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Research Papers: Forced Convection

# Prandtl Number Effect on the Laminar Convective Heat Transfer From a Rotating Disk

[+] Author and Article Information
Christian Helcig

Thermal and Power Engineering,
Department of Mechanical Engineering,
Muenster University of Applied Sciences,
Steinfurt 48565, Germany
e-mail: christian.helcig@fh-muenster.de

Stefan aus der Wiesche

Thermal and Power Engineering,
Department of Mechanical Engineering,
Muenster University of Applied Sciences,
Steinfurt 48565, Germany
e-mail: wiesche@fh-muenster.de

Igor V. Shevchuk

MBtech Group GmbH & Co. KGaA,
Fellbach-Schmiden 70736, Germany

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 6, 2016; final manuscript received May 6, 2017; published online June 6, 2017. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 139(10), 101702 (Jun 06, 2017) (10 pages) Paper No: HT-16-1633; doi: 10.1115/1.4036729 History: Received October 06, 2016; Revised May 06, 2017

## Abstract

Convective heat transfer in rotating disk systems is of great importance in many engineering applications. Despite the high practical relevance, there have been only a small number of experimental investigations regarding the influence of the Prandtl number larger than unity. Ever since Dorfman's pioneering work more than 50 years ago, various analytical works about the heat transfer of a rotating disk have been published. However, this study is a novelty because measurements of the laminar convective heat transfer over a free rotating disk for a wide range of Prandtl number up to $Pr=5000$ are presented. The accuracy of the employed experimental apparatus was assessed by heat transfer measurements in air, for which reliable literature data are widely available. Natural convection effects and temperature-dependent physical properties have been taken into consideration using the property-ratio method. The experimental results are in excellent agreement with analytical self-similar solutions and the theoretical correlation of Lin and Lin. The applicability of frequently used heat transfer correlations is assessed by the means of the new experimental data.

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## Figures

Fig. 1

Free rotating disk in a resting fluid

Fig. 2

CAD model of the complete test rig

Fig. 3

Disk design and dimensions (in millimeter)

Fig. 4

Step response of the surface temperature (glycerin, PH=4 W, Reω=32)

Fig. 5

(a) Primary and (b) secondary flow induced by the rotating disk

Fig. 6

Calculated and measured surface temperature radial coordinate (glycerin, PH=10 W, Reω=0)

Fig. 7

Rotordynamic model of the disk apparatus

Fig. 8

Comparison of the film temperature and the property-ratio method for data reduction

Fig. 9

Nusselt number NuNC against Grashof number Gr in case of air (Pr = 0.71)

Fig. 10

Nusselt number Nu against rotational Reynolds number Reω in case of air (Pr = 0.71)

Fig. 11

Nusselt number NuNC against Grashof number Gr in case of water (Pr=6.13)

Fig. 12

Nusselt number Nu against rotational Reynolds number Reω in case of water (Pr = 6.13)

Fig. 13

Nusselt number NuNC against Grashof number Gr in case of glycerin (Prm=4900)

Fig. 14

Nusselt number Nu against rotational Reynolds number Reω in case of glycerin (Prm=4685)

Fig. 15

Correlation for the constant K as a function of the Prandtl number in case of laminar flow over a rotating disk

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