Radiative-conductive Heat Transfer Research Articles

Transient Combined Radiative–Conductive Heat Transfer in Two-Dimensional Complex Geometries with Variable Gas Properties

Radiation is a major component of heat transfer in the modeling of furnaces. In the present work, transient coupled radiative and conductive heat transfer problems are analyzed in two-dimensional irregular geometries with a simple Cartesian practical method named the blocked-off. By this technique, Cartesian coordinate-based ray-tracing algorithm can be applied to the geometries with inclined or curved boundaries. The S–N discrete ordinates method used to solve the radiative transfer equation and finite difference method by applying the Taylor series for solving the energy equation to obtain the transient temperature distributions inside the participating medium. The walls of the enclosures are opaque, diffuse, and gray with specified temperatures. The medium was considered to be absorbing-emitting and linear anisotropic scattering with variable thermal conductivity, variable density, and variable specific heat, as a function of temperature. In the case of constant thermophysical gas properties, results have been compared with those reported in the literature, and good agreement was found.

Solution of the Stefan problem in a conventional modified formulation for semitransparent media with consideration of isotropic radiation scattering

Numerical simulation of radiation-conductive heat transfer with a phase transition of the first kind in a semitransparent, isotropically scattering medium is carried out. A hypothesis of zero total external energy flow in the course of the phase transition is used in the formulation of the problem. The fields of temperature and the resulting radiation fluxes over a wide range of single scattering albedo and two values of the reflection coefficient of boundaries are obtained. It is shown that there is an increase in the reflection coefficient of boundaries, the effect of the scattering albedo decreases, and the melting process in general is delayed in time.

Theoretical Rationale of Heating Block for Testing Bench of Aerospace Crafts Thermal Protection Elements

The theoretical rationale for the structural layout of a testing bench with zirconium dioxide heating elements on the basis of modelling radiative-conductive heat transfer are presented. The numerical simulation of radiative-conductive heat transfer for the two-dimensional scaled model of the testing segment with the finite-element analysis software package Ansys 15.0 are performed. The simulation results showed that for the selected layout of the heaters the temperature non-uniformity along the length of the sample over time will not exceed 3 % even at a temperature of 2000 K.

Semidiscrete approximations for the stationary radiative–conductive heat transfer problem in a two-dimensional system of plates

AbstractSpecial semidiscrete approximations, namely, basic, first, and second semidiscrete problems are proposed for a boundary value problem describing a stationary radiative–conductive heat transfer in a two-dimensional system of heat-conductive plates of width

Modelling of a Coupled Radiation-conduction Heat Transfer through a Heat Shield in Vacuum Thermal Isolation Applications

ITER (International Thermonuclear Experimental Reactor) is currently in design phase of the nuclear fusion research project, which is the world's largest experimental tokamak reactor. Process of plasma generation in the Vacuum Vessel requires an ultra-high quality of vacuum. To meet those requirements the Vacuum Vessel and adjacent diagnostic systems are exposed to elevated temperature after its assembly to outgas all volatile surface contaminants. The baking temperature peaks at 240°C for up to 24hours. On the other side most of diagnostic instruments and detectors adjacent to the Vacuum Vessel, which are exposed to the same conditions, require much lower temperature during measurement and slightly higher temperature in a stand-by mode. The strictest conditions are defined for liquid scintillators, which require the working temperature around 20°C and the temperature of destruction several degrees higher. In order to keep diagnostic instruments within required temperature range, a heat shield with a heat removal is necessary. The temperature range is often ± 2°C or even more narrow in time and space allotted for detectors. Due to space limitations only a thin multilayer solution, including vacuum layers, can be considered. Preliminary calculations indicate that to meet the above defined requirements, only a water jacket as the heat shield can be efficient enough to keep detectors at the required temperature level and within defined range. An additional multilayer vacuum insulation can significantly decrease the cooling demand for the water jacket cooling system. The aim of proposed paper is to find an optimal structure of the insulation thermal shield, based on the water jacket solution by using the CFD simulation in ANSYS Fluent software. Moreover an extended Parametric Analysis is carried out and discussed. The Surface-to-Surface (S2S) model is applied to simulate heat transfer by radiation. In addition the paper contains a discussion about multilayer solutions, characterized by a high thermal resistance, and dedicated particularly for vacuum transfer lines with high temperature difference.

Influence of Absorption of Thermal Radiation in the Surface Water Film on the Characteristics and Ignition Conditions

The results of the mathematical modeling of homogeneous particle ignition process of coal-water fuel covered with water film have been presented in article. The set co-occurring physical (inert heating, evaporation of water film) and thermochemical (thermal degradation, inflammation) process have been considered. Heat inside the film has been considered as the model of radiation-conductive heat transfer. Delay times have been determined according to the results of numerical modeling of the ignition. It has been shown that the water film can have a significant impact on performance and the ignition conditions. It has been found that heating main fuel layer occurs in the process of evaporation of water film. For this reason, the next (after the evaporation of the water film) thermal preparation (coal heating, thermal decomposition of the organic part of the fuel) and inflammation occur faster.

Galerkin method for solving combined radiative and conductive heat transfer

This article deals with a numerical solution for combined radiation and conduction heat transfer in a gray absorbing and emitting medium applied to a two-dimensional domain using triangular meshes. The radiative transfer equation was solved using the high order Discontinuous Galerkin method with an upwind numerical flux. The energy equation was discretized using a high order finite element method. Stability and error analysis were performed for the Discontinuous Galerkin method to solve radiative transfer equation. A new algorithm to solve the nonlinear radiative–conductive heat transfer systems was introduced and different types of boundary conditions were considered in numerical simulations. The proposed technique's high performance levels in terms of accuracy and stability are discussed in this paper with numerical examples given.

Two Stationary Radiative-Conductive Heat Transfer Problems for a System of Two-Dimensional Plates

UDC 517.95 We consider two nonlinear stationary radiative-conductive heat transfer problems in a system of two-dimensional heat-conducting plates of width e separated by vacuum in- terlayers. We establish comparison theorems and obtain estimates for the weak solu- tion, in particular, the two-sided estimate umin u umax and estimates of the form � DxuL 2 (G e ) = O( √ e) andDxuL 2 (G e ) = O ( √ e/λ). Bibliography :1 0titles. In applications, it is important to study the heat transfer process in media containing vacuum interlayers through which the heat transfer is realized by radiation. A numerical solution of such problems with a large number of heat transferring elements is, in fact, impossible, especially for two- and three-dimensional structures. Therefore, it is important to construct efficient approxi- mation methods which, in particular, could be based on constructing special homogenizations of the problem under consideration. Such approximations were constructed and justified in (1)-(6). We note that for studying the properties of approximation problems, it is necessary to perform a preliminary analysis of properties of the original problem. Such an analysis involves the proof of special estimates for the solutions and their derivatives in terms of the data. In this paper, we consider two boundary value problems describing the stationary radiative- conductive heat transfer in a system of n two-dimensional heat-conductive grey plates of width e = X/n and height Y separated by infinitely thin vacuum interlayers. We prove comparison theorems and estimate the solution. In particular, we obtain the two-sided estimate umin u umax and estimates of the formDxuL2(Ge) = O( √ e )a ndDxuL2(Ge) = O( √ e/λ). We emphasize that such estimates play an important role in the justification of semidiscrete and asymptotic approximations (cf., for example, (4, 6)).

Existence, uniqueness and construction of the solution of the energy transfer problem in a rigid and non-convex blackbody with temperature-dependent thermal conductivity

In this paper, we study the steady-state (coupled) conduction–radiation heat transfer phenomenon in a non-convex opaque blackbody with temperature-dependent thermal conductivity. The mathematical description consists of a nonlinear partial differential equation subjected to a nonlinear boundary condition involving an integral operator that is inherently associated with the non-convexity of the body. The unknown is the absolute temperature distribution. The problem is rewritten with the aid of a Kirchhoff transformation, giving rise to linear partial differential equation and a new unknown. An iterative procedure is proposed for constructing the solution of the problem by means of a sequence of problems, each of them with an equivalent minimum principle. Proofs of convergence as well as existence and uniqueness of the solution are presented. An error estimate, for each element of the sequence, is presented too.

Simultaneous Estimation of Properties in a Combined Mode Conduction–Radiation Heat Transfer in a Porous Medium

Simultaneous estimation of thermophysical and optical properties such as the thermal conductivity, the scattering albedo, and the emissivity of a 1‐D planar porous matrix involving combined mode conduction and radiation heat transfer with heat generation is reported. Coupled energy equations for the gas and solid phase account for the nonlocal thermal equilibrium between the two phases. Performances of the genetic algorithm (GA) and the global search algorithm (GSA) in simultaneous estimation of three properties are analyzed. Both the GA and the GSA utilize a priori knowledge of the axial gas temperature distribution, and the magnitudes of the convective and the radiative heat fluxes at the outer surface of the porous matrix. With volumetric radiative information needed in the solid‐phase energy equation computed using the discrete transfer method, the two energy equations are simultaneously solved using the finite volume method. GSA provides better estimation, and computationally, it is much faster than the GA.

Heat transfer in cellulose-based aerogels: Analytical modelling and measurements

A simple analytical approach for estimating the total heat transfer inside new cellulose-based aerogels has been investigated. The model accounts for the characteristic solid matrix at the nanometric scale by using a cellular representation of the nanofoam porous structure.The radiation-conduction heat transfer is taken into account. Previous analytical correlation for the fluid phase is used to model the conduction heat transfer in gas. New analytical formulations based on mean free path theory combined with phonon tracking approach are proposed to model the conduction heat transfer in the solid phase at the nanometric scale. The contribution of radiation heat transfer is obtained from Rayleigh scattering approach combined to the Rosseland approximation.These analytical relations validated experimentally are expected to be useful for researchers aiming at developing new insulating organic aerogels since they permit to determine conduction-radiation equivalent conductivity as a function of cell dimensions, phonon and optical properties of cellulose.

Simulation of the one-phase Stefan problem in a layer of a semitransparent medium

Radiative-conductive heat transfer in a semitransparent layer of a material with a phase transition is numerically simulated within the framework of solving the one-phase Stefan problem. Results of the solution describe the process of melting under equilibrium and nonequilibrium conditions of thermal energy supply. The possibility of simulation of thermal processes as applied to the development of both effective thermal protection and ideal technology of melting (evaporation) in layers of semitransparent materials is demonstrated.

Radiative-conductive heat transfer in a spherical cavity

A mathematical model describing joint radiative-conductive heat transfer in a spherical cavity, the shape of which can be considered as a statistical average in relation to the forms of closed pores in solids, is developed. The model determines an equivalent thermal conductivity of an arbitrary diathermic medium in a cavity that allows a material with a porous structure to be considered as a continuous inhomogeneous solid. The effect of the temperature field gradient in the vicinity of the cavity and the thermal conductivity of the diathermic medium on the equivalent coefficient of thermal conductivity is determined. In the case of a thermally nonconducting medium, the calculated dependence of this coefficient is compared to equations, similar in structure, derived on the basis of different approaches to account for heat transfer by radiation in pores.

Effects of thermal radiation and chemical reactions on peristaltic flow of a Newtonian nanofluid under inclined magnetic field in a generalized vertical channel using homotopy perturbation method

AbstractIn this paper, we study the influences of inclined magnetic field, heat source, thermal radiation, and chemical reactions on peristaltic flow of a Newtonian nanofluid in a vertical generalized (tapered asymmetric) channel. The flow is engendered because of an asymmetric sinusoidal wave on the non‐uniform channel walls. The Rosseland approximation is viewed in the modeling of the conduction radiation heat transfer, and temperatures of the walls are presumed constants. The governing equations are uttered in a non‐dimensional form, and the series solutions of coupled system of equations are constructed for temperature and nanoparticle concentration using a homotopy perturbation method. Analytical solutions have been developed for stream function and axial velocity. Numerical integrations have been applied to receive the graphical results for an average rise in pressure. The variations of various interesting dimensionless parameters are sketched and discussed. It is observed that the temperature profile increases with an increase of the non‐uniform parameter, while it decreases when the thermal radiation parameter is increased. © 2015 Curtin University of Technology and John Wiley & Sons, Ltd.

Collocation Spectral Method for the Transient Conduction–Radiation Heat Transfer With Variable Thermal Conductivity in Two-Dimensional Rectangular Enclosure

The collocation spectral method (CSM) is further developed to solve the transient conduction–radiation heat transfer in a two-dimensional (2D) rectangular enclosure with variable thermal conductivity. The energy equation and the radiative transfer equation (RTE) are all discretized by Chebyshev–Gauss–Lobatto collocation points in space after the discrete ordinates method (DOM) discretization of RTE in angular domain. The treatment of variable thermal conductivity is executed using the array multiplication. The present method can deal with different boundary conditions with high accuracy, the Dirichlet one and mixed one, for example. Based on our new method, the effects of several parameters on heat transfer processes are analyzed.

Optimal Design of Magnetohydrodynamic Mixed Convection Flow in a Vertical Channel with Slip Boundary Conditions and Thermal Radiation Effects by Using an Entropy Generation Minimization Method

Investigation of the effect of thermal radiation on a fully developed magnetohydrodynamic (MHD) convective flow of a Newtonian, incompressible and electrically conducting fluid in a vertical microchannel bounded by two infinite vertical parallel plates with constant temperature walls through a lateral magnetic field of uniform strength is presented. The Rosseland model for the conduction radiation heat transfer in an absorbing medium and two plates with slip-flow and no-slip conditions are assumed. In addition, the induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The non-dimensional governing equations are solved numerically using Runge–Kutta–Fehlberg method with a shooting technique. The channel is optimized based on the Second Law of Thermodynamics by changing various parameters such as the thermal radiation parameter, the temperature parameter, Hartmann number, Grashof to Reynolds ratio, velocity slip length, and temperature jump.

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.

Accelerative iteration for coupled conductive–radiative heat transfer computation in semitransparent media

Due to the intensive coupling effect and non-linear characteristic, coupled conductive–radiative heat transfer problem in semitransparent media always consumes an enormous amount of computing time. In present work, an accelerative iteration model is developed to speed up the convergence process of this kind of coupled calculation. It promotes the iterative efficiency by revising the temperature and incident radiation of media during the iteration of energy equation and radiative transfer equation. It can remarkably reduce the computing time of coupled conductive–radiative heat transfer calculation in semitransparent media, even in the cases with complicate boundary conditions. The accuracy of present model is verified by comparing with literature and traditional source iteration method. The influences of conduction–radiation parameter, optical thickness, scattering albedo, emissivity of walls and boundary conditions are investigated as well. The results indicate that the accuracy of present model is reliable and its accelerative effect is more significant for the optically thick and scattering-dominated media with complicate boundary conditions.

Solvability of P1 approximation of a conductive–radiative heat transfer problem

Conductive-radiative heat transfer in a scattering and absorbing medium bounded by two reflecting and radiating plane surfaces is examined. P1 approximation (diffusion model) is used for the simplification of the original problem. The existence and uniqueness of solutions of the diffusion model are proved. The convergence of an iterative procedure for finding solutions is proved. Numerical examples are discussed.

The Brightness Temperature of Aluminum Oxide When it is Heated by Concentrated Laser Radiation

The results of a calculation of the temperature fields in a plane layer of aluminum oxide when it is rapidly heated and melted by the radiation of a CO2-laser with different flux densities are presented. The calculations are carried out using a new mathematical model of nonstationary radiation-conduction heat transfer. It is shown that the brightness temperature, measured at a wavelength of 0.65 μm, differs from the surface temperature.