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Analysis of laminar free convection from a vertical plate of finite thickness with planar heat sources.

Courtesy of NTS Corp.

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 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.

Figure 1. Coolit computed solution. Temperature-colored board and air flow with velocity vectors.
Figure 2. Schematic of the experiment.
Figure 3. Comparison of computed results with experiment for ceramic board with the upper heater turned off.
Figure 4. Comparison of computed results with experiment for glass board with both heaters turned on.

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