Local Thermal Non-equilibrium Approach Research Articles

A Local Thermal Non-Equilibrium Approach to an Electromagnetic Hybrid Nanofluid Flow in a Non-Parallel Riga Plate Channel

The fluid flow in a non-parallel configuration exists in the electronic heat removal devices, microchannel heat sinks, and angled confusers/diffusers. The fluids in these applications are prone to flow separation and bifurcations. To deal with such type of problems, a novel idea of a converging or diverging type Riga plate channel is introduced in this study. The Riga plates are utilised to produce the cross-flow magnetic and electric fields which give rise to an exponentially decaying Lorentz force. Also, a porous matrix with variable permeability is considered to fill the Riga plate channel. The thermal equilibrium state between the hybrid nanofluid and porous media is ignored i.e., a local thermal non-equilibrium (LTNE) approach is adopted to model the energy balance equations. The dimension-free form of the guiding equations is tackled by using the Chebyshev pseudospectral quasi-linearization method. The heat transfer rate is respectively incremented by 21.42% and 63.12% in the converging and diverging flow regimes, with the inclusion of a Riga Sheet. The skin friction coefficient is depressed with modified Hartmann number (Ha*) and porosity (ε) for the converging/diverging flow regime. The LTNE state alters to the LTE with Nield number (Ni), thermal conductivity ratio (γ) and ε.

Numerical study of natural convection of fluid with temperature-dependent viscosity inside a porous cube under non-uniform heating using local thermal non-equilibrium approach

Numerical study of natural convection of fluid with temperature-dependent viscosity inside a porous cube under non-uniform heating using local thermal non-equilibrium approach

Computational Modeling of Latent Heat Thermal Energy Storage in a Shell-Tube Unit: Using Neural Networks and Anisotropic Metal Foam

Latent heat storage in a shell-tube is a promising method to store excessive solar heat for later use. The shell-tube unit is filled with a phase change material PCM combined with a high porosity anisotropic copper metal foam (FM) of high thermal conductivity. The PCM-MF composite was modeled as an anisotropic porous medium. Then, a two-heat equation mathematical model, a local thermal non-equilibrium approach LTNE, was adopted to consider the effects of the difference between the thermal conductivities of the PCM and the copper foam. The Darcy–Brinkman–Forchheimer formulation was employed to model the natural convection circulations in the molten PCM region. The thermal conductivity and the permeability of the porous medium were a function of an anisotropic angle. The finite element method was employed to integrate the governing equations. A neural network model was successfully applied to learn the transient physical behavior of the storage unit. The neural network was trained using 4998 sample data. Then, the trained neural network was utilized to map the relationship between control parameters and melting behavior to optimize the storage design. The impact of the anisotropic angle and the inlet pressure of heat transfer fluid (HTF) was addressed on the thermal energy storage of the storage unit. Moreover, an artificial neural network was successfully utilized to learn the transient behavior of the thermal storage unit for various combinations of control parameters and map the storage behavior. The results showed that the anisotropy angle significantly affects the energy storage time. The melting volume fraction MVF was maximum for a zero anisotropic angle where the local thermal conductivity was maximum perpendicular to the heated tube. An optimum storage rate could be obtained for an anisotropic angle smaller than 45°. Compared to a uniform MF, utilizing an optimum anisotropic angle could reduce the melting time by about 7% without impacting the unit’s thermal energy storage capacity or adding weight.

Forced Convection in a Transpired Passage With a Porous Medium Insert

Abstract Forced convective heat transfer in a passage with a porous medium matrix subjected to uniform blowing has been fully analyzed, using a local thermal nonequilibrium approach, in application of transpiration systems on the basis of porous medium. An exact solution was found for the asymptotic case of infinitely high interstitial Biot number. In order to extend the problem to general local nonthermal equilibrium cases, an analytical solution procedure has been developed, introducing six unknown parameters to describe both fluid and solid temperature profiles, which are then determined by solving six independent differential and integral equations based on the two energy equations for individual phases and their corresponding boundary conditions. The important performance index for the problem, namely, the overall cooling effectiveness is found quite sensitive not only to the blowing ratio, but also to the interstitial Biot number and fluid to solid effective thermal conductivity ratio. It rises with the blowing ratio and effective thermal conductivity ratio, while it drops as increasing the interstitial Biot number toward the local thermal equilibrium. The present analysis reveals that the local nonthermal equilibrium analysis is definitely needed for accurate estimation of the transpiration-cooled wall temperature.

Numerical Evaluation of the Transient Performance of Rock-Pile Seasonal Thermal Energy Storage Systems Coupled with Exhaust Heat Recovery

This study seeks to investigate the concept of using large waste rocks from mining operations as waste-heat thermal energy storage for remote arctic communities, both commercial and residential. It holds its novelty in analyzing such systems with an experimentally validated transient three-dimensional computational fluid dynamics and heat transfer model that accounts for interphase energy balance using a local thermal non-equilibrium approach. The system performance is evaluated for a wide range of distinct parameters, such as porosity between 0.2 and 0.5, fluid velocity from 0.01 to 0.07 m/s, and the aspect ratio of the bed between 1 and 1.35. It is demonstrated that the mass flow rate of the heat transfer fluid does not expressively impact the total energy storage capacity of the rock mass, but it does significantly affect the charge/discharge times. Finally, it is shown that porosity has the greatest impact on both fluid flow and heat transfer. The evaluations show that about 540 GJ can be stored on the bed with a porosity of 0.2, and about 350 GJ on the one with 0.35, while the intermediate porosity leads to a total of 450 GJ. Additionally, thermal capacity is deemed to be the most important thermophysical factor in thermal energy storage performance.

Three-dimensional thermal assessment in cancerous tumors based on local thermal non-equilibrium approach for hyperthermia treatment

An appropriate evaluation of thermal characteristics in biological bodies under the influence of external heat source during the hyperthermia therapy is inherently difficult, since living tissues have a non-uniform and non-homogeneous structure composed of solid-liquid interfaces. In general, biological bodies are very sensitive to temperature alteration as it leads to a drastic change of protein structures, which in turn causes a permanent thermal injury. Therefore, it can always be desirable to use a suitable model for determining the temperature response in therapeutic domains accurately. Recently, the local thermal non-equilibrium (LTNE) model develops based on the energy exchange in the vascular geometry confined with arteriol-venule systems. The present study establishes a hybrid analytical scheme by applying the LTNE bioheat approach for the three-dimensional (3-D) temperature response in a cancer domain under the hyperthermia treatment. To take care of non-uniformity and porous media approaches of living tissues, this study suggests a pertinent spatially dependent initial condition along with the appropriate boundary conditions in the physical domain for the accurate temperature prediction. A comparative study of temperature distribution between LTNE and local thermal equilibrium (LTE) models has been performed which justifies the necessity to include the porous media approach in the analysis. In order to understand a 3-D heat flow in the hyperthermia domain, thermal contours may give such information and thus 3-D heat transfer analysis with two different time lags always predicts the exact thermo-biological behaviour as a function of the therapeutic exposure time. Finally, the research output validated with the available experimental hyperthermia therapeutic data and the present 3-D thermal response is in good agreement with the existing experimental values, which indicates the present model is appropriate to determine the thermal behaviour of living tissues accurately.

Effect of porous material properties on thermal efficiencies of a thermocline storage tank

Thermocline energy storage systems can be adapted to store energy in a tank where the hot fluid is pumped in during a charging cycle and cold fluid during a discharging cycle, substituting the need for two storage tanks. Here, a numerical investigation of a hot air flow transferring thermal energy to a solid porous bed is performed to evaluate the influence of the thermal conductivity and capacity ratios on the efficiency of a charging cycle of a thermocline storage tank. The numerical model considers the mixed convection turbulent flow (k-ε model) through clear and porous media using the Local Thermal Non-Equilibrium approach to provide solutions for the solid and fluid phases separately. Macroscopic equations are obtained by the method of volume averaging and numerically processed by finite volume method. The system was modelled as a vented axisymmetric cavity, partially filled with a porous medium, with hot fluid inflow from the top and outflow at the bottom. The investigation included changing Reynolds number (Ret from 8.3 × 103 to 5 × 104), thermal conductivity ratios (ks/kf from 3.5 to 1062) and thermal capacity ratio (ρscps/ρfcpf from 1483 to 7415). It was found that lower ks/kf ratios decrease the heat loss throughout the charging cycle which allow for higher temperatures in the later stages of the cycle and thus improve charging efficiency. However, this effect decreases in importance as the system undergoes higher Ret number flows. On the other hand, increasing the ρscps/ρfcpf ratio affects the entire cycle, increasing the temperature difference between phases, lowering the velocity in which the solid raises its temperature but storing heat more efficiently. Finally, a design consideration is highlighted as the importance of the ks/kf ratio on the thermal efficiency is predominant at lower Ret flows, whereas as Ret increases, ρscps/ρfcpf becomes the dominant parameter providing efficiency gains.

Natural convection of a hybrid nanofluid affected by an inclined periodic magnetic field within a porous medium

Heat transfer enhancement for various engineering systems can be achieved by the inclusion of metal nanoparticles inside the heat transfer liquid. Such an effect can be improved by considering the hybrid nanofluid when nanoparticles of different materials are added to the base fluid. The present study is devoted to computational analysis of thermal gravitational convection within a porous chamber under the impact of tilted periodic magnetic force. Governing equations formulated employing the single-phase nanoliquid approach, Brinkman-extended Darcy model for transport processes within the porous layer with the local thermal non-equilibrium approach, Boussinesq approximation for the description of the buoyancy force and magnetic field, have been resolved using the Galerkin finite element method. Impacts of the Darcy number, Hartmann number, Rayleigh number, periodicity of the magnetic field, magnetic field inclination angle, thermal conductivity ratio, and medium porosity on flow and thermal patterns have been examined. It has been found that parameters of the periodic magnetic field have the non-monotonic influence of the heat transfer performance.

Possible effect of flow velocity on thawing rock-water-ice systems under local thermal non-equilibrium conditions

Climate change causes thawing of many permafrost regions, increasing the rockfall and landslide hazard when the cementing ice melts and slopes become unstable. The thermo-hydro-mechanical processes are strongly coupled and complex to describe in those intrinsic multi-phase systems. So far, thermal models often utilize the local thermal equilibrium approach, assuming that all three phases (solid rock or soil, liquid water and ice) are in thermal equilibrium. While this approach is very tempting due to its easy implementation, there are situations especially during thawing in which temperature gradients exist between the involved phases. In such cases, the local thermal equilibrium approach has to be replaced by the more complex local thermal non-equilibrium approach in which the thermodynamic state of each phase is described by its own temperature. In those models, the heat transfer between the phases is described explicitly in dependence of the heat transfer coefficient and the contact area. Parameterization of the heat transfer coefficient is a challenging task and mostly relies on empirical values and relationships. Most models using the local thermal non-equilibrium approach utilize a constant heat transfer coefficient. However, experiments under geothermal temperature conditions prove that the heat transfer coefficient depends, among others, on flow velocity. This is of special interest as strong dynamics are characteristic for thawing system which impose a unique challenge to heat transfer models. For example, the volume fraction of the liquid domain increases significantly during thawing of rock-ice systems due to the melting of the ice phase. This again, directly influences flow velocity. In this work, the possible effect of a velocity dependent heat transfer coefficient on thawing rock-water-ice systems is investigated. With higher flow velocity, advection effects of the intruding fluid become more significant but also heat transfer is increased. When the intruding liquid water is colder than the surrounding rock, the melting rate is maximum for a specific flow velocity, as advection of cold water and heating from the rock counteract. While this is a purely synthetic study and no experimental data yet exists for validation of the proposed scheme, this study indicates the existence of a way more complex interaction between liquid fluid flow and melting processes as previously expected and way beyond state-of-the-art modeling.

Non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium

Purpose This study aims to numerically analyze natural convection of alumina-water nanofluid in a differentially-heated square cavity partially filled with a heat-generating porous medium. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been considered for the description of the nanoparticles transport effect in the present study. Local thermal non-equilibrium approach for the porous layer with the Brinkman-extended Darcy model has been used. Design/methodology/approach Dimensionless governing equations formulated using stream function, vorticity and temperature have been solved by the finite difference method. The effects of the Rayleigh number, Ostrogradsky number, Nield number and nanoparticles volume fraction on nanofluid flow, heat and mass transfer have been analyzed. Findings It has been revealed that the dimensionless heat transfer coefficient at the fluid/solid matrix interface can be a very good control parameter for the convective flow and heat transfer intensity. The present results are original and new for the study of non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium. Originality/value The results of this paper are new and original with many practical applications of nanofluids in the modern industry.

Numerical investigation of rock-pile based waste heat storage for remote communities in cold climates

Remote communities in arctic climates are solely dependent on diesel generators for continuous power supply due to their detached loci from national power gridlines or natural gas pipelines. Moreover, to get along with the harsh, long winters, these communities directly or indirectly depend on fossil-fuel based heating systems. Due to the lower efficiency of the conventional diesel engines, these generators discard a significant amount of heat through the exhaust. Occasionally, during the wintertime, this waste heat from the exhaust is used directly as a heat source after recovery. However, during summer, when the heating demand is lower or nil, this heat is commonly discarded, and its energy potential wasted. A rock-pile based seasonal thermal energy storage is a viable solution that can sustainably resolve this issue. This paper presents a validated numerical study that focuses on the coupling of a waste heat recovery system to a diesel exhaust stream offering a performance assessment of the proposed rock-pile waste heat storage system in a remote, off-grid community located in northern Canada. It examines the impacts of local thermal equilibrium versus non-equilibrium approaches as well as temperature-dependent properties, variation of air mass flow rate, particle size and finally the thermo-physical properties on the proposed model. The presented results show that air should be treated as an ideal gas and that the local thermal non-equilibrium approach should be used for its considerably higher accuracy. Techno-economic assessment of the system resulted in a relatively short payback period of less than six years.

Constructal enhancement of thermal transport in metal foam-PCM composite-assisted latent heat thermal energy storage system

The aim of this study is to augment thermal transport in latent heat thermal energy storage (LHTES) system by the optimum allocation of metal foam-phase change material (PCM) composite. This study emphasizes on the optimal volume and distribution of metal foam-PCM composite (MFPC) to enhance melting performance without delay in the total melting time. Therefore, a MFPC is designed according to constructal theory. The fundamental principle of the theory is to configure high thermal conductivity agents at optimal thermal energy flow path for effective heat exchange. A numerical code based on local thermal nonequilibrium approach equipped enthalpy porosity method is formulated, and evaluated. The results of the proposed configuration show that the provision of MFPC only at high local temperature gradient enhances the conductive transport with improvement in the overall thermal transport. It is derived that the elimination of metal foam volume at low temperature gradient incorporates the advantageous effect of natural convective transport, which is seen to be suppressed. Additionally, the proposed configuration may increase the volume of PCM, thus, the TES capacity. It also reduces the total weight and economy of energy storage system. The overall melting rate is improved by 11.11% in comparison with the LHTES with full volume of this high thermal conductivity agent.

Combined heat and mass transfer analyses in catalytic microreactors partially filled with porous material - The influences of nanofluid and different porous-fluid interface models

This paper reports a theoretical analysis of heat and mass transfer in the microchannels partially filled with porous materials and used in thermos-chemical microreactors. A first order catalytic chemical reaction is considered on the internal surfaces of a parallel-plates microchannel. The local thermal non-equilibrium approach along with two well-established porous-fluid interface models is employed to investigate the heat transfer within the porous section of the microreactor. The analysis further accounts for the finite thickness of the surrounding solid walls of the microchannel. The dispersion equations in both porous and clear sections of the microchannel are coupled with the fluid temperature through considering the thermal diffusion of mass. In addition, to enhance heat transfer in the partially-filled microchannel, the base fluid is replaced by a nanofluid. The results show that inclusion of the finite thickness of the walls in the thermal analysis can majorly affect the temperature fields and Nusselt number (Nu). In particular, the optimal thickness of the porous insert for achieving the maximum Nu is found to be strongly influenced by the wall thickness. It is also shown that the specific porous-fluid interface model, thicknesses of the porous section and that of the walls, and the volumetric concentration of the nanoparticles can all impart significant effects upon the concentration of chemical species and their distribution across the microchannel. More specifically, the concentration field within the porous region is found to be considerably dependent on the implemented porous-fluid interface model.

MAGNETO CONVECTION HEAT TRANSFER IN A POROUS SQUARE CAVITY USING LOCAL THERMAL NON-EQUILIBRIUM APPROACH

This paper addresses the effect of magnetic field on natural convection heat transfer in a two-dimensional porous square cavity using local thermal non-equilibrium approach. The cavity is bounded by isothermal vertical walls and adiabatic horizontal walls. The governing non-dimensional equations are solved by finite volume method based on the SIMPLE algorithm. The numerical simulations are presented for various pertinent parameters such as Hartmann number (0 ≤ Ha ≤ 100), interphase heat transfer coefficient (0 ≤ H ≤ 1000), Rayleigh number (103 ≤ Ra ≤ 106), thermal conductivity ratio (0.1 ≤ γ ≤ 100), and Darcy number (10-5 ≤ Da ≤ 10-1). The computed results are presented in the form of streamlines for fluid phase and isotherms for fluid and solid phases. It is found that the local thermal non-equilibrium approach has a significant effect on the heat transfer performance. The influence of magnetic field on the solid phase is significant when H and γ are very high, but it is negligible for low values of H and γ.

Energetic and entropic analyses of double-diffusive, forced convection heat and mass transfer in microreactors assisted with nanofluid

This paper investigates the energetic and entropic characteristics of a microchannel with thick walls. A first-order, catalytic chemical reaction is imposed on the inner surfaces of the microchannel walls, and local thermal non-equilibrium approach is employed to analyse heat transfer within the porous section of the microchannel. Further, endo-/exothermic physicochemical processes are incorporated into the fluid phase and solid structure of the microchannel. Two models describing the fluid–porous interface conditions known as Models A and B are incorporated. It is shown that for both interface models, and with the considered parametric values, the optimum thickness of the porous insert to achieve the maximum Nu is around 0.6. However, when PEC is considered, this optimum thickness may vary between 0 and 0.5. It is further shown that depending on the specification of the microreactor, either Model A or B may result in the prediction of the minimum total entropy generation rate. It is also demonstrated that by altering the endothermicity of the microreactor it is possible to find an optimal value, which minimizes the total rate of entropy generation.

Effect of local heater size and position on natural convection in a tilted nanofluid porous cavity using LTNE and Buongiorno's models

Natural convection heat transfer within nanofluid porous cavities with local heaters occurs in different engineering applications. Therefore, analysis of nanofluid flow and heat transfer patterns in such systems has a significant value for development of industry. In the present study, free convection of nanofluid in a tilted porous cavity with a local isothermal heater has been investigated numerically. Governing equations with corresponding initial and boundary conditions formulated using the Darcy–Boussinesq model and local thermal non-equilibrium approach have been solved by the finite difference method under the effects of Brownian diffusion and thermophoresis. Effects of heater location (δ = 0.1–0.3) and dimensionless length (D = 0.2–0.8) as well as cavity inclination angle (γ = 0–π/2) and interphase heat transfer coefficient (H = 10–1000) on nanofluid flow and heat transfer have been studied for the following values of other governing parameters: Rayleigh number (Ra = 105), Prandtl number (Pr = 6.82), Darcy number (Da = 10−3), porosity of porous medium (ε = 0.5), buoyancy ratio parameter (Nr = 1), Brownian diffusion parameter (Nb = 10−6), thermophoresis parameter (Nt = 10−6), Lewis number (Le = 1000), thermal diffusivity ratio (Γ = 649.7) and heat capacitance ratio (ξ = 3.4). It has been found the heat transfer enhancement and convective flow attenuation when the distance between the heater and the cold vertical wall reduces.

Two-dimensional heat and mass transfer and thermodynamic analyses of porous microreactors with Soret and thermal radiation effects—An analytical approach

Transport of heat and mass and the thermodynamics of porous microreactors with thermal diffusion and radiation effects are investigated analytically. The examined configuration includes an axisymmetric, thick-wall microchannel with an iso-flux thermal boundary condition imposed on the external surfaces. The microchannel is filled with porous materials and accommodates a zeroth order homogenous chemical reaction. Internal radiative heat transfer is modelled in addition to heat convection and conduction, while the local thermal non-equilibrium approach is taken within the porous section of the system. The transport of species is coupled with that of heat via the inclusion of thermodiffusion or Soret effect. Two-dimensional heat and mass transfer differential equations are solved analytically. The results are subsequently used to predict the thermodynamic irreversibilities inside the reactor and a thorough analysis of local and total entropy generation rates is performed. Also, the changes in Nusselt number, calculated on the internal walls of the microreactor, versus various parameters are reported. It is shown that the radiation effects can impact the temperature of the solid phase of the porous medium and lead to alteration of Nusselt number. It is further observed that the transfer of mass is the main source of irreversibility in the system. The findings are of particular use for the design and analysis of the microreactors with homogenous chemical reactions and can be also used for the validation of computational models.

Non-Equilibrium Thermodynamic Analysis of Double Diffusive, Nanofluid Forced Convection in Catalytic Microreactors with Radiation Effects

This paper presents a theoretical investigation of the second law performance of double diffusive forced convection in microreactors with the inclusion of nanofluid and radiation effects. The investigated microreactors consist of a single microchannel, fully filled by a porous medium. The transport of heat and mass are analysed by including the thick walls and a first order, catalytic chemical reaction on the internal surfaces of the microchannel. Two sets of thermal boundary conditions are considered on the external surfaces of the microchannel; (1) constant temperature and (2) constant heat flux boundary condition on the lower wall and convective boundary condition on the upper wall. The local thermal non-equilibrium approach is taken to thermally analyse the porous section of the system. The mass dispersion equation is coupled with the transport of heat in the nanofluid flow through consideration of Soret effect. The problem is analytically solved and illustrations of the temperature fields, Nusselt number, total entropy generation rate and performance evaluation criterion (PEC) are provided. It is shown that the radiation effect tends to modify the thermal behaviour within the porous section of the system. The radiation parameter also reduces the overall temperature of the system. It is further demonstrated that, expectedly, the nanoparticles reduce the temperature of the system and increase the Nusselt number. The total entropy generation rate and consequently PEC shows a strong relation with radiation parameter and volumetric concentration of nanoparticles.

Evaluation of recoverable energy potential from enhanced geothermal systems: a sensitivity analysis in a poro‐thermo‐elastic framework

AbstractThis study presents application of an efficient approach to simulate fluid flow and heat transfer in naturally fractured geothermal reservoirs. Fluid flow is simulated by combining single continuum and discrete fracture approaches. The local thermal nonequilibrium approach is used to simulate heat transfer by conduction in the rock matrix and convection (including conduction) in the fluid. Fluid flow and heat transfer models are integrated within a coupled poro‐thermo‐elastic framework. The developed model is used to evaluate the long‐term response of a geothermal reservoir with specific boundary conditions and injection/production schedule. A comparative study and a sensitivity analysis are carried out to evaluate the capability of the integrated approach and understand the degree by which different reservoir parameters affect thermal depletion of Soultz geothermal reservoir, respectively. Also observed, there exists an optimum fracture permeability after which the reservoir stimulation does not change the recovery factor significantly. Estimation of fluid temperature by the assumption of local thermal nonequilibrium heat transfer between the fracture fluid and the rock matrix gives fluid temperature of about 3°C less than that of estimated by thermal equilibrium heat transfer at early stage of hot water production.

New models for heat flux splitting at the boundary of a porous medium: three energy equations for nanofluid flow under local thermal nonequilibrium conditions

One of the challenging points in the simulation of a nanofluid flowing through a porous medium is modeling the surface heat flux in the presence of nanoparticles and internal solid matrix. The question is how much energy is absorbed by the solid phase, fluid phase, and particles at the surface of imposing heat flux? To reach a suitable answer, a local thermal nonequilibrium approach (including three energy equations) is presented in this paper and three heat flux models are proposed for the first time. The proposed models are compared and analyzed. The effects of interstitial heat transfer coefficients on the heat transfer in a porous channel are completely studied. The fluid temperature distributions and heat transfer rate obtained by homogenous and nonhomogenous approaches (for the proposed models) are completely studied and compared. The results show that the nonhomogeneous approach experiences larger Nusselt number than the homogeneous one for all the recommended heat flux models.