Investigation of natural convection heat transfer from uniformly heated (isoflux), thin, stationary circular disks at arbitrary angles of inclination
Introduction
Substantial amounts of empirical data exist in the literature, and are presented in many current heat transfer textbooks [1], [2], [3], [4], [5], for natural convection heat transfer from geometries such as vertical, horizontal and inclined flat plates, horizontal and vertical cylinders, spheres, bispheres, oblate and prolate spheroids, horizontal upward and downward facing surfaces, cubes of various orientations, vertical and inclined channels, rotating geometries, as well as geometries within enclosures, and over a wide range of the Rayleigh number. A geometry that is missing from all of these lists is that of a thin fully three-dimensional circular disk (disk surfaces have been investigated experimentally [6], [7], [8] and theoretically [9], [10]). The disk-type geometry is relevant in the cooling of silicon wafers and electronic components, such as disk-shaped resistors and power transistors, and the use of disk-type thermistors for temperature and air flow measurements.
For the case of an isothermal circular disk, several papers have addressed some new experimental data and empirical correlations [11], [12]. To the best knowledge of this author, no empirical correlation exists in the available literature for natural convection from stationary vertical circular disks with an imposed heat flux, which is a more realistic condition in many practical applications such as electronic component cooling. Such is the objective of the current research.
Section snippets
Experimental measurement technique
The circular disks that were used as heat transfer models for the experimental data presented in this paper were commercially available disk-type thermistors. Thermistors are semiconductors of ceramic material made by sintering mixtures of metallic oxides such as manganese, nickel, cobalt, copper, iron, and uranium. Disks are made by pressing thermistor material under high pressure in a round die to produce flat coinlike pieces. These pieces are then coated with silver on the two flat surfaces.
Experimental results
The experimental results for natural convection are depicted in dimensionless form in Fig. 2, where Nud is plotted as a function of the modified Rayleigh number, . The data presented in this figure consist of multiple heat transfer models at various angles of inclination. An empirical correlation which fits all of the data, is given in Table 2 with the correlation displayed in Fig. 3. The experimental apparatus was limited in the maximum Rayleigh number with air because of the small size of
Summary and conclusions
Experimental heat transfer data have been presented and a dimensionless correlation proposed for natural convection from heated stationary uniformly heated (constant heat flux) circular disks over wide ranges of the modified Rayleigh number. Some studies have been done for isothermal disks but not for the imposed heat flux case which is more practical for many applications including electronic component cooling.
Since only air was tested, the current correlation is recommended for Prandtl
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