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St-Re-Pr RELATIONSHIP FOR A HEATED/COOLED CYLINDER IN LAMINAR CROSS FLOW

DOI: 10.1615/ICHMT.2008.CHT.210
16 pages

Frantisek Marsik
Institute of Thermomechanics, Czech Academy of Sciences, Dolejskova 5, 182 00 Prague 8, Czech Republic

Zdenek Travnicek
Institute of Thermomechanics of the Czech Academy of Sciences

Ruey-Hor Yen
National Taiwan University, Department of Mechanical Engineering, No. 1, Roosevelt Rd., Sec. IV, 106 Taipei, Taiwan Republic of China

Wen-Yun Tu
National Taiwan University, Institute of Applied Mechanics, No. 1, Roosevelt Rd., Sec. IV, 106, Taipei, Taiwan Republic of China

An-Bang Wang
National Taiwan University, Institute of Applied Mechanics, No. 1, Roosevelt Rd., Sec. IV, 106, Taipei, Taiwan Republic of China

Abstract

Based on the boundary layer approximation analysis of the integral balance laws, a general formula for the Strouhal-Reynolds relationship of no isothermal flow around a cylinder has been investigated in this paper. By assuming the temperature dependence of the boundary layer thickness, the following formula has been derived for not only isothermal but also the non-isothermal cases:

Sr·(Re, Pr, T*) = 0.2665 − (1.0175 (T*)ω/2/√ Re)·[ 1 + (0.227(1 − T*)/Pr1/3(2T* − 1))]1/2,

where the Reynolds, Strouhal and Pradtl numbers are commonly introduced as Re = Dvρ, Sr = f D/v, and Pr = cρμ/k . The temperature effect is introduced by the ratio T* = Tw/T of the cylinder wall temperature Tw and free stream temperature T. The effects of the viscosity and thermal conductivity of fluids are separated from the influence of the cylinder geometry. The unknown value of the geometrical parameter for a circular cylinder has been obtained from the experiments and is in good agreement with the numerical calculations by the spectral method. Excellent overlapping has been obtained from the comparisons of present formula and previous experiments of the heated and cooled cylinders in the Reynolds number from 47.5 to 180 for both air and water. The main part of the present derivation is dealing with air as the working fluid; however, the extension to the different fluids (through Prandtl number Pr) can be also expected.

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