galerkin weighted residual finite element method simulates the model's non-dimensional governing equations. We examine the effects of the significant model parameters on the flow and heat domains considering (104 ≤ Raf ≤ 106), (103 ≤ Rap ≤ 106), (10−3 ≤ Daf ≤ 10−1), (10−4 ≤ Dap ≤ 10−2),(0.7 ≤ ϕ ≤ 0.9) and (0.4 ≤ ε ≤ 0.7). It is found that the average Nusselt number in the macrophase, microphase, and solid matrix increased with the increase of the macro porosity for about 7.18%, 7.06%, and 9.86%, respectively, when it rises from 0.7 to 0.9. Furthermore, increasing the micro-porosity enhances the rate of heat transfer. As the Raleigh number advances, there is a noticeable increase in heat transfer in both the macrophase and the microphase.

Coupled THM formulation and wellbore analytical solution in naturally fractured media during injection/production

The heat extraction efficiency, storage, and safety of carbon dioxide (CO2) sequestration and methane (CH4) injection/post-production in naturally fractured formations have attracted significant interest. However, these studies require the examination of complex thermal-hydraulic-mechanical (THM) interacting processes, which include muti-discipline coupling and phase changes. Energy transfer mechanisms and thermally induced hydraulic and mechanical responses are critical for energy extraction efficiency , surface design optimization, and safety evaluation. The THM response in the wellbore, where fluids are injected and circulated, provides key information for design evaluation. A fully coupled formulation was developed based on a dual-porosity model to simulate the THM responses of a wellbore in naturally fractured aquifers under non-isothermal, two-phase fluid flow, and non-hydrostatic loading conditions. Local thermal non-equilibrium (LTNE) conditions are imposed for energy transportation between the fracture and matrix systems in the fissured porous solid skeleton. Different physical parameters reflecting various rock types and fracture characteristics are defined for the corresponding THM behavior models. Analytical solutions for the temperature perturbation and pressure changes in single-phase fluid flow in the vicinity of a wellbore in fissured media are developed to simulate the injection and production processes. Simulating a non-isothermal fluid circulation problem along a wellbore, an newly proposed mixed Type I (Dirichlet) and II (Neumann) boundary condition is imposed to study the heat exchange efficiency between wellbore fluid and the fissured NFM. The analytical solution has the advantages of being simple, explicitly possessing direct physical parameters, and serving as a tool for validating numerical solutions. The impacts of the newly proposed boundary condition on the near-well responses and THM results from the newly developed solution may be used to simulate the injectivity, storage capacity, reproduction, and design of supercritical carbon (scCO2) and CH4 are discussed.

Validity of Local Thermal Equilibrium Assumption for Heat Transfer in a Saturated Soil Layer

The assumption of local thermal equilibrium (LTE) between solid and fluid phases commonly is used for studies of heat transfer in saturated soil and is valid for a wide range of conditions. However, for certain conditions, the heat transfer process may give rise to local thermal nonequilibrium (LTNE) in which adjacent solid and fluid phases have different temperatures. This note presents the results of a numerical study of the validity of the LTE assumption for one-dimensional heat transfer in a saturated soil layer with fluid flow. For the conditions investigated, the LTE assumption holds for soil with particle sizes smaller than the gravel range. For soil with particles sizes in the gravel range and larger, the LTE assumption may be valid or invalid, depending primarily on fluid discharge velocity, with higher fluid velocity values more likely to produce LTNE conditions.

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.

Mixed convective flow of a Newtonian fluid through a porous medium with a lack of thermal equilibrium

The primary focus of this work is on the effects of thermal radiation and heat generation on mixed convective MHD steady flow of a Newtonian fluid via a porous channel under local thermal non-equilibrium (LTNE) condition. The resulting governing equations are converted into a set of ordinary differential equations (ODEs) using the proper similarity transformation. The shooting method is implemented in MATLAB code, which is then used to solve the set of dimensionless coupled ODEs. In the fluid phase, the external effects of heat generation and thermal radiation are taken into account. The effect of individual parameters on flow and heat transfer phenomena are discussed in detail with the help of plots and tables. From the study, it is noted that LTNE is predominant near the wedge compared to that far away from the wedge and also as heat transfer rate increases for greater values of thermal conductivity ratio parameter.

A macroscopic and mesoscopic model of Newtonian and non-Newtonian nanofluids with a two-energy equation method

We present an updated comprehensive macroscopic model of nanofluids, considering a revisited local thermal non-equilibrium (LTNE) condition to study the temperature difference between carrier fluid and nanoparticles. A new relation for thermal conductivity of solid and liquid phases in the LTNE condition is introduced which considers the possible particle aggregation. This model is thermodynamically consistent and covers the non-Newtonian models of nanofluids, including power-law and viscoplastic ones. A mesoscopic scheme based on the lattice Boltzmann method (LBM) which satisfies the presented macroscopic equations is introduced and derived. This investigation is a further development of our recent studies[G. H. R. Kefayati and A. Bassom, “A lattice Boltzmann method for single and two phase models of nanofluids: Newtonian and non-Newtonian nanofluids,” Phys. Fluids 33, 102008 (2021); G. H. R. Kefayati, “A two- and three-dimensional mesoscopic method for an updated non-homogeneous model of Newtonian and non-Newtonian nanofluids,” Phys. Fluids 34, 032003 (2022).] for simulating and analyzing nanofluids by a two-phase model. To assess the present numerical method, it is studied for a benchmark problem of natural convection in a cavity. The dimensional and non-dimensional macroscopic equations for the mentioned benchmark are defined and the implemented non-dimensional relations of LBM are shown. The present approach is verified with the obtained results of the mixture approach and a previous two-phase model, which demonstrated the accuracy of the presented method. The results including the temperature distributions of the solid and fluid phases, the nanoparticles distributions, and fluid flow behavior as well as the yielded/unyielded sections for the viscoplastic nanofluids are shown and discussed for the defined non-dimensional parameters. It was also demonstrated that the previous proposed thermal conductivity model of nanofluids in the LTNE approach generates a significantly different value compared to experimental results, and the current suggested model produces reliable results to the experimental ones.

The Thermal Performance Analysis of an Al2O3-Water Nanofluid Flow in a Composite Microchannel

Partial filling of porous medium insert in a channel alleviates the tremendous pressure drop associated with a porous medium saturated channel, and enhances heat transfer at an optimum fraction of porous medium filling. This study pioneered an investigation into the viscous dissipative forced convective heat transfer in a parallel-plate channel, partially occupied with a porous medium at the core, under local thermal non-equilibrium condition. Solving the thermal energy equation along the Darcy-Brinkman equation, new exact temperature fields and Nusselt number are presented under symmetrical isoflux thermal boundary condition. Noteworthy is the heat flux bifurcation at the interface between the clear fluid and porous medium driven by viscous dissipation, in cases where the combined hydrodynamic resistance to fluid flow and thermal resistance to fluid conduction is considerable in low Darcy number porous medium insert. However, viscous dissipation does not affect the qualitative variation of the Nusselt number with the fraction of porous medium filling. By using Al2O3-Water nanofluid as the working fluid in a uniformly heated microchannel, partially filled with an optimum volume fraction of porous medium, the heat transfer coefficient improves as compared to utilizing water. The accompanied viscous dissipation however has a more adverse impact on the heat transfer coefficient of nanofluids with an increasing Reynolds number.

Fully coupled thermo-hydro-mechanical modeling and simulation of a fluid-saturated porous medium under local thermal non-equilibrium condition

• Fully coupled THM model of porous media under LTNE condition is presented. • T s is always higher than T f due to the LTNE effect. • Dependences of multi-physical fields on the pertinent parameters are investigated. This paper presents a fully coupled thermo-hydro-mechanical (THM) model of a fluid-saturated and compressible porous medium under local thermal non-equilibrium (LTNE) condition and carries out the corresponding numerical simulation. First, the coupling among the temperature field, the pore fluid pressure field, and the solid stress/displacement field is fulfilled by means of strong explicit coupling of governing equations in this study. Then, the presented model is applied to the THM coupling problem in an infinite porous medium with a cylindrical borehole subjected to uniform fluid pressure and temperature at the borehole boundary. Subsequently, the partial differential equations (PDEs) module in COMSOL Multiphysics software is employed to numerically solve the studied problem. Consequently, the finite element solutions of the pore fluid pressure field, the strain/stress fields and the two temperature fields of pore fluid and skeleton solid are obtained, and the spatial-temporal distribution characteristics of the above multi-physical fields are investigated. Finally, the corresponding parametric studies are carried out. The numerical results show that the stress decreases with the increase of the bulk volumetric thermal expansion coefficient of porous media. And the pore pressure decreases when the pore fluid mobility increases. Meanwhile, it is found in this work that the solid temperature is always higher than that of pore fluid due to the LTNE effect. Besides, with increasing the specific solid–fluid interfacial heat transfer coefficient, the solid temperature decreases, while the temperature of pore fluid increases. Accordingly, the temperature difference between the solid and the pore fluid diminishes. In addition, the thermal conductivity of solid grains has a greater impact on the solid temperature but has a limited impact on the temperature of pore fluid, and vice versa. The findings in this work are of benefit to obtain in-depth understanding of THM fully coupling mechanism and LTNE effect in a fluid-saturated porous medium.

Investigation of thermal-hydraulic performance of metal-foam heat sink using machine learning approach

Metal foam heat sinks (MFHSs) are often used for electronic cooling because of their high specific heat transfer surface area, fluid mixing capability, and lightweight. Thermal-hydraulic performance of MFHS is known to be related to the morphological parameters of the metal foam (MF), physical dimensions of the heat sink, and coolant flow condition. Moreover, the highly random and complex geometrical nature of MFHS makes full-scale numerical simulation and experimental analysis expensive. In this paper, we have utilized machine learning (ML) methods to predict the thermal-hydraulic performance of MFHS, considering MF morphology, heat sink dimension, and coolant flow condition as input features. Considering local thermal non-equilibrium conditions for MFHS, a database of 1000 data points is generated utilizing a validated high-fidelity computational fluid dynamics/heat transfer (CFD/HT) model. The data sets consist of two non-dimensional descriptors, i.e., Nusselt number (Nu) and friction factor (f), along with the four input features such as MF morphological parameters, i.e., porosity and pore density, heat sink geometrical dimensions, i.e., hydraulic diameter (Dh) and flow condition, i.e., Reynolds number (Re). Five different ML-based regression models, namely k-nearest neighbor (KNN), random forest (RF), extreme gradient boosting (XGBoost), support vector regressor (SVR), and artificial neural networks (ANN), have been developed. Hyper-parameters of each ML model have been systematically optimized, and optimized model's performance have been compared using statistical score metrics and considering the initialization effect. Additionally, in order to demonstrate the robustness of the developed ML models, individual model performance has been evaluated by independent datasets. Results indicate that for testing datasets, all ML algorithms, except KNN, can predict the thermal-hydraulic performance of MFHS reasonably well, with a mean absolute percent error (MAPE) of about 4.59% and a 1.24 standard deviation (SD). However, SVR and ANN outperform other models for independent datasets with a MAPE of less than 3.1%.

Enthalpy-based immersed boundary-lattice Boltzmann model for solid-liquid phase change in porous media under local thermal non-equilibrium condition

Heat transfer enhancement structures are adopted to improve the performance of latent heat thermal energy storage (LHTES) systems, such as metallic porous matrix, multi-tube, and fin. The metallic porous matrix and complex geometries of the structures bring difficulties to the numerical studies of the solid-liquid phase transition in the enhanced LHTES system. In this work, an enthalpy-based immersed boundary (IB)-lattice Boltzmann (LB) model is proposed for solid-liquid phase change problems in porous media under the local thermal non-equilibrium (LTNE) condition. In this model, to reduce the numerical diffusion across the solid-liquid interface, a two-relaxation-time (TRT)-LB model is developed to obtain the temperature field of phase change material (PCM). Two single-relaxation-time (SRT)-LB equations (LBEs) are employed for the velocity field of the liquid PCM and the temperature field of the porous matrix, respectively. The partially saturated method is used for the non-slip boundary condition on the moving solid-liquid interface. Different discrete source term schemes are employed for source terms induced by surface heat transfer and IB. Based on the source term treatment, the multi-direct-forcing IB-LB method is employed for the implementation of velocity, enthalpy and temperature boundary conditions on the complex boundary. The proposed model is verified by four cases: one-dimensional conduction melting under the LTNE condition, natural convection in a metallic porous matrix-filled cavity, conduction melting in an annulus filled with metallic porous matrix, and constrained melting in an isothermal circular cylinder without porous media. As an example of application, a metallic porous matrix-enhanced LHTES system with different multi-tube arrangements at different Rayleigh numbers (Ra) and porosities is investigated.

Radiative and heat generation effects on MHD mixed convection of non-Newtonian nanofluids in lid-driven inclined odd-shaped porous cavity containing obstacle using local thermal non-equilibrium condition

The present work examines the local thermal non-equilibrium condition (LTNEM) on the mixed convection of non-Newtonian nanofluids in a lid-driven inclined odd-shaped porous cavity involving obstacles. The SIMPLE algorithm in the finite volume method (FVM) is adopted to handle the present physical problem. The impacts of pertinent physical parameters such as length/location of heaters, thermal radiation, heat generation parameter, Hartmann number, and microrotation parameter on the streamlines, isotherms of a fluid, isotherms of a solid, and iso-microrotations as well as the local Nusselt number, and average Nusselt number are investigated. The major achieved numerical results indicated the importance of the heater length and location on the improvement of the heat transport in fluid/solid phases within an odd-shaped cavity. Expanding enhances the values of local Nusselt number in a fluid phase and lowers the values of the mean Nusselt number . The heat generation parameter improves the isotherms, , and . The thermal radiation parameter acting effectively in enhancing isotherms of a solid phase and local Nusselt number in a solid phase .

CFD simulation of the Sabatier process in a shell-and-tube reactor under local thermal non-equilibrium conditions: Parameter sensitivity and reaction mechanism analysis

The Sabatier process is a competitive technology applied for carbon capture and utilization. This process increases the risk of carbon deposition and catalyst thermal degradation because of its exothermic property. In this study, a CFD model verified through existing experimental data was established to systematically investigate the Sabatier process in a shell-and-tube reactor. The effects arising from several operating parameters (e.g., gas flow rate, feed gas composition, the thermal conductivity of catalyst pellet, the inlet temperature of cooling phase, as well as phase change refrigeration) on temperature profile and reaction performance were studied. Moreover, a mechanism of three reactions was investigated, including CO 2 methanation, CO methanation, as well as RWGS reaction. Furthermore, the competition between CO 2 methanation and RWGS reaction was explored. According to the further sensitivity analysis, increasing the thermal conductivity of the catalyst particles would be effective to inhibit hot spots, while keeping the carbon conversion rate unchanged. • A CFD model of the Sabatier process under local thermal non-equilibrium conditions. • The conjugate heat transfer among gas, catalyst bed, reactor, and cooling phase. • A mechanism of three reactions on the Sabatier process was explored. • Parameter sensitivity of operating parameters for the Sabatier process was analyzed.

Numerical study of natural convection in an annulus between two concentric cylinders provided with metal foam fins

Natural convection in an annular space provided with metal foam fins attached to the inner cylinder is studied numerically. The metal foam fins made of copper were inserted in different axial sections with three fins in each section. The temperature of the inner cylinder is kept constant while the annular outer surface is adiabatic. The thickness effect of the inner pipe wall was considered. Naiver Stokes equation with Boussinesq approximation is used for the fluid regime while Brinkman-Forchheimer Darcy model is used for metal foam. In addition, the local thermal non-equilibrium condition in the energy equation of the porous media is presumed. The effect of Rayleigh number and number of foam fins in the axial direction, on fluid flow and heat transfer characteristics, were examined. The current model was valid with the available published results and good agreement is noticed. Results showed that as the Rayleigh number increases the dominated of convection mode increases and average Nusselt increases. It was found that at Rayleigh of 106 Nusselt reached its higher value which is 4.6 for the case of adding seven axial metal foams. A comparison between adding foam fins and copper fins was established for a range of Rayleigh numbers between 104 and 106. It showed a good enhancement in Nusselt number and the greatest enhancement percentage was 45.9% at Rayleigh equal 106 for the case of using seven sections of foam fins.

The effect of local thermal non-equilibrium on the onset of thermal instability for a metallic foam

Mixed convection in metallic foams modeled with Darcy's law under local thermal non-equilibrium conditions is investigated, where the solid phase thermal conductivity is assumed to be infinitely larger than its fluid phase counterpart. A linear and modal stability analysis was employed to evaluate the convective and absolute instability thresholds as well as their respective cell patterns. This analysis indicates that local thermal non-equilibrium always has a stabilizing effect and the spanwise uniform mode is always the most unstable. At the onset of convective instability, however, the number of equally unstable cell patterns increases with both the aspect ratio and the local thermal non-equilibrium strength.