Performance Evaluation of Two Heat Transfer Models of a Walking Beam Type Reheat Furnace

Two different heat transfer models for predicting the transient heat transfer characteristics of the slabs in a walking beam type reheat furnace are compared in this work. The prediction of heat flux on the slab surface and the temperature distribution inside the slab have been determined by considering thermal radiation in the furnace chamber and transient heat conduction in the slab. Both models have been compared for their accuracy and computational time. The furnace is modeled as an enclosure with a radiatively participating medium. In the first model, the three-dimensional (3D) transient heat conduction equation with a radiative heat flux boundary condition is solved using an in-house code. The radiative heat flux incident on the slab surface required in the boundary condition of the conduction code is calculated using the commercial software FLUENT. The second model uses entirely FLUENT along with a user-defined function, which has been developed to account for the movement of slabs. The results obtained from both models have a maximum temperature difference of 2.25%, whereas the computational time for the first model is 3 h and that for the second model is approximately 100 h.     

Inverse radiation–conduction design problem in a participating concentric cylindrical medium

Inverse conduction–radiation problem for design analysis in a two-dimensional concentric cylindrical absorbing, emitting and isotropically scattering medium has been solved, when the desired boundary conditions are available on the design surface. The finite-volume method was adopted to deal with energy conservation equation including conduction and radiation. The radiative transfer equation was also taken into consideration in direct problem, whereas the Levenberg–Marquardt method was used to solve a set of equations in inverse problem, which are expressed by errors between estimated and desired total heat fluxes on the design surface. The automatic differentiation as well as the Broyden combined update was utilized to reduce computational time in calculating the sensitivity matrix. The results have shown that the desired total heat flux distribution on design surface could be successfully estimated with less computational time using the present inverse procedure developed here.     

Thermal radiation effects in phase-change energy-storage systems

A numerical model was developed to determine the transient temperature distribution, solid/liquid interface location, and energy-storage capacity of a semi-transparent phase-change medium. The medium is bounded between two concentric cylinders and internal energy transfer occurs simultaneously by conduction and thermal radiation. The radiation transport equation was coupled with the energy equation; both enthalpy and temperature were employed as dependent variables. The spherical harmonic approximation (P-N approximation) was used to obtain solutions for the radiative heat flux. The coupled conservation of energy and moment differential equations were solved by using iterative numerical finite-difference schemes with appropriate thermal and radiant boundary and interface conditions. The numerical model was used to study the effects of radiation on solidification (melting), transient temperature distribution and energy-storage capacity of an absorbing, emitting, and isotropically scattering, semi-transparent, gray medium contained in a cylindrical annulus. The results increase our understanding of internal energy transfer and show the effects of optical properties, conduction/radiation parameter, and geometric dimensions and should lead to better designs and optimization of phase-change energy-storage systems.     

TRANSIENT CONDUCTION AND RADIATION HEAT TRANSFER WITH VARIABLE THERMAL CONDUCTIVITY

The effect of variable thermal conductivity on transient conduction and radiation heat transfer in a planar medium is investigated. Thermal conductivity of the medium is assumed to vary linearly with temperature, while the other thermophysical properties and the optical properties are assumed constant. The radiative transfer equation is solved using the discrete transfer method, (DTM) and the nonlinear energy equation is solved using an implicit scheme. Transient as well as steady state results are found for an absorbing, emitting, and anisotropically scattering gray medium. Thermal conductivity has been found to have significant effects on both transient as well as steady state temperature and heat flux distributions. Some steady state results are compared with the results reported in the literature.     

Effects of particulate concentrations on temperature and heat flux distributions in a pulverized-coal fired furnace

A simple methodology for numerical modelling of total heat transfer in an axisymmetric, cylindrical pulverized coal-fired furnace is introduced. The solution for the flow field and energy equations are coupled with the solution of the radiative transfer equation. The SIMPLER code is employed to solve all the equations numerically. The radiation part is modelled using the first-order spherical harmonics approximation. The radiative properties of the gases and particulates such as soot, coal/char and fly-ash are obtained locally to account for the temperature and concentration distribution effects. Using a k - ε model, the turbulence closure is obtained. Parametric studies are performed and are presented graphically to demonstrate the effects of particulate concentrations on the distributions of medium radiative and physical properties, temperature, and the wall total and radiative heat fluxes.     

Radiative heat transfer in semitransparent solidifying slab considering space–time dependent refractive index

Radiative heat transfer in semitransparent phase-change media is of great interest in many engineering fields. Its essence is the transient coupled heat transfer of radiation and conduction along with liquid–solid phase change. The difficulty is to solve radiative heat transfer with the consideration of time–space dependent radiative properties. Especially when the refractive index is considered to vary with space and time in phase change, the problem becomes more complicated. This paper investigates the problem of the variable radiative properties with space and time during phase change in semitransparent media. The phase-change medium is assumed to have solid, mushy and liquid zones, and the solid/mushy and liquid/mushy interfaces are considered to be semitransparent and diffuse reflecting. In different zones, there are different physical property parameters. Phase interfaces are always moving in phase change, while the interfaces of control volumes are fixed. Therefore, the interfaces of control volumes and phase interfaces are not always coincided, which will bring errors into the simulation of radiative transfer in phase-change media. However, the errors can be reduced by dividing the medium into enough sub-layers. As long as the number of sub-layers is big enough, the errors can be limited in a very small range. Then using the multilayer radiative transfer model, we can solve the radiative transfer problem in the semitransparent phase-change medium. Considering time–space dependent refractive index, this paper analyzes coupled radiative and conductive heat transfer in semitransparent solidifying media. The results show that the effects of variable refractive index with time and space on transient coupled heat transfer are significant and could not be neglected inside the semitransparent phase-change medium under some conditions.     

Numerical prediction of effective thermal conductivity of ceramic fiber board using lattice Boltzmann method

Abstract

Application of the lattice Boltzmann method has been extended for the analysis of combined transient conduction and radiation heat transfer through highly porous fibrous insulation media. Firstly, LBM has been employed for the analysis of combined mode of transient conduction radiation heat transfer in a 2?D rectangular enclosure containing an absorbing, emitting and scattering medium and results are compared with already published ones. The results have been found in good accord for different values of radiation-conduction parameter, scattering albedo and south (hot) wall emissivity. Furthermore, the proposed LBM for the calculation of effective thermal conductivity of ceramic fiber board has been employed. A random-generation growth method for generating micro morphology of natural ceramic fiber board has been selected. The conductive, radiative and effective thermal conductivity has been numerically estimated using the present LBM. It is found that the predicted effective thermal conductivity for different values of fibrous bulk density is in good agreement with the experimental data.     

Thermal radiation in layered participating cylindrical media using an integral equation method

Radiative transfer in a layered cylindrical medium is analyzed using a newly developed S-type integral equation of transfer in terms of incident radiation and net radiative heat flux. The physical systems in hollow and solid cylindrical geometry are modeled as nonhomogeneous participating media with stepwise variable properties. Thus, the necessity to establish the equation of transfer for each layer and combine these layers through the intensity continuity on interface is avoided. Numerical predictions from a collocation method are presented to illustrate the effects of radiation properties on the radiative transfer for the systems considered. Comparison of the results with other available data in literature shows that highly accurate results are obtainable by current method with simplicity.     

Comparison of experimental data and analytical solution for cooling of cylindrical produces

Experimental and analytical investigations have been made for transient heat transfer from individual cylindrical produce in a package of 5 kg exposed to cold air stream. Surface boundary condition was solved first by pure convective heat transfer coefficient and then with the sum of convective and radiative heat transfer coefficients. Theoretical results for the second case were found to have better overall agreements with the measured values.     

Radiative heat transfer in preforms for microstructured optical fibres

Air inclusions in any preform for microstructured optical fibres can greatly reduce conductive heat transfer. Modelling the heat transfer therefore requires that radiation be properly included. In this paper we use the Rosseland approximation to consider radiative heat transfer within the matrix material and present a method of including radiative heat transfer across the air inclusions for the first time. We apply the thermal model to the transient heating process of a silica preform with a hole structure that restricts conduction. The resultant heat transfer model yields realistic heating times.     

ANALYSIS OF TWO-PHASE RADIATION IN THERMALLY DEVELOPING POISEUILLE FLOW

Combined conductive and radiative heat transfer in a thermally developing two-phase Poiseuille flow in a cylindrical duct is studied here. A two-phase radiative transfer equation (RTE) considering radiation by both gas and particles is taken into account. A complexform of nonlinear integrodifferential RTE is solved by the discrete ordinates method (DOM, or so called SN method) in axisymmetric geometry. After such validation, namely, the solution in a two-dimensional channel flow between two flat plates is compared with that solved by the zone method, the program is then applied to fully developed gas-particle two-phase flow in a cylindrical duct. A parametric study is performed for gas and particle absorption coefficients, particle number density, particle emissivity, and wall emissivity. The results show a significant effect of two-phase radiation on the thermal characteristics. However, in all cases, it was found that conduction is predominant near the wall.     

On the transient thermal behaviour of structural walls — the combined effect of time varying solar radiation and ambient temperature

The aim of the present work is to investigate the transient conduction heat transfer in structural walls. The developed finite difference numerical simulation code, which is suitable to run in conventional microcomputers, has the flexibility to incorporate a wide range of boundary and initial conditions and time-dependent forcing functions for the investigation of the transient heat transfer in walls of any design. The analysis was employed for the prediction of the dynamic thermal behaviour of two wall designs under the effect of a step temperature change and a combined time varying ambient temperature and solar radiation corresponding to typical local weather conditions. The results allow the prediction of the transient duration, the transient temperature fields as well as the quasi-steady state heat fluxes. They also allow the investigation of the dynamic effects of realistic time varying meteorological forcing functions and the strong influence of the wall surface absorptivity, something which confirms its importance as a handy instruction and research tool in the renewable and rational use of energy fields.     

Numerical study on the importance of radiative heat transfer in building energy simulation

ABSTRACT

A neural network-based model for interior longwave radiative heat transfer has been developed and implemented into a new computer code, BERHT (Building Energy with Radiative Heat Transfer). The model accounts for the non-gray effect of absorbing species in a building environment and the geometric effect of a three-dimensional building structure. Numerical studies have been carried out on a rectangular single-story building. For nominal concentration of CO₂, H₂O, and small particulates, results show that the effect of radiative heat transfer is important. The surface emissivity of enclosure walls and optical properties of the absorbing/emitting medium are demonstrated to have significant effects on the distribution of heat transfer between convection and radiation, as well as the transient behavior of the indoor air temperature. Supplemental studies provide an insight that the one-zone, well-mixed model used in building energy simulation generates a “fictitious” non-local heat transfer behavior, leading to uncertainties in the understanding of the radiative heat transfer effect.     

Two dimensional numerical simulation of transient natural convection in freezer

A two dimensional model of the transient natural convection in a freezer is studied numerically by finite volume approach. The temperatures of the freezer outside surfaces and the evaporator vary in specified manners, which were taken from an experimental work. The fluid in the freezer is of the Bousinnesq type and the flow is assumed laminar. The transient heat conduction in the insulating layers and the temperature and velocity fields of the fluid are solved conjugately. The radiation heat transfer between the freezer inner surfaces is taken into account by using the additional source term method. The distributions of the local Nusselt number along the upper and lower surfaces of the evaporator and their average values in the period of periodically unsteady operation are calculated. Comparisons are made between the results with and without consideration of inner surface radiative heat transfer. It is found that the radiative heat transfer between the inner surfaces has a profound effect on the evaporator heat transfer characteristics.     

THE METHOD OF LINES SOLUTION OF THE DISCRETE ORDINATES METHOD FOR RADIATIVE HEAT TRANSFER IN ENCLOSURES

A radiation code based on the method of lines (MOL) solution of the discrete ordinates method (DOM) for transient three-dimensional radiative heat transfer in rectangular enclosures for use in conjunction with a computational fluid dynamics (CFD) code based on the same approach was developed. Assessment of the predictive accuracy of the code by benchmarking its steady-state solutions against exact solutions on one- and three-dimensional test problems shows that the MOL solution of the DOM provides accurate and computationally efficient solutions for radiative heat fluxes and source terms and can be used with confidence in conjunction with CFD codes for transient problems.     

An Iterative Technique for Coupled Conduction–Radiation Heat Transfer in Semitransparent Media

An iterative technique is developed to solve coupled conduction–radiation heat transfer in semitransparent media. Apart from a high convergence rate, the present algorithm preserves the conservation nature of the governing equation far better than other common methods and it is readily combined with other methods in solving radiative transfer. Using the technique described in this study, parametric studies are carried out for coupled heat transfer in a semitransparent slab and the results illustrate the “peak” effects of wall emissivity and scattering albedo on conductive and radiative heat fluxes, which are rarely mentioned in the existing research.     

Indirect heating strategy for laser induced hyperthermia: An advanced thermal model

A novel heating strategy based on laser irradiation of surrounding tissues as an alternative to direct irradiation of superficial tumors is proposed and analyzed for the first time. The computational analysis is based on two-dimensional axisymmetric models for both radiative transfer and transient heat transfer in the human body. A diffuse component of the radiation field is calculated using P₁ approximation. Coupled transient energy equations and kinetic equations for composite human tissue take into account the metabolic heat generation and heat conduction, blood perfusion through capillaries, the volumetric heat transfer between arterial blood and tissue, the thermal conversions in blood and tumor tissue, the periodic laser heating, and also heat exchange between a human body and ambient medium. An example problem for a superficial human cancer has been solved numerically to illustrate the relative role of the problem parameters on the transient temperature field during hyperthermia treatment. In particular, the effect of embedded gold nanoshells which strongly absorb the laser radiation is analyzed. It is shown that required parameters of tumor hyperthermia can be also reached without gold nanoshells.     

Combined conduction and radiation heat transfer with variable thermal conductivity and variable refractive index

This article deals with the solution of conduction–radiation heat transfer problem involving variable thermal conductivity and variable refractive index. The discrete transfer method has been used for the determination of radiative information for the energy equation that has been solved using the lattice Boltzmann method. Radiatively, medium is absorbing, emitting and scattering. To validate the formulation, transient conduction and radiation heat transfer in a planar participating medium has been considered. For constant thermal conductivity and constant and variable refractive indices, results have been compared with those available in the literature. Effects of conduction–radiation parameter and scattering albedo on temperature have been studied for variable thermal conductivity and constant and/or variable refractive index. Lattice Boltzmann method and the discrete transfer method have been found to successfully deal with the complexities introduced due to variable thermal conductivity and variable refractive index.     

Numerical Modeling of Combined Radiation and Conduction Heat Transfer in Mineral Wool Insulations

This article addresses numerical modeling of coupled heat conduction and radiation in mineral wools under steady-state condition for prediction of its effective thermal conductivity. The radiative heat transfer is modeled using the Monte Carlo Ray-Trace Method. The radiation model is based on a random distribution of fibers in the media. The radiation distribution factor is employed in order to compute the fraction of the total radiation emitted from one fiber that is absorbed by another, due to both direct radiation and to all possible reflections within the enclosure. The radiation model is coupled with the nonlinear heat conduction equation. The results obtained by the proposed model compare well with experimental measurements of the heat flow meter apparatus. The method is easy to code, and the number of calculations during each iteration is considerably reduced.     

Model of radiative transfer in fibrous media—matrix method

A matrix model of radiative transfer is presented. Beginning with the radiative properties of a medium, two characteristic matrices representing the transmissive and reflective contributions to energy transfer are written and the intensity distribution is then calculated numerically. Applications to pure radiative transfer and combined transfer with conduction are presented. A case of a material composed of silica fibres is discussed, showing that the model is in good agreement with experimental results. Since no simplifying hypotheses concerning the properties of the medium are incorporated into the model, it can be used to study any fibrous medium.