Soot and radiation modeling in laminar ethylene flames with tabulated detailed chemistry

A strategy has been developed in order to compute unsteady convective and radiative heat transfers in an industrial combustion device. This strategy involves a tabulation method to describe gas-phase chemistry, coupled with a semi-empirical soot model. A Monte Carlo method is used to evaluate gas and soot radiative transfer. This paper presents the first validation step of this strategy, in which four laminar premixed ethylene flames have been simulated. The tabulation method well predicts gas-phase species concentrations, including acetylene, considered as the main soot precursor. The soot model gives results in the experimental uncertainty range of measurements, whereas radiative powers highlight the dominating role of soot particles.     

Buoyancy-dominated laminar convection and radiation transfer in rod arrays

Laminar combined free and forced convection together with radiation transfer in flow of steam at 68 bar through rods in triangular and square arrays have been investigated numerically. The pitch to diameter ratio has been varied from 1.2 to 2.0. Heat transfer results have been obtained for both up and down forced flow influenced by bouyancy with and without the effects of variable thermophysical fluid properties. The Rosseland diffusion approximation has been used for radiative transfer. First- and second-orde r density changes have been investigated.     

Coupled conductive radiative transfer in CO2 with narrow band statistical model and Monte-Carlo simulation

This paper describes an approach in order to determine the radiative source term and the temperature fields in a coupled conductive and radiative transfer. We consider an emitting and absorbing gas (carbon dioxide) enclosed between two horizontal and parallel reflecting plates. The medium is in local thermodynamic equilibrium (LTE). Only radiative and conductive exchanges are considered. An implicit finite difference technique is used to solve the energy conservation equation, and the narrow band statistical model (NBSM) with the Monte Carlo method (MCM) are used for simulation of radiative transfer equation in a coupled manner. This study of coupled conductive-radiative shows many phenomenons: The interaction radiation conduction in an emitting and absorbing gas is sensitive to the molar fraction of gas and the emissivities of walls. Received on 6 July 1999     

A simple heat transfer model for furnaces based on the zoning method

A simplified method for calculation of the radiative heat transfer in furnaces with rectangular crosssection based on the zoning method has been developed. The furnace is divided longitudinally into chambers. The net radiative intensity between any two chambers is considered to be independent of the angle. The chambers are also coupled by the gas mass flow.     

A nongray analysis of radiating–convecting rectangular plate-fin arrays

A complete analysis of heat transfer in rectangular fin arrays has been conducted taking into consideration convection and radiation at all surfaces, as well as radiative exchange between the fins and all neighboring surfaces. The analysis assumes diffuse nongray surfaces and uses the spectral optical properties of stainless steel AISI 430. Three different gray models were proposed in order to assess the effect of the gray assumption on the heat-transfer characteristics. Results are presented for the temperature and radiative-flux distributions along the fin, the radiative flux along the base, the contribution of the radiative component to the overall heat transfer, and the effectiveness of the fin array. Significant deviations in some of these results were found between the nongray model and the gray models. In general, convection was found to be the more effective mode of heat transfer in fin arrays and the effectiveness of the array decreases as the contribution of the radiative component increases.     

Effect of surroundings on the transient energy transfer in a layer of radiating gas

Summary An analysis is presented for the transient cooling or heating of a stagnant layer of hot radiating gas surrounded by a cold gas capable of absorbing and emitting radiation. Scattering of radiation is neglected, and energy transfer by conduction and convection is considered to be negligible compared with radiation. The gas is assumed to be perfect and in local thermodynamic equilibrium. The heating of a cold gas by a diffuse and a collimated radiation flux incident on the boundary of the gas from some external source is considered, and the dependence of physical and radiative properties on temperature is taken into account. The problem is formulated exactly using radiative transfer theory. A scheme is developed for the numerical solution of the nonlinear integrodifferential equations of energy conservation. Starting with arbitrary, but given, initial temperature profiles, temperature distributions and local radiative fluxes are predicted as a function of time for a wide range of physically interesting conditions.     

Estimation of radiative properties and temperature distributions in coal-fired boiler furnaces by a portable image processing system

This paper presented an experimental investigation on the estimation of radiative properties and temperature distributions in a 670 t/h coal-fired boiler furnace by a portable imaging processing system. The portable system has been calibrated by a blackbody furnace. Flame temperatures and emissivities were measured by the portable system and equivalent blackbody temperatures were deduced. Comparing the equivalent blackbody temperatures measured by the portable system and the infrared pyrometer, the relative difference is less than 4%. The reconstructed pseudo-instantaneous 2-D temperature distributions in two cross-sections can disclose the combustion status inside the furnace. The measured radiative properties of particles in the furnace proved there is significant scattering in coal-fired boiler furnaces and it can provide useful information for the calculation of radiative heat transfer and numerical simulation of combustion in coal-fired boiler furnaces. The preliminary experimental results show this technology will be helpful for the combustion diagnosis in coal-fired boiler furnaces.     

Numerical modelling of combined conductive and radiative heat transfer within square enclosure using discrete ordinate method

The current study addresses the mathematical modeling aspects of coupled conductive and radiative heat transfer in presence of absorbing, emitting and isotropic scattering gray medium within two-dimensional enclosure. The walls of the enclosure are considered to be opaque, diffuse and gray. The enclosure comprises isothermal vertical walls and insulated horizontal walls. The discrete ordinate method has been employed for modeling the radiative transport equation and the finite volume method has been adopted as the numerical technique. The effect of various parameters, i.e., radiation-conduction parameter, surface emissivity single scattering albedo and optical thickness has been illustrated.     

The modelling of radiation heat transfer in forehearths units in glass melting

The interaction between conduction, convection and radiation heat transfer in molten glass has been studied with specific reference to the forehearth units of a glass tank furnace. In shallow molten glass flows as typically encountered in forehearth units, the radiation-conductivity approach for modelling the radiative transfer process is found inappropriate. This is especially so for colourless glasses which are not optically thick below 2.8 microns. In the present work radiative heat transfer process in molten glass has been treated more rigourously by incorporating both optically thick and thin limits. The radiative interaction at the boundaries is treated more realistically. In the case of colourless glasses, the results obtained by the present method show the necessacity to account for the direct radiative interaction between the interior layers of the glass and refractory walls at the top and the bottom. The forehearth exit temperature profiles obtained by using the present method are quite different with those obtained using the radiation conductivity approach.     

Transformational-zone method of calculation of complex heat exchange during flow of optically active medium inside tube of diffuse grey surface

The paper presents analytical and experimental investigations of influence of radiative heat transfer on complex heat exchange during flow of optically active gas inside a pipe of diffusegrey properties. It was assumed that the pipe is heated from the outside by a constant heat flux and gas flowing inside is both absorbing and emitting and of small optical density. The influence of length and radiative properties of the pipe surface and of the gas temperature distribution on the wall and in the gas were analysed. The influence of radiative energy transfer on overall heat transfer coefficient was estimated. Mathematical model of radiative convective heat exchange in a system of one-dimensional temperature field, based on zone division method of Hottel and surface transformation, was verified numerically and experimentally. The results of numerical calculations were compared with experimental results obtained during carbone dioxide (CO₂) flow inside electrically heated ceramic tube. The set of nonlinear differential equations was solved by Runge-Kutta method with Hamming modification and with the use of separable-kernel method.     

Opposing mixed convection and its interaction with radiation inside eccentric horizontal cylindrical annulus

In the present investigation, the coupled phenomenon of opposing mixed convection and radiation within differentially heated eccentric horizontal cylindrical annulus has been numerically simulated. The radiation transfer contributed from the participating medium is obtained by solving the nonlinear integro‐differential radiative transfer equation using discrete ordinate method. The participating gray medium is considered to be emitting, absorbing and isotropically scattering. The walls of the annulus are considered to be opaque, diffuse and gray. In the study it has been observed that the Richardson number ‘Ri’ has a small effect on the total Nusselt number ‘Nu’ in mixed convection heat transfer with or without radiation. From the present investigation it is found that substantial changes occur in isotherms as well as in flow patterns, when the Richardson number is allowed to vary in the range of 0.01–1. The influence of radiative parameters on the interaction phenomenon has been delineated through isotherm and streamline pattern. Copyright © 2008 John Wiley & Sons, Ltd.     

Interaction of mixed convection in two-sided lid driven differentially heated square enclosure with radiation in presence of participating medium

The current study addresses the mathematical modeling aspects of transport phenomena in steady, two-dimensional, laminar flow accompanied by heat transfer in a lid-driven differentially heated cavity in presence of radiatively absorbing, emitting and scattering gray medium. The walls of the enclosure are considered to be opaque, diffusive and gray. Mixed convection is the outcome of the interaction of forced convection induced by the moving vertical hot and cold wall with the natural convection induced due to the differentially heated enclosure. Two different orientations of the wall movement have been considered to simulate opposing and aiding mixed convection phenomenon and to study its interaction with radiation. Vorticity-stream function formulation of N–S equation has been employed. The discrete ordinate method has been used in modeling the radiative transport equation followed with finite volume method as discretisation technique. The effect of influencing parameters on fluid flow and heat transfer has been studied.     

Heat exchange between a selectively emitting liquid and a laminar gas flow in the presence of an external source of radiation

An investigation is conducted in the solution of a number of practical problems of the radiative and combined heat exchange in nonuniform systems having widely different physical properties. The processes of thermal interaction between the ocean and the atmosphere have been treated in the paper [1], the effect of thermal radiation on the melting and solidification of semitransparent crystals has been investigated in [2], the flow of a selectively emitting gas around the lateral surface of an object evaporating under the action of radiative heating has been discussed in [3], and heat transfer from a jet to the molten mass of glass in a glassmaking furnace tank has been investigated in [4]. The radiative and combined heat exchange between a selectively emitting liquid and a transparent heat-conducting laminar gas flow in the case of a specified external thermal radiation field is discussed in this paper. The energy conservation equations are set up taking into account the heat transfer by radiation, convection, and molecular thermal conduction. A differential approximation is used in calculating the values of the radiation fluxes. A system of fundamental computational equations is solved by the method of finite differences and iterations and by the Runge-Kutta method. The results of the calculations are presented in the form of graphs.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 116–122, May–June, 1976.     

Analysis of coupled conduction and radiation heat transfer in presence of participating medium- using a hybrid method

The current study addresses the mathematical modeling aspects of coupled conductive and radiative heat transfer in presence of absorbing, emitting and isotropic scattering gray medium within two-dimensional square enclosure. The walls of the enclosure are considered to be opaque, diffuse and gray. The enclosure comprised of isothermal vertical walls and insulated horizontal walls. A new hybrid method where the concepts of modified differential approximation employed by blending discrete ordinate method and spherical harmonics method, has been developed for modeling the radiative transport equation. The finite volume method has been adopted as the numerical technique. The effect of various influencing parameters i.e., radiation-conduction parameter, surface emissivity, single scattering albedo and optical thickness has been illustrated. The compatibility of the method with regard to solving coupled conduction and radiation has also been addressed.     

Radiative transfer effects of an axisymmetric particulate jet into a cylindrical pipe

This paper discusses the radiative transfer effects of an axisymmetric gas-particles jet into a cylindrical pipe. The medium is gray and it participates to radiation by emission, absorption and scattering. The two-phase flow problem is solved numerically by the finite volume method. We investigate the radiative transfer through a sensitivity analysis which considers the effects of the particle radiative properties and the particle number density on the temperature field and on the radiative heat fluxes of the two-phase flow domain. Analysis of the temperature profile in the cylinder, without and then with particle radiation effects, shows a decrease in the medium temperatures and thus an important role of the radiative transfer. These results also show that the presence of scattering makes the medium temperature more uniform. Finally, analysis of the particle number density, through the variation of the injection velocity, shows that a decrease in the injection velocity decreases the temperatures of the gas and particles and rapidly equilibrates the gas and particle temperatures.     

On radiative heat transfer in a plane layer of an absorbing medium

Recently there has arisen increased interest in the study of radiative heat transfer between geometrically simple systems, both as autonomous problems and as elements of more complex problems.Problems of this kind have been treated by many authors [1–111 who have considered gray, diffusely emitting and absorbing boundaries and gray nonscattering media. In most cases these investigations were restricted either to the derivation of approximate formulas for the net radiative flux, without an exact analysis of the temperature distribution in the layer [5–7], or to numerical computation [1–4], In the latter case, with the exception of [8], which contains a numerical analysis for the case of optical symmetry, no attempt was made to analyze the effect of the optical properties of the boundaries on the temperature field in the layer.These papers can be divided into two groups according to the method of analysis used. The first group includes papers based on the integral equations of radiative transfer, with the corresponding integral analytical methods [1, 2], Similar in nature are [3, 4] which use the slab method, applicable to electrical-analog computation, as well as a recent paper [8] based on probability methods.The second group of papers [5–7] is based on the so-called differential methods. Of particular interest is [7], which develops these methods to an advanced degree. In several papers the problem of radiative transfer is analyzed in conjunction with more complex problems (cf., e.g. [10, 11]).In the present work we shall attempt to carry out an approximate analytical study of problems connected with radiative heat transfer in a plane layer of an absorbing, emitting, nonscattering gray medium with temperature-independent optical properties. The layer is bounded by two parallel, diffusely emitting and diffusely reflecting, isothermal, gray planes.The paper presents the fundamental formulation of the problem, which consists in: (a) the determination of the net heat flux on the basis of given temperature distribution (direct formulation), and (b) the determination of the temperature distribution on the basis of given distribution of the net radiative heat source per unit volume and boundary temperatures (inverse formulation). The analysis is based on integral methods appropriate to the integral equations which represent the net total and hemispherical radiation flux densities [12].The author would like to thank S. S. Kutateladze for his interest in this work.     

Attenuation of forced weak plane pressure waves in a gas with radiative heat transfer

This paper considers the effect of radiative heat transfer on the propagation of forced plane harmonic pressure waves of small amplitude in an infinite emitting-absorbing inviscid nonconducting gas. The radiative pressure and radiative energy are neglected. The purpose of this paper is: a) to construct a theory based on the exact directional distribution of the total (frequency-integrated) specific intensity and to use this theory to calculate the parameters of the wave motion, b) to compare the exact theory with results obtained on the basis of the direction-averaged equation of radiative transfer [1] so as to estimate the errors introduced by various directional approximations and to demonstrate the importance of the anisotropy of radiation in radiation gasdynamics.In the linear theories of Stokes, Rayleigh, Kirchhoff, and Langevin the problem of wave attenuation is separated into special cases, in each of which only one single process is considered. This separation is admissible when to the first approximation the effects of the different dissipation mechanisms (viscosity, thermal conductivity, radiation, etc.) are additive. When only one factor is considered the problem becomes much simpler and the results are more amenable to physical interpretation, and these results can then be used in the solution of the complete problem.     

Statistical theory of radiative transfer in layered media

An equation for the probability density of the wave intensity which takes into account absorption, is obtained with a help of the invariant imbedding method. The limiting case when the medium occupies a half-space, is considered. The field intensity is found for the case of a source inside the medium. The conditions of applicability of the linear theory or radiative transfer are obtained. Numerical solutions of the equations corresponding to the statistical theory of radiative transfer in a layered medium with random inhomogeneities are discussed.     

Thermal radiation effect on non-Darcy natural convection with lateral mass transfer

 A boundary layer analysis has been presented to study the influence of thermal radiation and lateral mass flux on non-Darcy natural convection over a vertical flat plate in a fluid saturated porous medium. Forchheimer extension is considered in the flow equations, and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. Similarity solution for the transformed governing equations is obtained and the combined effect of thermal radiation and fluid suction/injection on the heat transfer rate is discussed. Numerical results for the details of the velocity and temperature profiles as well as Nusselt number have been presented. Received on 7 July 1999