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Laboratory Experiment [1]
Thermocouples and laser holographic interferometers [2] were used
in this study to measure the surface and boundary layer temperatures
on a glass (Corning 7059) and ceramic ((AlSiMag 772, 99.5 Al2O3)
printed circuit boards, Figure 1. The boards had three 4,000-angstrom
film heating elements made of nitride tantalum. Electrical contact
between heaters and the exterior energy source was maintained using
thin gold connectors.
For each material, three film heaters allowed 7 variants of heating.
In all experiments the power dissipated by each heater was 2 W,
corresponding to the dimensionless heat flux Gs = qgba4/(lairn2) = 1.669e+09. Several additional dimensionless
groups were as follows: b/a = 0.012, Pr=0,72; lceramic/lair=1100, lglass/lair=40, e=0.366
(for ceramics coated with tantalum nitride) and e=0.387 (for glass coated with tantalum nitride);
where a and b are the plate's height thickness, respectively
(Figure 2), Pr is the Prandtl number, l is the thermal conductivity, and e
is the emissivity. The emissivity coefficients were obtained
using radiometric microscope Barnes RM-2B. The temperature was measured
using 0.076 mm diameter chromel-alumel thermocouples calibrated
to within 1oC near the water freezing and boiling points.
Coolit Model
The results computed by Coolit are shown in Figure 1. The board
there was specified as a Solid Block component. On one side of the
board an adiabatic Wall binds it. Top and bottom and the side parallel
to the board were set to Opens and the two sides parallel to the
flow direction were Symmetry. Heating elements were modeled as Wall
Patches with specified power dissipation on the adiabatic wall.
Results
Results from the first experiment are shown in Figure 3. In this
experiment carried out on the ceramic board, only the lower heated
was turned on. The plot shows the dimensionless temperature rise
(Grashof number), Q, as a function of distance,
X, from the bottom of the board and as a function of Y - distance
perpendicular to the board.
The second experiment had both heaters on and the measurements
were done on the glass board. The results of measurements against
Coolit simulation are shown in Figure 4. The same nomenclature is
used in this case except that both the interferometer and thermocouples
were used for measurements (only thermocouples were used in the
first experiment).
[1] Zinnes A.E., An Investigation of Steady, Two-Dimensional
Laminar Natural Convection From a Vertical Flat of Finite Thickness
With Plane Localized Heat Sources on Its Surface;, PhD dissertation,
Lehigh University, 1969.
[2] Helfinger L.O., Wuerker R.F., Brooks R.E.,
Holographic Interferometry, Journal of Applied Physics, Vol. 37,
N 2, Feb. 1966, pp. 642-649.
[3] Belyaev, K. , Ph.D. thesis, St. Petersburg Polytechnic Institute,
2000, unpublished.
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