Interphase Heat Transfer Coefficient Research Articles

Perspectives on local thermal non-equilibrium (LTNE) Darcy–Bénard convection: Variable permeability and viscosity effects

The interplay between variations in permeability and viscosity on the onset of local thermal non-equilibrium in Darcy–Bénard convection has been investigated. Specifically, permeability is modeled as decreasing linearly with depth, while viscosity decreases exponentially. The validity of the principle of exchange of stabilities is confirmed. A linear instability analysis of the quiescent state is conducted through normal mode decomposition of disturbances, with threshold values for instability onset computed numerically using the Galerkin method. The individual and combined effects of increasing the variable permeability and viscosity parameters on the instability characteristics of the system are examined in detail, highlighting both commonalities and distinctions. It is observed that increasing each parameter individually hastens the onset of convection. However, their combined influence produces both stabilizing and destabilizing effects under certain parametric conditions. In all scenarios, an increase in the scaled interphase heat transfer coefficient consistently delays the onset of convection, whereas a higher ratio of porosity-modified conductivities has the opposite effect. Furthermore, the size of the convection cells remains unchanged at the extreme values of the scaled interphase heat transfer coefficient.

Dissipation induced instability in porous medium using Brinkman model: Thermal non-equilibrium effect

The convective instability that arises in a porous layer solely because of dissipative energy in the medium is studied. The thermal non-equilibrium model is considered for energy equation. The boundary at top is kept at constant temperature, and an adiabatic lower boundary is considered. The momentum equation is written according to the Brinkman model. A basic flow in the horizontal plane is considered, and the basic velocity and temperature profile have been derived. A comparison between the basic temperature profiles for solid and fluid of the porous medium is presented for Darcy and Brinkman models. Infinitesimal disturbance is introduced to the basic flow. A linear stability analysis has been carried out to study the stability of the basic flow. The parameters influencing the stability of the system are critical Rayleigh number (RaC), Gebhart number (Ge), ξ associated with the Darcy number (Da), and interphase heat transfer coefficient (H). The values of the critical Rayleigh number and wavenumber are compared by varying other variables. The flow is more stable when the Brinkman medium is considered. With the increase in interphase heat transfer coefficient, the critical Rayleigh number increases in both Darcy and Brinkman media. The longitudinal rolls appear as the most unstable rolls for all cases. The variation of convective rolls with respect to ξ and heat transfer coefficient is presented.

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.

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.

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

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

Modeling filtered heat transfer model by considering dimensionless temperature difference between gas and solid phases

AbstractComputational fluid dynamics–discrete element method is used to simulate gas–solid flows with heat transfer. The strategy of repetitively resetting the gas phase temperature is adopted to maintain the temperature difference between the gas and solid phases. The difference between the heat transfer characteristics produced by this strategy and the traditional heat source method is analyzed. It is found that heat transfer in dense regions is artificially enhanced by the heat source method. Therefore, the results obtained by the temperature reset method are filtered to develop a three‐marker model for the filtered interphase heat transfer coefficient (IHTC). In the developed model, the filtered gas–solid temperature difference is nondimensionalized by the average gas–solid temperature difference in surrounding grids, which is shown to have an impact on the filtered IHTC. The developed model is demonstrated to be effective and accurate in both a prior and a posterior tests.

Impact of Thermal Nonequilibrium on Flow Through a Rotating Disk with Power Law Index in Porous Media Occupied by Ostwald-de-Waele Nanofluid

Abstract The current study is made to analyze the impact of local thermal nonequilibrium (LTNE) on the steady, incompressible, and viscous Ostwald-de-Waele nano-liquid over a rotating disk in a porous medium with the various power law index, due to many remarkable applications, such as aeronautical systems, rotating machineries, air cleaning machineries, electrical power-generating systems, heat exchangers, gas turbines, centrifugal pumps. To describe the modeling of the nano-liquid, Brownian movement and thermophoresis are employed with the passive control boundaries. Three temperature model is adopted to distinguish the temperature among the fluid, particle, and solid. The governing transport equations have been converted to a system of nonlinear coupled ordinary differential equations by employing von Karman transformation. Numerical results of the flow and heat and transfer characteristics of the fluid, particle, and solid are obtained by applying Runge–Kutta–Fehlberg method (RKF) together with the shooting technique. The numerical results in the present work are compared with the published results for the case of thermal equilibrium and found that they are in good agreement. It is observed that the temperature profile significantly varies with the fluid-particle, fluid-solid interphase heat transfer coefficients and the modified thermal capacity ratios.

Heat transfer and thermal conductivity of magneto micropolar fluid with thermal non-equilibrium condition passing through the vertical porous medium

This paper investigates the incompressible mixed convection flow of electrically conductive micropolar fluid with a thermal non-equilibrium condition that passes through the vertical circular (pipe) porous medium. The extension of the non-Darcy–Brinkman–Forchheimer model is considered to formulate the governing non-linear system of differential equations for the problem. Furthermore, the rigorous impact of different parameters such as thermal conductivity ratio , inter-phase heat transfer coefficient , Darcy number , Grashof number , Eringen micro-polar parameter , Hartmann number , solid-heat generation , and fluid heat generation parameter on velocity profile , micro-rotational (angular velocity) , temperature of solid and fluid has been investigated by using the computational strength of artificial intelligence based Elman neural networks (ENN) and Levenberg–Marquardt algorithm (LMA). We have compared the solutions calculated by the designed ENN-LM algorithm with the Cuckoo Search Algorithm (CSA), Chebyshev spectral collocation method (CSCM), particle swarm optimization (PSO) algorithm, and Runge–Kutta method. The convergence rate and stability of the ENN-LM technique show that it can be applied to solving complex models involving partial and fractional differential equations.

Fluid dynamics and thermal characteristics of a conical bubbling fluidized bed riser

Conical fluidized beds show a unique inherent dynamic feature due to a lower pressure drop than conventional fluidized beds. Although the literature deliberating on the hydrodynamics of this type of riser is rich, the thermal characteristics of this type of riser are yet to be investigated. Moreover, the interphase heat transfer has not been deeply understood in previous literatures by considering the effect of air velocity. As in real fluidized bed industries, hot air is supplied through the inlet of a riser to heat the particles in the drying process and other phenomena. As a result, the interphase heat transfer characteristics are more important than the core-to-wall thermal characteristics. The thermal phenomena are ineluctably directed by the two-phase flow hydrodynamics. The present investigation is conducted to research fluid dynamics and interphase heat transfer phenomena of the air-sand mixture in a conical bubbling fluidized bed riser of cone angle 10° with varying inlet air velocity. Air velocity is the main parameter which leads to the fluidization in fluidized beds. It is this parameter that materializes the elutriation of particles and determines the nature of the bed, whether bubbling or recirculating. This, in turn, affects the heat transfer and overall efficiency of the bed. Experiments along with corresponding three-dimensional (3-D) numerical simulations are performed at five superficial air velocity conditions (1, 1.25, 1.5, 1.75 and 2 m/s) and a 30 cm height of bed materials. The results are then compared between experimental and simulation conditions. Both the experimental and 3-D numerical results indicate that a velocity of 2 m/s results in the lowest pressure drop of 2830 Pa. Similarly, the average bed temperature in this velocity is 444 K which is the highest, whereas the interphase heat transfer coefficient is 320 W/m2K. The bed-to-wall heat transfer coefficient is found to increase by 47.2% and 45.8% at the central axial locations of 10 and 20 cm, respectively. Hence, it can be concluded that air velocity plays an important role in the operation of a fluidized bed in terms of pressure drop, heat transfer and thermal efficiency. Air velocity of 2 m/s is found to be the best value for the present study because the bed pressure drop decreases and heat transfer increases.

Nonlinear Stability and Linear Instability of Double-Diffusive Convection in a Rotating with LTNE Effects and Symmetric Properties: Brinkmann-Forchheimer Model

The major finding of this paper is studying the stability of a double diffusive convection using the so-called local thermal non-equilibrium (LTNE) effects. A new combined model that we call it a Brinkmann-Forchheimer model was considered in this inquiry. Using both linear and non-linear stability analysis, a double diffusive convection is used in a saturated rotating porous layer when fluid and solid phases are not in the state of local thermal non-equilibrium. In addition, we discussed several related topics such as the effect of solute Rayleigh number, symmetric properties, Brinkman coefficient, Taylor number, inter-phase heat transfer coefficient on the stability of the system, and porosity modified conductivity ratio. Moreover, two cases were investigated in non-linear theory, the case of the Forchheimer coefficient F=0 and the case of the Taylor-Darcy number τ=0. For the validation of this work, some numerical experiments were made in the non-linear energy stability and the linear instability theories.

Thermosolutal LTNE Porous Mixed Convection Under the Influence of the Soret Effect

Abstract The onset of thermosolutal convection in a fluid-saturated porous medium in the presence of a horizontal pressure gradient and the Soret effect under the two-temperature model of local thermal nonequilibrium (LTNE) is investigated. The Darcy model with the time-dependent velocity term in the momentum equation is employed together with the Oberbeck–Boussinesq approximation. The eighth-order eigenvalue differential equation obtained by employing linear stability analysis is solved using Galerkin's method of weighted residuals (GMWR) and also analytically. The onset of convection instills through oscillatory rather than stationary mode, and the critical stability parameters for the same are determined. The horizontal pressure gradient reinforces together with the solute concentration gradient and the scaled interphase heat transfer coefficient in evidencing mixed behavior on the criterion for the onset of oscillatory convection. Besides, the similarities and differences between the results of thermal and thermosolutal LTNE porous mixed convection are discerned.

Experimental–Theoretical Determining of the Interphase Heat Transfer Coefficient in the Process of Combustion of a Granular SHS Mixture in a Gas Flow

Experimental–Theoretical Determining of the Interphase Heat Transfer Coefficient in the Process of Combustion of a Granular SHS Mixture in a Gas Flow

Thermal analysis on natural-convection coupled with radiative heat transfer in a saturated porous cavity

Porous foam is an ideal material for enhancing radiative heat transfer in numerous thermal equipment. The solid skeletons of porous foams can absorb/release radiative energy and transfer convective energy with the surrounding fluid in the pores. In this paper, the conduction-convection-radiation coupling heat transfer in a porous cavity is investigated. A local thermal non-equilibrium model is used to represent the energy transport during the solid and fluid phases. The heat flux caused by thermal radiation is obtained by solving the radiation transfer equation. The thermal and fluid fields are studied to discern various parameters, including the Planck numbers, the modified Rayleigh numbers, and the interphase heat transfer coefficients, H. Our study indicates the following: the effect of radiation can be neglected when Pl > 20, the modified Rayleigh numbers have little influence on the solid temperature when the radiative heat transfer is dominant and the convective heat transfer between the two-phases is weak, and the local thermal-equilibrium can be formed when H exhibits high values.

Density maximum and finite Darcy–Prandtl number outlooks on Gill's stability problem subject to a lack of thermal equilibrium

The Gill stability problem encompasses the investigation of stability of natural convection flow in a vertical porous layer governed by Darcy's law under a local thermal equilibrium (LTE) perspective and was proved analytically by Gill [Gill, J. Fluid Mech. 35, 545–547 (1969)] that the flow is always stable. The present study deals with the simultaneous influence of the Darcy–Prandtl number and the density maximum property on Gill's stability problem subject to a lack of thermal equilibrium. The density variation with fluid temperature is assumed to be pure quadratic, and it is established that the linear stability of the basic state for a three-dimensional problem can be Squire-transformed. It is observed that Gill's proof of linear stability cannot be extended to the present model and hence we approached numerically by evaluating the growth rate of normal mode perturbations. The neutral stability curves are obtained, and the critical parameters at the onset of instability are determined. Even though the isolation presence of time-dependent velocity term and the density maximum property evidence the basic flow to be stable for all infinitesimal perturbations, their simultaneous occurrence induces instability under certain parametric conditions. The finite range of values of the scaled interphase heat transfer coefficient within which the flow is stable is found to increase with increasing Darcy–Prandtl number but vanishes with increasing porosity-modified conductivity ratio. Moreover, the basic state becomes stable when the Darcy–Prandtl number is larger than 7.08. The results of LTE model are delineated as a particular case from the present study.

Two-fluid modeling of heat transfer in flows of dense suspensions

We develop a two-fluid model (TFM) for heat transfer in dense non-Brownian suspensions. Specifically, we propose closure relations for the inter-phase heat transfer coefficient and the thermal diffusivity of the particle phase based on calibration against experimental data. The model is then employed to simulate non-isothermal flow in an annular Couette cell. We find that, when the shear rate is controlled by the rotation of the inner cylinder, both the shear and thermal gradients are responsible for particle migration. Within the TFM framework, we identify the origin and functional form of a “thermo-rheological” migration force that rationalizes our observations. Furthermore, we apply our model to flow in eccentric Couette cells. Our simulations reveal that the system’s heat transfer coefficient is affected by both the classic shear-induced migration of particles and the newly identified thermo-rheological migration effect.

Effect of rotation on Brinkman-Bénard convection of a Newtonian nanoliquid using local thermal non-equilibrium model

Rayleigh-Bénard-Taylor convection in a Newtonian, nanoliquid-saturated high porous medium using the local thermal non-equilibrium model (LTNE) is studied analytically using the single term Galerkin technique. The Bousinessq approximation is considered to be valid and the exerted centrifugal force due to rotation is taken. A high porosity porous material glass reinforced fiber with porosity 0.88% is considered and hence the Brinkman model is adopted. The rate of rotation is quantified by the Taylor number and the stability of the system is controlled by thermal Rayleigh number. The expression for the critical eigenvalue (Rayleigh number) is obtained for both idealistic and realistic boundary conditions, that is, stress-free, isothermal and rigid-rigid, isothermal boundary conditions. The presumption of LTNE advances the inception of convection and increases the transport of heat in comparison with that of the local thermal equilibrium (LTE) assumption whereas the opposite phenomenon is seen with the effect of rotation. The effect of various non-dimensional parameters on the convection onset and on transport of heat is also investigated. The results of Rayleigh-Bénard-Taylor convection using the LTE assumption are obtained as limiting cases of the present study for infinite values of the ratio of thermal conductivities and the interphase heat transfer coefficient.

A study on entropy generation and heat transfer in a magnetohydrodynamic flow of a couple‐stress fluid through a thermal nonequilibrium vertical porous channel

AbstractThe effect of local thermal nonequilibrium (LTNE) on the entropy generation and heat transfer characteristics in the magnetohydrodynamic flow of a couple‐stress fluid through a high‐porosity vertical channel is studied numerically using the higher‐order Galerkin technique. The Boussinesq approximation is assumed to be valid and the porous medium is considered to be isotropic and homogeneous. Two energy equations are considered one each for solid and fluid phases. The term involving the heat transfer coefficient in both equations renders them mutually coupled. Thermal radiation and an internal heat source are considered only in the fluid phase. The influence of inverse Darcy number, Hartmann number, couple‐stress fluid parameter, Grashof number, thermal radiation parameter, and interphase heat transfer coefficient on velocity and temperature profiles is depicted graphically and discussed. The entropy generation, friction factor, and Nusselt number are determined, and outcomes are presented via plots. The effect of LTNE on the temperature profile is found to cease when the value of the interphase heat transfer coefficient is high, and in this case, we get the temperature profiles of fluid and solid phases are uniform. The physical significance of LTNE is discussed in detail for different parameters' values. It is found that heat transport and friction drag are maximum in the case of LTNE and minimum in the case of local thermal equilibrium. We observe that LTNE opposes the irreversibility of the system. The corresponding results of a fluid‐saturated densely packed porous medium can be obtained as a limiting case of the current study.

Local Thermal Nonequilibrium Natural Convection in a Cavity with Heat-Generating Porous Layer

Natural convection in a partially porous cavity with a heat generating source in the solid phase is studied numerically under a local thermal nonequilibrium condition. The right and left walls of the cavity are maintained at hot and cold temperatures, respectively. The horizontal walls are thermally insulated. The finite volume method and the semi-implicit method for pressure-linked equations (SIMPLER) algorithm are used to solve the conservation equations. The effects of relevant parameters, such as internal and external Rayleigh numbers , , interphase heat transfer coefficient , modified thermal conductivity ratio , and dimensionless porous layer thickness are discussed. The results revealed that at high values of the interphase heat transfer coefficient, the impact of an internal Rayleigh number on the dynamic and thermal fields decreases with an increase in the modified thermal conductivity ratio.

Improved filtered mesoscale interphase heat transfer model

Mesoscale structures that form in gas–solid flows considerably affect interphase heat transfer. A filtered interphase heat transfer model accounts for the effects of unresolved mesoscale structures is required in coarse-grid simulations. In the literature, researchers obtain the filtered interphase heat transfer coefficient using a correction (Q) to the microscopic interphase heat transfer coefficient. Available models are based on filtered data in the range 0<Q<1. However, the percentage of filtered data in the range Q<0 and Q>1 is non-negligible. This percentage can reach approximately 20% when the dimensionless filter size is smaller than 1.028 (66.7×the particle diameter). We proposed an improved filtered interphase heat transfer model by considering the data in the range Q<0 and Q>1. We evaluated the predictive power of our model in an a priori test. Our model has much better performance than other models when the dimensionless filter size Δˆ<8.222.

Study of filtered interphase heat transfer using highly resolved CFD–DEM simulations

AbstractAccurately predicting the complex inhomogeneous heat transfer behavior in gas–solid fluidized beds is of fundamental importance. In this work, we constitute an enhanced filtered interphase heat transfer coefficient (IHTC) closure by systematically filtering the dataset from highly resolved three‐dimensional (3D) computational fluid dynamics–discrete element model simulations. Particularly, effects of several potential filtered variable markers on filtered IHTC predictions are examined by statistical analysis. We reveal the formulated filtered IHTC correction closure manifests a systematic dependence on filtered interphase temperature difference as an additional marker. The proposed closure shows good agreement with the filtered fine‐grid simulation data in an a priori analysis. Moreover, the difference of filtered IHTC corrections deduced from 3D Euler–Euler and Euler–Lagrange simulations is quantified. Finally, the comparative analysis between our proposed filtered IHTC formulation and those in literature is implemented. This work holds a potential to facilitate the development of thermal gas–solid flow modeling.