Local Thermal Non-equilibrium Research Articles

Thermal analysis of natural convection in rectangular porous fin wetted with CNTs nanoparticles and thermal radiation

AbstractIn the present investigation, the phenomenon of heat conduction in rectangular shaped porous fin wetted with nanofluid (a mixture of carbon nanotube [CNT] with water as base liquid) is examined using the local thermal non‐equilibrium (LTNE) paradigm. The heat transport mechanism involving the nanofluid and solid phases is represented by the dimensional thermal governing ordinary differential equations (TGODEs). These equations are transformed into nonlinear ordinary differential equations (ODEs) using relevant non‐dimensional variables. To solve the resultant dimensionless TGODEs, probabilists collocation method with Hermite polynomials (PCMHPs) is utilized. This study of temperature analysis has examined the characteristics of internal and exterior radiation, convection, and thermal conductivity to determine the attributes affecting heat transfer. For both the nanofluid and solid phase aspects, temperature distribution characteristics are revealed in tables and graphs. Subsequently, it is determined that as surface‐ambient radiation parameter levels decreased, the temperature profile of both solid and nanofluid phase augmented. The temperature variance among the solid and nanofluid phases decreased with an escalation in the wet porous parameter. The numerical outcomes illustrate that the presented PCMHP approach is not only convenient to execute but also provides accurate results.

Characteristics of synovial trihybrid nanofluid activation energy and Marangoni convective flow: A Computational framework of local thermal non-equilibrium

The impact of nonlinear heat source and activation energy on magnetized Synovial trihybrid nanofluid Marangoni convective flow across a sheet combining two viscosity models is investigated in this study. Heat sources, activation energy, and conditions of local thermal non-equilibrium (LTNE) are all considered in the modelling. Based upon energy equations, the LTNE model provides unique heat transport for both liquid and solid phases. This leads to the utilization of different temperature profiles for the fluid and solid phases in this work. A trihybrid fluid is created by combining the basic fluid blood with MWCNT (multi-wall carbon nanotubes), SWCNT (single-wall carbon nanotubes) and sliver nanoparticle. This study significant potential in several fields. The effects of parameters on friction between joints are examined, which aids in the analysis of the lubricant nature of Synovial trihybrid nanofluid. A significant finding of the current work is that the thermal profiles decrease with higher values of the Concentration-dependent viscosity parameter, but the velocity profile increases. An increase in the inter-phase heat transfer characteristic raises the liquid phase's thermal profile while lowering the solid phase's thermal profile.

Optimizing of a metal foam-assisted solar air heater performance: a thermo-hydraulic analysis of porous insert placement.

A numerical assessment of the heat transfer efficacy of a solar air heater (SAH) was carried out. The SAH is supplied with a porous metal foam layer to improve thermal mixing. Both the local thermal non-equilibrium (LTNE) and Darcy-extended Forchheimer (DEF) models were employed to forecast fluid and thermal transport within the partly filled SAH channel. The analysis was performed for various values of dimensionless foam layer lengths ( ), pore densities ( ), and Reynolds numbers ( ) at a fixed value of layer thickness ( ). Based on the position of the porous layer, three distinct arrangements, marked as Case 1, Case 2, and Case 3, were explored. Regarding the parameters examined, the findings indicate a definite improvement in the average Nusselt number ( ), but unfortunately, the friction factor also increases unfavorably. By reducing the length of the porous layer, a reasonable reduction in heat transfer rate and a significant decrease in pressure drop were noticed. The results showed about 26.64%, 48.73%, and 70.74% reductions in pressure drop by reducing the dimensionless foam length from 1 to 0.25, 0.5, and 0.75 respectively for at . On the other side, there are only about 11.05%, 23.11%, and 40.78% reductions in . The exhaustive analysis of the thermal performance of SAH was conducted using the thermal performance factor (TPF), which considers the trade-off between the SAH channel's potential for improved heat transmission and its cost for pressure loss. The TPF may reach a maximum of 2.82 compared to the empty channel when the metal foam layer is inserted with , for , and .

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.

Local thermal non-equilibrium effects on phase transition of fiber reinforced thermoplastic composites with temperature-dependent heat generation

Under the excitation of external fields, fiber reinforced thermoplastic (FRTP) composites can be thermally processed due to the internal heat generation, in which the local thermal non-equilibrium (LTNE) can be significant during the phase transition. In this study, a representative elementary volume scale Lattice Boltzmann model was developed to simulate the phase transition process of FRTP composites with the temperature-dependent internal heat source. The results from LTNE model and local thermal equilibrium (LTE) model were compared in terms of the phase interface evolution and the local temperature difference between fibers and matrix, so that the LTNE effects on phase transition behaviors were examined with different material properties and internal heat sources. It is found that the LTNE effects cannot be ignored in FRTP composites, and the main mechanisms include the dynamic local heat generation, endothermic phase transition of matrix, and relatively high thermal conductivity of fiber. A small heat exchange between the fibers and matrix results in a large local temperature difference and a slow phase transition. A high internal heat generation enhances the phase transition and LTNE effects, but an increase in the temperature range for heat generation leads to a slow phase transition with slight change in LTNE effects. With the increase of matrix fraction, LTNE effects first increase and then decrease due to the combined results of the more internal heat generation and the increase of endothermic mass of matrix and the less heat loss through fibers. This study is significant for guiding the reliable thermal processing of FRTP composites in emerging industrial applications.

Stability of penetrative convective currents in local thermal non-equilibrium

The aim of this paper is to investigate the onset of penetrative convection in a Darcy–Brinkman porous medium under the hypothesis of local thermal non-equilibrium. For the problem at stake, the strong form of the principle of exchange of stabilities has been proved, i.e. convective motions can occur only through secondary stationary motions. We perform linear and nonlinear stability analyses of the basic state, with particular regard to the behaviour of stability thresholds with respect to the relevant physical parameters characterizing the problem. The Chebyshev- τ method and the shooting method are employed and accurately implemented to solve the differential eigenvalue problems arising from linear and nonlinear analyses to determine critical Rayleigh numbers. Via numerical simulations, the stabilizing effect of the upper bounding plane temperature, of the Darcy number and of the interaction coefficient for the heat exchange, is demonstrated.

Impact of Local Thermal Non-Equilibrium and Gravity Fluctuations on the Onset of a Darcy-Brinkman Porous Convection

The numerical investigation of the Darcy-Brinkman convective problem with gravity fluctuations in a Local Thermal Nonequilibrium (LTNE) model is conducted. Utilizing linear stability analysis, the convective problem is explored, and the numerical values of the Rayleigh and wave numbers for onset convection are computed through the one-term Galerkin approach. Three distinct types of gravity fluctuations (linear, parabolic, and exponential) are considered. The results show the Darcy number and gravity parameter delay the onset of convection. The porosity-scald conductivity ratio and interface heat transfer coefficient have a significant effect on the stability of the configuration. Graphical representations depict the effects of various parameters, highlighting the significant impacts of incorporating gravity fluctuations and non-equilibrium conditions in determining convection stability thresholds.

LTNE effects on two‐layer configuration with throughflow

AbstractThe effect of throughflow on the beginning of convective motion in a fluid layer overlying a fluid‐saturated porous layer is examined theoretically in this article under the local thermal nonequilibrium model. We considered boundaries to be insulating to temperature perturbations. The normal mode approach is employed to analyze the governing equation for a composite configuration, with the solution sought through the regular perturbation technique to assess linear stability. The critical Rayleigh number, signifying the initiation of stationary convection, has been determined by solving the system of coupled equations. It is found that the system attains stability with increased porosity–conductivity ratios, regardless of the throughflow direction. This stability is consistently observed for depth ratios of 0.1 and 0.2. However, for higher depth ratios (0.5 and 1.0), the system exhibits dual nature stability when throughflow is present. Further, the stability of the system is enhanced by a graphical depiction illustrating how the throughflow parameter, porosity‐scaled conductivity ratio, depth ratio, Darcy number, and Prandtl number collectively influence the onset of convective motion.

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.

An Analytical Study of the Impact of an Inclined Magnetic Field on Couette Flow with Jeffrey Fluid under Local Thermal Non-Equilibrium (LTNE) and Viscous Dissipation

In this work, we examine the effects of viscous dissipation and local thermal non-equilibrium (LTNE) on Couette flow in a duct filled with a porous media under the influence of an angled magnetic field. The bottom plate of the duct is in motion and subjected to a constant heat flux, while the top plate remains stationary and adiabatic. The Jeffrey fluid flow model is consistent with the unidirectional flow in the porous zone. The studies provide more precise measurements of the effects of the Jeffrey parameter (λ), inclined angle (ϕ), Hartmann number (MW), thermal conductivity ratio (ν), Brinkman number (BrW), and Biot number (BiW) on improving heat transmission. The governing equations are solved analytically. The present investigation gives dimensionless temperatures for fluid-solid phases and fully developed Nusselt number (FDNN) profiles. Variation of Jeffrey parameter, inclined angle, Brinkman number, and Hartman number in the temperature field in both phases and FDNN. Furthermore, the temperature in the solid phase is higher than the temperature in the fluid phase for the Jeffrey parameter and Hartman number in the Couette flow, which supports LTNE validation.

Analytical and numerical investigation of heat transfer of porous fin in a local thermal non-equilibrium state

This research employs a local thermal non-equilibrium (LTNE) model to analyze the heat transfer phenomenon through a porous fin, considering natural convection and radiation effects. The infiltration velocity within the porous medium is evaluated using the Darcy model, and buoyancy effects are accounted for using the Boussinesq approximation. The Akbari-Ganji method (AGM) is applied to address the governing energy equations. The accuracy of the proposed solution is verified by comparing it with numerical results obtained from the finite difference method (FDM), the finite element method (FEM), and earlier investigations. The results are presented regarding the total average Nusselt number and temperature profiles. These results shed light on the influence of several important parameters, such as the thermal conductivity ratio, dimensionless thickness, convectional heat transfer, and external and internal radiation. The analysis reveals that decreasing Rayleigh and Biot numbers reduces the temperature profiles of the solid phase. Additionally, when the Rayleigh number is low but the assigned Biot number is high, the temperature difference between the solid and fluid phases diminishes. Furthermore, increased thermal conductivity ratio and dimensionless thickness for assigned Biot and Rayleigh numbers lead to higher solid phase temperatures. The Nusselt number exhibits a decreasing trend with a decreasing thermal conductivity ratio but increases with higher Rayleigh and Biot numbers and increased external radiation.

Impact of rainfall on the thermal performance of geothermal permeable pavement systems

Geothermal permeable pavement (GPP) systems are a nascent type of energy geo-structures. GPP combine ground-source heat pump (GSHP) systems with permeable pavements to enable the additional functionality of heating and cooling, through energy harvesting using roads alongside existing drainage controls. GPP thermal performance is relatively unknown, hence, this research focuses on the development of a detailed 3D finite element (FE) model that considers local thermal non-equilibrium (LTNE) for exploring the influence of rainfall infiltration on the thermal performance of GPPs. The 3D numerical model was successfully validated and was used to evaluate the short-term thermal response of GPPs during rainfall events in both cooling (summer) and heating (winter) demand conditions. Furthermore, the diurnal rainfall effects and the influence of raindrop temperature and rainfall duration on GPPs were also examined. Results show that rainfall can have significant impacts on the thermal performance of GPPs and the raindrop temperature is an important parameter in yield predictions. Compared to no-rainfall events, the GSHP system fluid temperature during rainfall can differ by up to 19% when in the cooling operation model (air conditioning) and 63% in heating mode. These results indicate the significantly better performance of GPPs than impervious geothermal pavements, depending on the climatic conditions and end-use.

Local thermal nonequilibrium perspective of heat transfer and fluid flow in a slender anisotropic porous cavity due to lateral uniform heat flux

The influence of the local thermal nonequilibrium (LTNE) state on steady-state natural convection due to the heating and cooling of the side walls of the slender porous cavity has been addressed analytically and numerically. The porous medium is assumed to be hydrodynamically anisotropic. The Darcy model has been adopted. A closed-form solution, based on a parallel hypothesis, is reported for a slender cavity. The combined impact of media anisotropy and LTNE state on the heat transfer rate, as well as flow dynamics, have been analyzed. The help of boundary layer analysis is taken to report the boundary layer thickness and heat transfer rate of fluid flow analytically. It has been found that the maximum (minimum) heat transfer rate of the fluid phase as well as solid phase takes place at orientation angle, ϕ , equal to π / 2 when permeability along the horizontal (vertical) direction is higher than the same along vertical (horizontal) direction.

Numerical study on mixed convection heat transfer of copper-water nanofluid in a porous cavity with an isothermal solid block in local thermal non-equilibrium

This manuscript reports a numerical study on mixed convection heat transfer of Cu-water nanofluid in a porous cavity with an isothermal solid block in the state of local thermal non equilibrium. The set of governing equations are solved by finite volume method combined with SIMPLE algorithm. Through streamlines and isothermal contour plots as well as the average Nusselt number, the impact of various parameters like the nanoparticle concentration, Richardson number, Darcy number, and inter phase heat transfer coefficient is highlighted. The main findings indicate that the Local thermal non-equilibrium state (H = 1, 10) produces the maximum heat transfer rate than the local thermal equilibrium state (H = 1000).

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.

COMBINED EFFECT OF LOCAL THERMAL NONEQUILIBRIUM AND GRAVITY MODULATION ON THERMAL INSTABILITY IN MICROPOLAR NANOFLUID SATURATED POROUS MEDIA

In the present paper an effect of gravity modulation in a horizontal parallel flat plate having micropolar nanofluid saturated by a porous medium is examined. Local thermal nonequilibrium (LTNE) has been observed for the problem, i.e., the fluid, particle, and solid matrix are at different temperatures. Onset of convection and heat and mass transfer for both the cases, i.e., linear stability and nonlinear stability, is analyzed. We conclude that rate of convection in the LTNE case is faster than in the LTE case. Effect of porosity is observed in the LTNE region, which is opposite to the effect observed in the LTE region. Increase in value of A, K<sub>1</sub>, and δ delay the rate of convection. Small value of frequency of gravity modulation forms a greater number of small periods which delay the rate of convection. On increasing the value, heat transfer increases. At higher frequency of modulation we obtain the case similar to unmodulated case.

Numerical Investigation on Transpiration Cooling Performance of Oriented Porous Structure Under Local Block Conditions

With the development of an active thermal protection system (TPS) for hypersonic vehicles, reliability improvement and weight reduction of TPS are key issues to be considered. In this paper, an oriented porous structure (OPS) is proposed to solve the local overheating problem in transpiration cooling. The transpiration cooling performances are investigated in a two-dimensional computational domain using a local thermal nonequilibrium model. The cooling mechanisms of OPS and uniform porous structure (UPS) under local block conditions have been numerically analyzed and compared. The results show that OPS leads to effective cooling of the overheated region by regulating the coolant flow behavior, especially in the case of serious block conditions. The maximum temperature reduction can be up to more than 200 K, and the maximum optimization rate can reach up to 23% compared to UPS. Moreover, OPS consumes less coolant and uses less driving force to deliver coolant when reaching the same peak temperature as OPS. This study shows that OPS has a better thermal protection effect in transpiration cooling, which can improve the reliability of TPSs, and that OPS can also achieve the lightweight of the aircraft.

A Unified Approach to Two-Dimensional Brinkman-Bénard Convection of Newtonian Liquids in Cylindrical and Rectangular Enclosures.

A unified model for the analysis of two-dimensional Brinkman-Bénard/Rayleigh-Bénard/ Darcy-Bénard convection in cylindrical and rectangular enclosures (CE/RE) saturated by a Newtonian liquid is presented by adopting the local thermal non-equilibrium (LTNE) model for the heat transfer between fluid and solid phases. The actual thermophysical properties of water and porous media are used. The range of permissible values for all the parameters is calculated and used in the analysis. The result of the local thermal equilibrium (LTE) model is obtained as a particular case of the LTNE model through the use of asymptotic analyses. The critical value of the Rayleigh number at which the entropy generates in the system is reported in the study. The analytical expression for the number of Bénard cells formed in the system at the onset of convection as a function of the aspect ratio, So, and parameters appearing in the problem is obtained. For a given value of So it was found that in comparison with the case of LTE, more number of cells manifest in the case of LTNE. Likewise, smaller cells form in the DBC problem when compared with the corresponding problem of BBC. In the case of RBC, fewer cells form when compared to that in the case of BBC and DBC. The above findings are true in both CE and RE. In other words, the presence of a porous medium results in the production of less entropy in the system, or a more significant number of cells represents the case of less entropy production in the system. For small and finite So, the appearance of the first cell differs in the CE and RE problems.

The onset of anisotropic Darcy–Brinkman penetrative convection with local thermal nonequilibrium due to heat generation and extraction

AbstractAn anisotropic, fluid‐saturated porous medium with local thermal nonequilibrium is the subject of this paper's analysis of the stability of the commencement of convection caused by internal heat generation. The classical Darcy's momentum equation is applied with the Brinkman model. To observe the thermal instabilities in the fluid layer, it is assumed that there is steady heat extraction through the bottom boundary and constant heat generation inside the fluid layer. The critical internal Darcy Rayleigh and associated wave numbers are computed using linear instability and energy approaches using the Chebyshev pseudospectral method to determine the existence of instability or otherwise. The fluid layer becomes unstratified as a result of heat generation inside the fluid, which encourages the occurrence of any subcritical instability. The critical Darcy–Rayleigh number has been found to be significantly influenced by a number of parameters, including the anisotropy parameter, internal heat parameter, porosity‐modified conductivity ratio, inter‐phase heat transfer parameter, and Darcy–Brinkman number.

A new LTNE analysis process for predicting the steady-state temperature distribution in a fixed bed of randomly packed mono-sized rough spheres based on pore-scale simulations

A new analysis process for the LTNE (local thermal non-equilibrium) model to solve for steady-state, fully-developed convection in mono-sized-sphere packed bed is proposed to predict the temperature distribution inside a fixed bed. For an actual mono-sized-sphere packed bed, the voidage lies between those of the regularly arranged beds of FCC, BCC, and SC. Through an interpolation/extrapolation process based on the pore-scale computation results of the SC, BCC, and FCC packings, the heat transfer parameters of a randomly packed bed can be calculated. To reliably estimate the local heat transfer rate, the regional mass flow rates in a packed bed are accurately predicted first. Then, the regional solid-phase thermal conduction can be independently evaluated without interference from the regional fluid-solid convection heat transfer. Additionally, a finite-thickness wall is constructed into the computational model to significantly improve the accuracy of the predicted radial temperature profiles. With realistic temperature self-adjustment within the wall, there is no need to set unrealistic boundary conditions of either isothermal, isoflux or their combinations at the outer face of the porous zone, as many conventional methods in the literature do. The solution process and necessary parameters are summarized into flowcharts. Finally, the accuracy of the new LTNE analysis process in predicting the temperature distribution throughout the packed bed is validated with the literature experiment. In contrast, the conventional methods fail to provide the correct trend of the temperature variation.