Local Thermal Non-equilibrium Effects Research Articles

Numerical investigation on transpiration cooling with phase change based on multiphysics coupled finite element method

Transpiration cooling with phase change is an efficient active thermal protection method in aerospace. However, conducting numerical simulation of transpiration cooling with phase change is still a challenge, because porous flow, heat transfer and phase change are coupled with each other, which lead to numerical difficulties. In this article, the previous model is modified and the Zero Thickness Area Model (ZTAM) is proposed, which improves the efficiency and convergence significantly. In addition, the local thermal nonequilibrium effect and latent heat can be considered. To verify this ZTAM model, one-dimensional control equations of mass, momentum, and energy transpiration are solved using finite element method. Furthermore, the position of phase change is determined by fixed point iteration numerical algorithm, which shows good convergence. Finally, the influence on cooling effect by heat flux, coolant mass flow rate, porosity and pore diameter is investigated numerically.

A modified local thermal non-equilibrium model of transient phase-change transpiration cooling for hypersonic thermal protection

Aiming to efficiently simulate the transient process of transpiration cooling with phase change and reveal the convection mechanism between fluid and porous media particles in a continuum scale, a new two-phase mixture model is developed by incorporating the local thermal non-equilibrium effect. Considering the low-pressure and high overload working conditions of hypersonic flying, the heat and mass transfer induced by capillary and inertial body forces are analyzed for sub-cooled, saturated and super-heated states of water coolant under varying saturation pressures. After the validation of the model, transient simulations for different external factors, including spatially-varied heat flux, coolant mass flux, time-dependent external pressure and aircraft acceleration are conducted. The results show that the vapor blockage patterns at the outlet are highly dependent on the injection mass flux value and the external pressure, and the reduced saturation temperature at low external pressure leads to early boiling off and vapor blockage. The motion of flying has a large influence on the cooling effect, as the inertial force could change the flow pattern of the fluid inside significantly. The comparison of the results from 2-D and 3-D simulations suggests that 3-D simulation shall be conducted for practical application of transpiration cooling, as the thermal protection efficiency may be overestimated by the 2-D results due to the assumption of an infinite width length of the porous plate.

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.

Conjugate local thermal non-equilibrium heat transfer in a porous medium-filled cavity with a rotating cylinder: Analysis and insights

In this work, local thermal non-equilibrium effects are examined as they relate to conjugate natural convection heat transfer in a cavity filled with a porous medium. The investigation also considers the rotation of the central cylinder and the undulation of the cavity’s solid sides. Additionally, the analysis includes the consideration of heat transfer bifurcation occurring at the interface between the solid walls and the porous medium. The equations that govern the behavior of the fluid within the porous region and the heat transfer equations for the porous matrix and solid walls are mathematically expressed as partial differential equations. To solve these equations, the finite element method is employed. The study reports and analyzes the influence of parameters such as Darcy number, Rayleigh number, Prandtl number, and thermal conductivity ratio on flow and thermal fields. Additionally, the study examines the effect of rotational cylindrical motion on fluid flow and heat transfer via its speed rotation. The results indicate that undulated walls and rotational speed significantly impact fluid streamlines and isotherm contours within the porous space, as well as the distribution of isotherms within the solid walls. The findings of this study could have practical implications in the design and optimization of porous media-based systems involving heat transfer.

Experimental study on the melting performance of phase change materials embedded with different material skeletons

Embedding a skeleton in an organic phase change material changes its heat transfer properties. The melting process of a composite phase change material embedded respectively with nylon, stainless steel, and aluminum alloy skeleton was investigated experimentally, and the effect of the skeleton material on the phase change process was analyzed in detail. The evolution of the phase-change interface was captured using visible-light imaging, and the temperature field distribution was obtained using an infrared camera. The temperature variations inside the composite phase change material were measured using high-precision thermocouples. The local thermal non-equilibrium effect between the skeleton and phase change material was analyzed using the difference between the temperatures of the skeleton surface and paraffin close to the surface. The results showed that the metal skeleton accelerated the migration of the phase change interface, whereas the nylon skeleton retarded the phase change process, in contrast to the pure phase change material. The complete melting time and energy storage rate of the composite phase change material with the aluminum alloy were lesser (53%) and 59.6% higher than those of the pure phase change material, respectively. The local thermal non-equilibrium effects in the melting process of composite phase change material with different material skeletons were significantly different. The larger the thermal conductivity ratio between the skeleton and phase change material, the more significant the thermal non-equilibrium effect. The maximum thermal non-equilibrium effect in the melting process of the composite phase change material with aluminum alloy skeleton was 1.59℃.

Effects of LTNE on Two-Component Convective Instability in a Composite System with Thermal Gradient and Heat Source

An analytical study is conducted to examine the influence of thermal gradients and heat sources on the onset of two-component Rayleigh–Bènard (TCRB) convection using the Darcy model. The study takes into account the effects of local thermal non-equilibrium (LTNE), thermal profiles, and heat sources. The composite structure is horizontally constrained by adiabatic stiff boundaries, and the resulting solution to the problem is obtained using the perturbation approach. The various physical parameters have been thoroughly examined, revealing that the fluid layer exhibits dominance in the two-layer configuration. It has been observed that the parabolic profile demonstrates greater stability in comparison to the step function. Conversely, in the setup where the porous layer dominates, the step function plays a crucial role in maintaining stability. The porous layer, model (iv), exhibits greater stability in the predominant combined structure, while the linear configuration is characterized by higher instability.

Experimental investigation on melting heat transfer of paraffin embedded with periodic structure metal framework

Experiments on the melting of pure paraffin and paraffin embedded with a periodic structure metal framework (PEPSMF) in a rectangular cavity are conducted to investigate the effect of the metal framework on phase change. The test section is a closed cavity composed of plexiglass and heating copper plates that is filled with pure paraffin, or PEPSMF. During experiments, constant wall temperatures (Twall = 50, 55, and 60 °C) are applied to the left sides of the test section. Visible and infrared imaging technologies are used to capture the phase fields and temperature fields. High-precision thermocouples are employed to measure the temperature at different locations inside the PEPSMF and on the surface of the heating wall. In addition, the local thermal non-equilibrium effect between the metal framework and the paraffin is analyzed thoroughly. The results reveal that the evolution of the PEPSMF's mushy zone shows unique features due to the heat conduction of the metal framework. PEPSMF has a reduced melting time and a more uniform temperature distribution than pure paraffin. The significant local thermal non-equilibrium effect is found in PEPSMF, which becomes more prominent closer to the heating wall horizontally. The local thermal non-equilibrium effect shows complex fluctuations, with a maximum value of 1.25 °C.

Natural Convection in a Newtonian Nanoliquid-Saturated Porous Enclosure with Local Thermal Non-Equilibrium Effect

Buoyancy-driven convective flow and heat transfer characteristics in a Newtonian nanoliquid-saturated porous square enclosure are analyzed numerically using a local thermal non-equilibrium model. An enclosure’s horizontal walls are considered free–free and adiabatic, and the vertical walls are free–free isothermal boundaries. The dimensionless governing equations are solved using a central finite difference scheme with second-degree accuracy, and the results are in satisfactory agreement with the earlier works. The impact of various parameters on streamlines and isotherms is analyzed and depicted graphically. The effect of Darcy number, thermal Rayleigh number, and the ratio of thermal conductivities slow down the liquid flow. The temperature distribution is maximum at sidewalls and diminishes the amount of heat transport. The opposite phenomenon is observed for the solute Rayleigh number and interphase transfer coefficient of liquid-particle phases. For large values of interphase heat transfer coefficients, liquid-solid and liquid-particle are said to be in the local thermal equilibrium phase. The amount of heat transfer increases with an increasing interphase heat transfer coefficient and the ratio of the phases’ thermal conductivities. Results of local thermal equilibrium situation can be obtained as the particular case of the study. The amount of heat transfer is maximum in the local thermal non-equilibrium situation, and enhanced by 0.09% compared with the local thermal equilibrium situation. Heat transport is 0.74% less in the sparsely packed porous medium compared with the low-porosity medium.

Bio-thermal response and thermal damage in biological tissues with non-equilibrium effect and temperature-dependent properties induced by pulse-laser irradiation

Comprehension of thermal behavior underlying the living biological tissues helps successful applications of current heat therapies. The present work is to explore the heat transport properties of irradiated tissue during tis thermal treatment, in which the local thermal non-equilibrium effect as well as temperature-dependent properties arose from complicated anatomical structure, is considered. Based on the generalized dual-phase lag (GDPL) model, a non-linear governing equation of tissue temperature with variable thermal physical properties is proposed. The effective procedure constructed on an explicit finite difference scheme is then developed to predict numerically the thermal response and thermal damage irradiated by a pulse laser as a therapeutic heat source. The parametric study on variable thermal physical parameters including the phase lag times, heat conductivity, specific heat capacity and blood perfusion rate has been performed to evaluate their influence on temperature distribution in time and space. On this basis, the thermal damage with different laser variables such as laser intensity and exposure time are further analyzed.

LTNE effect on non-linear radiative MHD mixed convective flow in an annular porous medium: Intelligent Computing Paradigm

In this study, the back-propagated Levenberg-Marquardt algorithm-based neural network intelligent computing paradigm is used to examine the influence of non-linear thermal radiation, induced magnetic field and local thermal non-equilibrium effect on the magnetohydrodynamic mixed convective flow in the vertical annular porous region. In the annular porous region the inner cylinder is considered as electrically conducting and the outer cylinder as electrically non-conducting. The heat transfer is expected due to mixed convection and non-linear thermal radiation. The Galerkin finite element method is adopted to solve the governing equations. In the vertical annulus an increase in the magnetic Prandtl and Hartmann number reduces the velocity and induced magnetic field due to a strong external magnetic field and the Lorentz force. The higher Brinkmann values decelerate the conduction of heat generated by viscous dissipation hence, the temperature increases. The fluid and solid temperature increase with the buoyancy parameter. The non-linear radiation term enhances the fluid temperature, whereas it decelerates the solid temperature. The ANN model utilises finite element method output for training, validating and testing to predict the heat transfer characteristics. The performance of the BLM-NN algorithm is assessed using mean square error, error histogram and regression.

The Well-posedness and the Regularity of Global Attractor for a Couple Stress Fluid Through Porous Layer with the Local Thermal Non-equilibrium Effect

In the article, we aim to investigate the well-posedness of solution and the regularity of the global attractor for the couple stress fluid in saturated porous media with the local thermal non-equilibrium effect. To be more specific, we firstly show the existence and uniqueness of global weak solution to the model by making use of the standard Galerkin method. Second, relying on verifying the uniformly compact condition required, we prove the existence of the global attractor of the model in the space where the weak solution resides. Finally, we improve the regularity of global attractor by uniformly compact condition and obtain the \(C^{\infty}\) attractor for the model.

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.

INFLUENCE OF LOCAL THERMAL NON-EQUILIBRIUM ON THE STABILITY OF NANOFLUID FLOW IN AN INCLINED CHANNEL FILLED WITH POROUS MEDIUM

The effect of local thermal nonequilibrium on the stability of nanofluid flow in an inclined channel filled with a porous medium is numerically investigated. The Buongiorno model for nanofluid and Darcy-Brinkman model for flow in a porous medium are utilized, along with a three-field model for temperature, with each field representing the fluid, particle, and solid-matrix phases individually. The Chebyshev spectral collocation approach is used to determine the solution of the eigenvalue problem, which is obtained for perturbed states using a normal mode analysis. The impacts of various local thermal nonequilibrium parameters, the critical Rayleigh number, and associated wavenumber are displayed through graphs. It is worth noting that the LTNE parameters have a major impact on convective instability. Also, the dynamics of the flow field, behavior of temperature, and volume fraction are presented through streamlines, isotherms, and isonanoconcentration at the critical level.

THE EFFECT OF LOCAL THERMAL NON-EQUILIBRIUM AND MAGNETIC FIELD ON THE STABILITY IN A VERTICAL CHANNEL FILLED WITH NANOFLUID

In this investigation, the influence of local thermal non-equilibrium (LTNE) on the onset of convection in a channel occupied with nanofluid was examined. The flow took place in the presence of a transverse magnetic field. The Buongiorno and two-field models (each independently signifying the fluid and particle phases) were used for the nanofluid and energy equation, respectively. A normal mode analysis was applied to obtain the eigenvalue problem for the disturbed state, which was solved using the Chebyshev spectral collocation technique. The effects of the governing parameters on the Rayleigh number and corresponding wavenumber are presented graphically. It was noticed that the concentration Rayleigh number, inter-phase heat transfer parameter, and modified diffusivity ratio had a destabilizing effect, while the modified thermal capacity ratio, thermal diffusivity ratio, Lewis number, and modified particle density increment had a stabilizing effect on the system.

THERMAL INSTABILITY OF BLOOD-COPPER CASSON NANOFLUID SATURATED POROUS MEDIUM UNDER LTNE, ROTATION, AND THROUGH-FLOW

Because of the antibacterial characteristics of copper, the thermal instability of blood-copper (B-Cu) nanoliquid plays a crucial role in the field of medical science, specifically in the cardiovascular system. In this article, the convective instability of B-Cu nanoliquid filled in a porous medium is investigated using a Casson model. A thermal nonequilibrium condition is taken for the nanoliquid and porous matrix. The Brinkman model is used because of the high porosity of the material. The influence of rotation and through-flow (both positive and negative) over the instability has also been examined. The amount of through-flow and rate of rotation are respectively governed by Peclet number and Taylor number. A comparison between the impacts of through-flow and rate of rotation is done, and it is found that through-flow is more effective than the rate of rotation to delay the onset of convection. Both steady and unsteady weakly nonlinear analyses are performed to understand the heat transport in the system. It is concluded that the Casson nanofluid parameter has both stabilizing and destabilizing impact depending upon the rate of rotation and therefore the current work can be possibly utilized in both places where heat removal and heat conservation is required. One more important thing is observed: the effect of local thermal nonequilibrium (LTNE) can also be regulated using the Casson nanofluid parameter.

LOCAL THERMAL NON-EQUILIBRIUM CONDITION FOR THE FLOW OF WALTERS-B FLUID OVER A SHEET SATURATED IN A POROUS MEDIUM

Local thermal non-equilibrium (LTNE) has garnered significant interest in engineering applications like electronic cooling, heat pipes, nuclear reactors, drying technology, and multiphase catalytic reactors. Owing to this, the study numerically emphases on the LTNE effects on the flow of Walters-B liquid over a stretching sheet with Dufour and Soret effects. The LTNE model, which creates distinct thermal profiles for both solid and liquid phases, is utilized to formulate the energy equations, which constitutes the novelty of the present study. The governing equations for the flow assumptions are transformed to ordinary differential equations using the apt similarity transformations. The Runge-Kutta approach and the shooting technique are then used to numerically solve these reduced equations. The significant results of the current analysis are that an upsurge in Dufour number diminutions the heat transport in liquid phase. The increase in Soret number advances the mass transport. The augmented values of viscoelastic parameter drop down the velocity, but advance the fluid phase heat transference. Finally, the heat transport of the liquid phase increases and solid phase drops as inter-phase heat transfer parameter rises.

Local Thermal Non-Equilibrium Dominant Darcy-Rayleigh-Benard-Magneto-Marangoni Convection in a Composite Layer

The domination by Local Thermal Non-Equilibrium (LTNE) with regard to the onset of Darcy-Rayleigh-Benard-Marangoni (DRBM) convection swayed by magnetic field in a composite layer set-up is studied pertinent to incompressible fluid. The precinct above the fluid layer is presumed to be free and that below the porous layer is presumed to be rigid. Regular perturbation technique is exercised on the acquired problem to achieve the analytical solution taking adiabatic-adiabatic conditions into account at the boundaries. Effects of parameters such as solid phase thermal expansion ratio, solid phase thermal diffusivity ratio and inter-phase thermal diffusivity ratio that influences LTNE are discussed. The impact of change in measures of variables viz. fluid phase thermal expansion ratio, fluid phase thermal diffusivity ratio, porous parameter, thermal ratio, Chandrasekhar number and Marangoni number with respect to both LTNE and LTE situations are together explored and portrayed graphically. It is to be noted that for smaller values of fluid phase thermal expansion ratio and fluid phase thermal diffusivity ratio, the LTNE effects are prominent and cannot be ignored.

Influence of local thermal non-equilibrium on enhanced geothermal system

Effective development of hot dry rock depends on complex fracture network formed by the enhanced geothermal system. Different scales of mass and heat transfer environment are formed between tight matrix and different fractures, which leads to the complexity of mass and heat transfer process of porous media. In order to analyze the influence of local thermal non-equilibrium on the mass and heat transfer process of complex fracture system, a micro pore scale mass and heat transfer model considering local non-thermal equilibrium is established. The microscopic mechanism of the effect of local non-thermal equilibrium assumption on mass and heat transfer process in matrix-fracture system is revealed. An embedded discrete fracture model considering local thermal non-equilibrium assumption and the solution method are also established. The necessity of considering local thermal non-equilibrium is analyzed by studying the sensitivity of formation physical parameters. The results show that ignoring the local thermal non-equilibrium assumption will underestimate the rock temperature near the fracture zone and overestimate the fluid temperature in the heat transfer front zone. The effect of local thermal non-equilibrium on the enhanced geothermal system is mainly reflected in the early stage of injection. The higher the injection intensity, the lower the matrix fracture permeability, the greater the matrix fracture porosity difference, the greater the rock thermal diffusion coefficient, the smaller the convective heat transfer coefficient, the more it is necessary to consider the local thermal non-equilibrium assumption. The research results can provide reference for the collection and collation of field data.

A dual-scale transport model of the porous ceria based on solar thermochemical cycle water splitting hydrogen production

Solar thermochemical cycle converts the full-spectrum range of solar irradiation into chemical energy, which can then be stored or transported, paving the route to achieving carbon neutrality. This cycle involves complex heat and mass transfer processes in porous media, and a relatively complete mathematical model has not been established yet. In particular, there is a lack of a heat and mass transfer model that couples particle scale and macro scale, which is of great theoretical value for the design of solar thermochemical cycle reactors. A comprehensive model combining transport of species in the porous bed (macroscopic) and the lattice oxygen within the particles (mesoscopic) is developed. Dilute mass transfer model and P-1 radiation model are adopted in this model. Based on the model validation by comparing it with existing experimental data, the unsteady heat and mass reaction process, and transportation in the solar thermochemical cycle are investigated under dual-scales. For the oxidation and reduction process respectively, the peak deviation between the model and the experiment is less than 2 s, which thoroughly validated our model. The additional results show that the local thermal and mass non-equilibrium effect and the parameters at the macro and micro scales have a significant influence on the temperature distribution and reaction kinetics. The oxidation process is faster than the reduction process, but the transport time scales in macroscopic (axial) and mesoscopic (radial) direction is of the same order. The increase of reactant concentration can effectively raise the peak value of the hydrogen production, but the product in the oxidation stage is not only limited by the oxidant concentration but also affected by the final state in the reduction stage.

A numerical study on heat transfer and MHD flow of a Newtonian through a porous channel—Local thermal nonequilibrium model

Abstract Vast numbers of studies concentrate on the thermal equilibrium state whereas in many real‐world applications the model exists in the nonequilibrium state. Also, local thermal non‐equilibrium precisely represents the thermohydroflow characteristics. Therefore, the current study examines the heat transfer and fluid flow characteristics of the magnetohydrodynamic flow of a Newtonian fluid through a local thermal non‐equilibrium (LTNE) porous channel in the presence of the induced magnetic field. The mathematical model of the prescribed flow encloses the coupled nonlinear equations which are difficult to approach analytically. Hence, they are solved numerically using the shooting method with the Newton–Raphson method. The implications of various physical parameters of the problem on fluid flow, induced magnetic field, current density, temperature profiles, and heat transfer are elucidated with the aid of plots and tables. From the examination, it is clear that the porous medium significantly influences the characteristics of the fluid flow. That is, the least value of the Darcy number is related to a higher momentum field. Another interesting phenomenon is that the induced magnetic field remarkably enhances when the Darcy number is high, whereas the process is contrary to the current density. The effect of LTNE on the flow characteristics and heat transfer ceases for higher values of inter‐phase heat transfer coefficient and the ratio of thermal conductivities, which gives rise to the local thermal equilibrium (LTE) situation. Furthermore, the amount of heat transport is maximum in the LTE case compared to that of the LTNE case.