Alejo Sánchez A*, Rafael Rosales*, Iris Jiménez de P*, and Antonio Campo**
*Escuela de Ingeniería Mecánica
Universidad de los Andes
Mérida, Edo. Mérida 5101, Venezuela
**College of Engineering
Idaho State University
Pocatello, Idaho, U.S.A.

Convective cooling has received, so far, more attention than any other cooling mechanism that could be associated with the problem of electronic packaging. This is particularly interesting since the few publications where radiation has been considered show, consistently, that radiative cooling could account for 30-50 % of the total heat transfer.

In the present paper, the Discrete Ordinates method is combined with a control volume approach to simulate the thermal performance of several arrays of electronic components in situations selected to emphasize the importance of the radiation effect. The simulations include radiation combined with pure natural and pure forced convection, as well as radiation combined with mixed convection. In particular, it is demonstrated that in some applications radiation cooling can be orders of magnitude higher than convection cooling. Simultaneously, it is demonstrated that the maximum temperature of electronic components can not be correctly estimated if radiation effects are not accounted for.


Pierre Labourdette*, Sergey T. Surzhikov**
*CNES, Toulouse, France
**Institute for Problems in Mechanics Russian Academy of Sciences, Moscow, Russia

The problem of the dynamics and radiation of high temperature fire balls in free atmosphere is discussed in terms of environmental, fire and explosion safety issues, analysis of the possible consequences of nuclear and major industrial explosions1, as well as explosions of launch vehicles at the active part of the flight2,3.

Numerous experimental and theoretical research established that hot gas clouds rise in free atmosphere in accordance with laws that in many aspects are similar, irrespective of the causes that generated the clouds1.

Throughout the rising process the heated gas emits heat unto the environment which results in the thermic cooling down. The main heat exchange mechanisms are convection and heat conductivity (for large-scale fire balls-effective turbulent heat conductivity). At the initial process stage the important factors are radiant losses from the heated area.

In spite of the fact that the initial stage is relatively short in terms of time, there are two reasons due to which radiation is of major practical interest. First of all, the development of the hot cloud rise is determined to a great extent by the cloud cooling rate, which is, in its turn, depends to a great extent on voluminous radiant losses. Secondly, the data given in work1 confirms the fact that heat radiation from fire balls generated by chemical explosions caused death to hundreds of people. Fire ball heat radiation is one of the most important hazard factors. Typical spatial and time scales corresponding to major chemical explosions were established by analysis of major accidents: fire ball radii reached hundreds of meters, while the fire balls lived dozens of seconds.

The two-dimensional numerical model has been formulated for problems involving gas dynamics and radiative heat exchange of large-scaling high temperature hydrogen-oxygen fire balls. The mathematical model is based on the system of Navier-Stokes equations, together with equations for energy conservation, selective heat radiative transfer and for continuity of water vapour and environmental air. When this model is implemented in practice at a computer, it turns out to be convenient to present the computational process in the form of three consecutive stages: gas dynamics, energy and radiation stage, that is, to implement a scheme of splitting into physical processes. With reasonable combination of global iterative solution of the whole system of equations with local iterations (for instance, between energy and radiation stages), the efficiency of computations proves to be quite high.

To solve the system of gas dynamics stage equations the method of unsteady dynamically variables4 is applied. P1-approximation of Spherical Harmonics method is used for solution of the radiation part of the problem. The real optical and thermodynamical properties of the gases are taken into account5,6. The dynamics of large-scale thermics, is determined by effective (turbulent) transfer coefficients7 which allow to describe such an important element of the process as turbulent mixing of the environment.

The calculation results for large-scaling hydrogen-oxygen fire balls dynamics are presented. The following scheme was used for calculations based on the model:

  • calculations in volumetric luminescence approximation,
  • calculations with regard to radiant heat exchange,
  • calculations not taking radiation processes into account.
In the last case neither volumetric luminescence, nor transfer of radiant energy in the fire ball were taken into account.

The numerical investigation have indicated that taking radiant heat exchange into account in the case under consideration leads to very significant changes in the results.

  1. Marshall, V.C., Major Chemical Hazards, Ellis Horwood Ltd. John Wiley & Sons, New York, Chichester, Brisbane, Toronto, 1987.
  2. High, R.W., The Saturn Fireball, Annals of New York Academy of Sciences, Vol. 152, Part 1, pp. 441-451, 1968.
  3. Bader, B.E., Donaldson, A.B., Hardee, H.C., Liquid-Propellant Rocket Abort Fire Model, J. Spacecraft, Vol. 8, No.12, pp. 1216-1219, 1971.
  4. Surzhikov, S.T., Computation of Nonsteady Subsonic Viscous Compressible Gas Flows in the Region of Local Heat Release, Physics-Doklady, Vol. 39, No.5, pp. 357-359, 1994
  5. Ludwig, C.B., Measurements of the Curves-of-Growth of Hot Water Vapour, Appl. Optics, Vol.10, No.5, pp. 1057-1073, 1971.
  6. Siegel, R., Howell, J.R., Thermal Radiation Heat Transfer, McGraw-Hill Book Company, 1972.
  7. Penner, J.E., Hoselman, L.C., Edwards, L.L., Buoyant plume calculations, AIAA Pap., No. 459, p. 1-9, 1985.


Pei-feng Hsu*, Research Associate
Jerry C. Ku, Associate Professor
Mechanical Engineering Department
Wayne State University
Detroit, Michigan 48202

The purpose of this paper is to study the effects of the radiative properties of soot particles and CO2 and H2O gases on detailed radiative heat transfer calculations using a simulated ethylene jet diffusion flame. The YIX method is applied to calculate the radiative transfer quantities over the spectral range of 1-20 m in a finite cylindrical enclosure with distributions for flame temperature, soot volume fraction, and gas concentrations precalculated from a modeling analysis. Scattering from soot particles is neglected. Soot only, gases only, and the combined cases are examined. The Rayleigh solution is used to calculate the absorption coefficient spectra for soot aggregates. Soot Complex refractive index spectra are generated from the Drude-Lorentz dispersion model based on three frequently cited dispersion parameter sets. Results from these three dispersion parameter sets show that the difference in maximum flux divergence is 45% and that the difference in maximum radial flux is 62%. Thus current uncertainties about soot spectral refractive indices are the main limitation on accurate estimates of the radiation heat transfer from sooting combustion systems. The exponential-wide-band model is used to calculate gas absorption coefficient spectra. Generally, radiation from soot is two to three times of that from gases. Therefore both soot and gas contributions are significant, and accurate models for gas absorption coefficient spectra are crucial. More than 95% of the total gas radiation comes from the 2.73 and 4.3 m bands of CO2 and from the 2.67 m bands of H2O. The 6.3 m H2O band can be added to essentially account for all gas radiation, and other gas absorption bands make very little contribution. Practically, for the type of flames considered here, it is concluded that spectral contributions from beyond the 5 m range can be neglected with less than 5% loss of accuracy in calculating the total radiative flux and its divergence.
*Presently Assistant Professor, Mechanical and Aerospace Engineering Programs, Florida Institute of Technology, Melbourne, Florida 32901.


Mohammad-Ali Jamnia, and Michael S. Engelman
Fluid Dynamics International
500 Davis St., Suite 600
Evanston, Illinois 60201

A numerical technique for the simulation of the effects of nongray media radiation is presented in which the wave length dependency is approximated by a number of bands. Each band is assumed to have a gray absorbing-emitting, scattering media radiation and the P-1 method is utilized to calculate the radiation flux. Inclusion of multi-layered materials as well as transparent windows and transparent bands - which allow the walls to exchange radiation energy in those bands alone - are discussed.

In this approach, the Navier-Stokes equations are solved along with the energy equation and the n transport equations resulting from the n bands of radiation, to predict the flow and temperature of radiating fluids. The coupling between the radiation equations and the energy equation is through the gradient of the irradiance flux which enters the energy equation as a source term. However, this particular formulation allows a separation of terms which leads to a redistribution of certain terms to the left hand side of the system of equations. This adds greatly to the stability of the nonlinear iterative procedure used to solve the discrete equations. These equations are implemented in FIDAP, a general purpose program for the analysis of viscous fluids.

Several examples are presented to validate the technique and also its application to2-D, 2-D axisymmetric 3-D problems.

The first two examples presented are comparisons with published results for a gray medium. Unfortunately, no suitable benchmark problem has been found to validate the banded-gray approach. The third example shows that the banded-gray formulation will reduce to gray provided that the spectrum under consideration is wide enough. Finally, the last two problems solved include a variety of realistic physical phenomena that are present in crystal growth and solidification problems. Both linear and quadratic quadrilateral finite elements have been employed in the simulations. The walls are assumed black unless stated otherwise.

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