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Analytical study of heat transfer from circular cylinder in liquid metals

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Abstract

In this study the influence of a thin hydrodynamic boundary layer on the heat transfer from a single circular cylinder in liquid metals having low Prandtl number (0.004–0.03) is investigated under isothermal and isoflux boundary conditions. Two separate analytical heat transfer models, viscous and inviscid, are developed to clarify the discrepancy between previous results. For both models, integral approach of the boundary layer analysis is employed to derive closed form expressions for the calculation of the average heat transfer coefficients. For an inviscid model, the energy equation is solved using potential flow velocity only whereas for a viscous model, a fourth-order velocity profile is used in the hydrodynamic boundary layer and potential flow velocity is used outside the boundary layer. The third-order temperature profile is used inside the thermal boundary layer for both models. It is shown that the inviscid model gives higher heat transfer coefficients whereas viscous flow model gives heat transfer results in a fairly good agreement with the previous experimental/numerical results.

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Abbreviations

c p :

specific heat of fluid [J/kg·K]

D :

diameter of circular cylinder [m]

h :

average heat transfer coefficient [W/m2·K]

k :

thermal conductivity [W/m·K]

Nu D :

Nusselt number based on diameter ≡ Dh/k f

Pe D :

Peclet number based on diameter ≡ Re D Pr

q :

heat flux [W/m2]

Re D :

Reynolds number based on diameter ≡ D U app/ν

s :

distance along curved surface of cylinder measured from forward stagnation point [m]

T :

temperature [°C]

U app :

approach velocity [m/s]

U(s):

velocity in inviscid region just outside boundary layer [m/s]

UWF:

uniform wall flux

UWT:

uniform wall temperature

u :

s - component of velocity in boundary layer [m/s]

v :

η - component of velocity in boundary layer [m/s]

x, y :

Cartesian coordinates

α:

thermal diffusivity [m2/s]

Δ:

thermal boundary-layer thickness [m]

δ:

hydrodynamic boundary-layer thickness [m]

δT :

thermal boundary layer thickness [m]

η:

distance normal to and measured from surface of elliptical cylinder [m]

λ:

pressure gradient parameter

ν:

kinematic viscosity of fluid [m2/s]

ρ:

fluid density [kg/m3]

θ:

angle measured from stagnation point [radians]

ζ:

ratio of hydrodynamic to thermal boundary layer thickness ≡ δ/δT

a:

ambient

f:

fluid

H:

hydrodynamic

s:

separation

T:

thermal

w:

wall

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Acknowledgments

The authors gratefully acknowledge the financial support of Natural Sciences and Engineering Research Council of Canada and the Center for Microelectronics Assembly and Packaging.

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Authors and Affiliations

  1. Microelectronics Heat Transfer Laboratory, Department of Mechanical Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    W. A. Khan, J. R. Culham & M. M. Yovanovich

Authors
  1. W. A. Khan
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  2. J. R. Culham
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  3. M. M. Yovanovich
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Corresponding author

Correspondence to W. A. Khan.

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Khan, W.A., Culham, J.R. & Yovanovich, M.M. Analytical study of heat transfer from circular cylinder in liquid metals. Heat Mass Transfer 42, 1017–1023 (2006). https://doi.org/10.1007/s00231-005-0068-4

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  • DOI: https://doi.org/10.1007/s00231-005-0068-4

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