MODELING OF COMPREHENSIVE SYSTEMS I
ABOUT THE IMPORTANCE OF RADIATIVE COOLING
IN ELECTRONIC PACKAGING
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
THE RADIATIVE-CONVECTIVE INTERACTION IN LARGE-SCALE
OXYGEN-HYDROGEN FIRE BALLS
Sergey T. Surzhikov**
*CNES, Toulouse, France
**Institute for Problems in Mechanics Russian Academy of Sciences,
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
The calculation results for large-scaling hydrogen-oxygen fire balls dynamics
are presented. The following scheme was used for calculations based on the
In the last case neither volumetric luminescence, nor transfer of radiant
energy in the fire ball were taken into account.
- calculations in volumetric luminescence approximation,
- calculations with regard to radiant heat exchange,
- calculations not taking radiation processes 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.
- Marshall, V.C., Major Chemical Hazards, Ellis Horwood Ltd. John Wiley &
Sons, New York, Chichester, Brisbane, Toronto, 1987.
- High, R.W., The Saturn Fireball, Annals of New York Academy of Sciences,
Vol. 152, Part 1, pp. 441-451, 1968.
- 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.
- 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.
- Ludwig, C.B., Measurements of the Curves-of-Growth of Hot Water Vapour,
Appl. Optics, Vol.10, No.5, pp. 1057-1073, 1971.
- Siegel, R., Howell, J.R., Thermal Radiation Heat Transfer, McGraw-Hill Book
- Penner, J.E., Hoselman, L.C., Edwards, L.L., Buoyant plume calculations,
AIAA Pap., No. 459, p. 1-9, 1985.
DETAILED SPECTRAL RADIATION CALCULATIONS FOR
NONHOMOGENEOUS SOOT/GAS MIXTURES BASED ON A SIMULATED ETHYLENE JET DIFFUSION
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
*Presently Assistant Professor, Mechanical and Aerospace Engineering
Programs, Florida Institute of Technology, Melbourne, Florida 32901.
A FINITE ELEMENT SIMULATION OF NON GRAY PARTICIPATING
MEDIA RADIATION FOR GENERAL ENGINEERING PROBLEMS
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.