A Lattice Boltzmann Formulation for the Analysis of Radiative Heat Transfer Problems in a Participating Medium

Use of the lattice Boltzmann method (LBM) has been extended to analyze radiative transport problems in an absorbing, emitting, and scattering medium. In terms of collision and streaming, the present approach of the LBM for radiative heat transfer is similar to those being used in fluid dynamics and heat transfer for the analyses of conduction and convection problems. However, to mitigate the effect of the isotropy in the polar direction, in the present LBM approach, lattices with more number of directions than those being used for the 2-D system have been employed. The LBM formulation has been validated by solving benchmark radiative equilibrium problems in 1-D and 2-D Cartesian geometry. Temperature and heat flux distributions have been obtained for a wide range of extinction coefficients. The LBM results have been compared against the results obtained from the finite-volume method (FVM). Good comparison has been obtained. The numbers of iterations and CPU times for the LBM and the FVM have also been compared. The number of iterations in the LBM has been found to be much more than the FVM. However, computationally, the LBM has been found to be much faster than the FVM.     

Solving transient heat conduction problems on uniform and non-uniform lattices using the lattice Boltzmann method

The lattice Boltzmann method (LBM) has been used to solve transient heat conduction problems in 1-D, 2-D and 3-D Cartesian geometries with uniform and non-uniform lattices. To study the suitability of the LBM, the problems have also been solved using the finite difference method (FDM). To check the performance of LBM for the non-uniform lattices, the results have been compared with uniform lattices. Cases with volumetric heat generation have also been considered. In 1-D problems, the FDM with implicit scheme was found to take more number of iterations and also the CPU time was more. However, with explicit scheme, with increase in the number of control volumes, the LBM was found faster than the FDM. In 2-D and 3-D problems, with increase in the number of control volumes, the LBM was found faster than the FDM. In 2-D problems, number of iterations in the two methods was comparable, while in 3-D problems, the LBM was found to take less number of iterations. The accurate results were found in all the cases.     

The influence of binary mixture thermophysical properties in the analysis of heat and mass transfer processes in solar distillation systems

Although a substantial amount of research work has already been devoted to various aspects of modeling the convective and mass transport processes in solar distillation systems, it appears that the role of thermophysical and transport properties of the working medium and their effect on the thermal behavior and performance analysis of such systems has been left almost completely unnoticed. The working medium in these systems, which is a binary mixture of water vapor and dry air in equilibrium, appears to exhibit a completely different set of properties than dry air, especially at saturation conditions and at the higher region of the solar still operational temperature range. An analysis is presented aiming to signify the effect of binary mixture thermophysical properties on the transport processes and the associated quantities and evaluate the thermophysical properties of the working medium in these systems, based on contemporary data for dry air and water vapor. The derived results, in the form of convenient algebraic correlations, are employed to investigate the effect of using the appropriate thermophysical properties on the calculation of the convective heat and mass transfer, as well as the distillate mass flow rates. According to the results from the present investigation, although the use of improper dry air data leads to a significant overestimation of the convective heat transfer coefficient, the errors associated with the use of improper dry air properties is a moderate overestimation of distillate output which is estimated to be up to 10% for maximum average still temperatures of 100 °C.     

Lattice Boltzmann method applied to the solution of the energy equations of the transient conduction and radiation problems on non-uniform lattices

Application of the lattice Boltzmann method (LBM) to solve the energy equations of conduction–radiation problems is extended on non-uniform lattices. In the LBM on non-uniform lattices, the single relaxation time based on the minimum velocity is used. This minimum velocity corresponds to the smallest size lattice. Because information propagates with the same minimum velocity in the prescribed directions from all the lattice centers, in a given time step, they are not equidistant from the neighboring lattices. Collisions in the LBM take place at the same instant. Therefore, in the LBM on non-uniform lattices, in every time step, interpolation is required to carry the information to the neighboring lattice centers. To validate this very concept in heat transfer problems involving thermal radiation, transient conduction and radiation heat transfer problems in a 1-D planar and a 2-D rectangular geometries containing absorbing, emitting and scattering medium are considered. The finite volume method (FVM) is used to compute the radiative information. In both the geometries, results for the effects of various parameters are compared for LBM–FVM on uniform and non-uniform lattices. To establish the LBM–FVM on non-uniform lattices for the combined conduction and radiation heat transfer problems, numerical experiments were performed with different cluster values. The accurate results were found in all the cases.     

Natural convection due to horizontal temperature and concentration gradients—1. Variable thermophysical property effects

Typically for single component fluids, the variation of thermophysical properties is negligible except in the presence of large temperature differences, and, therefore, has no appreciable effect on the heat transfer. In contradistinction, thermophysical properties can vary significantly due to concentration differences which affect the heat and mass transfer. This work examines the effects of thermophysical property variation on the heat and mass transfer in a cavity due to natural convection driven by combined thermal and solutal buoyancy forces. Results indicate that thermophysical property variations can appreciably influence heat and mass transfer and velocity distribution.     

A Review on the Discrete Boltzmann Model for Nanofluid Heat Transfer in Enclosures and Channels

Utilizing nanofluids to enhance heat transfer is shown to be a promising option with many practical applications. As the dimensions of the enclosures and channels for fluid flows steadily decrease, the energy carrying particle behavior for thermal transport becomes more significant. Therefore, the thermal analysis requires a mesoscale approach to describe the enhanced mechanism of heat transfer at the micro-scale level, and the interactions between the multicomponent fluid and its boundary conditions. For this purpose, the spatial and temporal discretization of the Boltzmann model leading to a thermal lattice Boltzmann method (LBM) recovers the macroscopic conservations of momentum and energy through particle collisions and streaming at mesoscale discrete nodes. In this article, the LBM studies for convective heat transfer, including the external forces, is reviewed in order to allow us to identify the research gaps and to reveal the promising future possibilities of its use for nanofluids.     

Effects of Non-Darcian and Inlet Conditions on the Forced Convection Along a Vertical Plate With Film Evaporation

The present study analyzes theoretically the non-Darcian effects and inlet conditions of forced convection flow with liquid film evaporation in a porous medium. The physical scheme includes a liquid–air streams combined system; the liquid film falls down along the plate and is exposed to a cocurrent forced moist air stream. The axial momentum, energy, and concentration equations for the air and water flows are developed based on the steady two-dimensional (2-D) laminar boundary layer model. The non-Darcian convective, boundary, and inertia effects are considered to describe the momentum characteristics of a porous medium. The paper clearly describes the temperature and mass concentration variations at the liquid–air interface and provides the heat and mass transfer distributions along the heated plate. Then, the paper further evaluates the non-Darcian effects and inlet conditions on the heat transfer and evaporating rate of liquid film evaporation. The numerical results show that latent heat transfer plays the dominant heat transfer role. Carrying out a parametric analysis indicates that higher air Reynolds number, higher wetted wall temperature, and lower moist air relative humidity will produce a better evaporating rate and heat transfer rate. In addition, a non-Darcy model should be adopted in the present study. The maximum error for predictions of heat and mass transfer performance will be 21% when the Darcy model is used.     

Hydrodynamic and thermal performance prediction of functionalized MWNT-based water nanofluids under the laminar flow regime using the adaptive neuro-fuzzy inference system

ABSTRACT

Adaptive Neuro-Fuzzy Inference System (ANFIS) opens a new gateway in understanding the complex behaviors and phenomena for different fields such as heat transfer in nanoparticles. The ANFIS method is a shortcut to find a nonlinear relation between input and output and results in valid outcomes, especially in engineering phenomena, which is used here for determining the convective heat transfer coefficient. Using the ANFIS, the critical parameters in heat transfer including convective heat transfer coefficient and pressure drop are determined. To realize this issue, the thermophysical properties of non-covalently and covalently functionalized multiwalled carbon nanotubes-based water nanofluid were investigated experimentally. The results of simulation and their comparison with the experimental results showed an excellent evidence on the validity of the model, which can be expanded for other conditions. The proposed method of ANFIS modeling may be applied to the optimization of carbon-based nanostructure-based water nanofluid in a circular tube with constant heat flux.     

Thermodynamic and thermophysical effects enabling high-forced convection heat transfer coefficients in supercritical fluids

Abstract

The strong variation of thermophysical properties of working fluids operating in the vicinity of the critical point makes this thermodynamic domain attractive to several energy applications. Therefore, herein a two-dimensional numerical method is used to investigate the effect of local thermophysical property variations on the local and overall thermal performance of internal convective heat transfer in a pipe in 324 operational conditions. Focusing on carbon dioxide and water as heat transfer fluids, an association of the variation of key thermophysical properties with thermohydraulic performance metrics is proposed, namely: (a) the local and (b) mean convective heat transfer coefficient and (c) the maximal temperature obtained at the tube wall. It is shown that there is an optimal combination of parameters such as mass flow rate, operating pressure, wall heat flux, and inlet temperature that, when properly selected, allow for a minimal maximal wall temperature. As expected, optimality is strongly associated with the Widom—or pseudo critical—line that extends from the critical point. Interestingly, however, contrary to what is observed in constant-property fluids, high heat transfer coefficient or minimal maximum temperature lead to different sets of optimal operating conditions. This difference is explained by how thermophysical properties vary locally along heat exchangers, which significantly affects overall heat transfer.     

Meshless element free Galerkin method for unsteady nonlinear heat transfer problems

In this paper, meshless element free Galerkin (EFG) method has been extended to obtain the numerical solution of nonlinear, unsteady heat transfer problems with temperature dependent material properties. The thermal conductivity, specific heat and density of the material are assumed to vary linearly with the temperature. Quasi-linearization scheme has been used to obtain the nonlinear solution whereas backward difference method is used for the time integration. The essential boundary conditions have been enforced by Lagrange multiplier technique. The meshless formulation has been presented for a nonlinear 3-D heat transfer problem. In 1-D, the results obtained by EFG method are compared with those obtained by finite element and analytical methods whereas in 2-D and 3-D, the results are compared with those obtained by finite element method.     

Three-dimensional computational analysis of gas and heat transport phenomena in ducts relevant for anode-supported solid oxide fuel cells

Various transport phenomena occurring in an anode duct of medium temperature solid oxide fuel cell (SOFC) have been simulated and analyzed by a fully three-dimensional calculation method. The considered composite duct consists of a thick porous layer, the gas flow duct and solid current interconnector. Unique fuel cell boundary and interfacial conditions, such as the combined thermal boundary conditions on solid walls, mass transfer associated with the electrochemical reaction and gas permeation across the interface, were applied in the analysis. Based on three characteristic ratios proposed in this study, gas flow and heat transfer were investigated and presented in terms of friction factors and Nusselt numbers. It was revealed that, among various parameters, the duct configuration and properties of the porous anode layer have significant effects on both gas flow and heat transfer of anode-supported SOFC ducts. The results from this study can be applied in fuel cell overall modeling methods, such as those considering unit/stack level modeling.     

Modeling of steam–water direct contact condensation using volume of fluid approach

Direct contact condensation (DCC) of steam in subcooled water has paramount importance in many heat transfer devices in different industrial areas like nuclear, thermal, chemical plants. This work aims at the exploration of underlying physics of steam–water DCC in two dimensions using ANSYS FLUENT 14.5. The volume of fluid method is utilized for performing direct simulation of the phenomenon at the phase interface. In this work, thrust is given on the modeling of the interphase heat transfer using interfacial jump approach instead of proposed empirical correlations which have different applicability limits. User-defined functions in the FLUENT software are used for evaluating the interfacial mass transfer rate, thermal gradient across the phase interface, and interface curvature. This study also emphasizes on the prediction of transient temperature field and interface characteristics under different parametric conditions (e.g., variation of water injection velocity and water temperature). Observation reveals that the present condensation model is capable of capturing the transient temperature history as well as the flow regime transition (stratified to slug flow) induced by the interfacial instability.     

木材热解过程中颗粒内部传热模型的探析

木材快速热解液化是农林生物质热化学利用的手段之一.木材颗粒内部的传热控制其快速热解反应,是快速热解工艺优化研究的关键.文中建立了一个二维圆柱体的非稳态传热模型,对木材热解过程中颗粒内部传热进行模拟,并且充分考虑了木材颗粒的各向异性和热解过程中木材热物理性质随温度的变化以及热解过程中反应热、含水率等因素;采用有限元的计算...     

Simulation of CO2 under supercritical pressure in solar collectors by variable Lattice Boltzmann method

Abstract

Supercritical CO₂ is widely used in the HVAC facilities, such as gas coolers and solar collectors. The solar collector is a fluid-filled cavity, and the heat and mass transfer characteristics in the cavity is the key factor that affects the performance of solar collector. Considering that the thermophysical properties of supercritical CO₂ change dramatically, this article employs the Lattice Boltzmann Method (LBM) to implement the numerical simulation of supercritical heat and mass transfer. Based on analysis of the simulate results, it is found that the heat transfer in the solar collector is mainly related to Rayleigh number. Consequently, several correlations for the average Nusselt number are derived using Rayleigh number. Furthermore, a new concept named the critical Rayleigh number is proposed for the bifurcation phenomenon that occurs during the simulation. The numerical simulation results and the newly proposed correlations in this article could be used directly to improve and evaluate the performances of solar collectors.     

Comparative Analysis of Thermal Models in the Lattice Boltzmann Method for the Simulation of Natural Convection in a Square Cavity

In this article, a comparative analysis of thermal models in the lattice Boltzmann method for the simulation of natural convection in a square cavity is presented. A hybrid method, in which the thermal equation is solved by the Navier-Stokes equation method while the mass and momentum equations are solved by the lattice Boltzmann method (LBM), is introduced and its merits are explained. All the governing equations are discretized on a cell-centered, nonuniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with a deferred-correction method to ensure accuracy of solutions. The resulting algebraic equations are solved by a strongly implicit procedure. The hybrid method is applied to the simulation of natural convection in a square cavity and the predicted results are compared with the benchmark solutions given in the literatures. The predicted results are also compared with those by the double-population LBM and by the Navier-Stokes equation method. In general, the present hybrid method is as accurate as the Navier-Stokes equation method and the double-population LBM. The hybrid method shows better convergence and stability than the double-population LBM. These observations indicate that this hybrid method is an efficient and economic method for the simulation of incompressible fluid flow and heat transfer problems involving complex geometries.     

Modeling aspects of vapor bubble condensation in subcooled liquid using the VOF approach

Direct contact condensation of a vapor bubble during subcooled boiling flow scenario has diverse applications in many fields such as thermal, chemical, and nuclear energies. The present work aims at the exploration of the underlying physics of single vapor bubble condensation in subcooled water following the volume of fluid method approach using ANSYS FLUENT 14.5. This work emphasizes on the modeling of the mass transfer rate using interfacial jump conditions for investigating the effect of various parametric conditions on the collapse phenomenon. A comparative study is also performed between the interface jump approach and the models based on the proposed empirical correlations to assess the condensation heat transfer (in terms of the collapse rate and Nusselt number) and bubble shape. The mass transfer model based on the interfacial jump condition is found to be the more realistic among all models for capturing the collapse rate as well as its shape.     

Performance evaluation of four radiative transfer methods in solving multi-dimensional radiation and/or conduction heat transfer problems

This article reports results of the four popular and widely used numerical methods, viz., the Monte Carlo method (MCM), the discrete transfer method (DTM), the discrete ordinates method (DOM) and the finite volume method (FVM) used to calculate radiative information in any thermal problem. Different classes of problems dealing with radiation and/or conduction heat transfer problems in a 2-D rectangular absorbing, emitting and scattering participating medium have been considered. In radiative equilibrium and non-radiative equilibrium cases, the MCM results have been used as the benchmark data for comparing the performances of the DTM, the DOM and the FVM. In the combined radiation and conduction mode problem, the energy equation has been formulated using the lattice Boltzmann method (LBM). To compare the performance of the DTM, the DOM and the FVM, the required radiative field data computed using these methods have been provided to the LBM formulation. Temperature distributions obtained using the four methods and those obtained from the LBM in conjunction with the DTM, the DOM and the FVM have been compared for different parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the wall emissivity, the aspect ratio and heat generation rate. In all the cases, results of these methods have been found in good agreements. Computationally, the DTM was found the most time consuming, and the DOM was computationally the most efficient.     

Convective Heat and Mass Transfer in Water at Super—Critical Pressures under Heating or Cooling Conditions in Vertical Tubes

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Modeling heat and mass transport phenomena at higher temperatures in solar distillation systems - The Chilton-Colburn analogy

In the present investigation efforts have been devoted towards developing an analysis suitable for heat and mass transfer processes modeling in solar distillation systems, when they are operating at higher temperatures. For this purpose the use of Lewis relation is not new although its validity is based on the assumptions of identical boundary layer concentration and temperature distributions, as well as low mass flux conditions, which are not usually met in solar distillation systems operating at higher temperatures associated with considerable mass transfer rates. The present analysis, taking into consideration these conditions and the temperature dependence of all pertinent thermophysical properties of the saturated binary mixture of water vapor and dry air, leads to the development of an improved predictive accuracy model. This model, having undergone successful first order validation against earlier reported measurements from the literature, appears to offer more accurate predictions of the transport processes and mass flow rate yield of solar stills when operated at elevated temperatures.     

Analyses of non-Fourier heat conduction in 1-D cylindrical and spherical geometry – An application of the lattice Boltzmann method

This article deals with the implementation of the lattice Boltzmann method (LBM) for the analyses of non-Fourier heat conduction in 1-D cylindrical and spherical geometries. Evolution of the wave like temperature distributions in the medium is obtained, and analysed for the effects of different sets of thermal perturbations at the inner and the outer boundaries of the geometry. The LBM results are validated against those available in the literature, and those obtained by solving the same problems using the finite volume method (FVM). Results of the LBM are in excellent agreement with those reported in the literature, and with the results from the FVM. Computationally, the LBM has an advantage over the FVM.