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Dimensionless correlations for forced convection in liquid metals: Part I. single-phase flow

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Abstract

Two main objectives were addressed in this article. First, a dimensionless heat-transfer correlation for single-phase flow forced convection in liquid aluminum has been derived using a novel experimental method. An aluminum sphere was rotated with a specific tangential velocity in liquid aluminum. Its melting time was measured and correlated with the convective heat-transfer characteristics. The resulting correlation has the following form:

$$\begin{gathered} \overline {Nu_D } = 2 + 10^{2.811} \times \operatorname{Re} _D^{0.585} \times \Pr ^{2.386} \hfill \\ 5162 \leqslant \operatorname{Re} _D \leqslant 21,273, \Pr \approx 0.014 \hfill \\ \end{gathered} $$

The second objective of the study was to assess the accuracy of various correlations using an annular channel, which was available at an independent setting, at the Alcan Research and Development Laboratory. The correlations investigated were those derived from the current experimental work as well as those derived by other investigators, as presented in their respective published work. Results indicated that when applied to liquid metals, theoretically derived equations as well as equations developed for fluids with a Prandtl number greater than 0.7 exhibit a very large error. As such, these equations are unsuitable for liquid metals. A considerably smaller error is exhibited by equations derived experimentally, specifically for liquid metals, thereby attesting to the careful consideration that must be exercised in the choice of correlations that are employed.

This study also provides a critical assessment of various exponents used in dimensionless equations for convective heat transfer in liquid metals. While there is a general consensus that the exponent of the Reynolds number is around 0.5, the exponent for the Prandtl number varies considerably.

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Abbreviations

α s :

thermal diffussivity of aluminum

k :

thermal conductivity

R 0 :

sphere radius at time t = 0

R(t) :

sphere radius at time t

R T :

interfacial thermal resistance at the shell solid aluminum interface

T :

temperature

T bath :

temperature of the aluminum bath far away from the sphere

T melting :

melting temperature of aluminum sphere

T*shell :

shell temperature at the shell solid aluminum interface

T*sphere :

sphere temperature at the shell solid aluminum interface

T initial :

initial temperature

q″ :

heat flux at the sphere shell interface

q″convection :

convective heat flux from the aluminum bath to metal sphere

ρ S :

density of solid aluminum

LH fusion :

latent heat of fusion for aluminum

t melting :

time for the complete melting of aluminum sphere

t shell :

time for which solidified shell exists around sphere

g :

gravitational acceleration (9.807 ms−1

#x0044-0304; :

average sphere diameter during the t melting

h D :

average heat-transfer coefficient during t melting

μ :

viscosity of aluminum at T bath

μ S :

viscosity of aluminum close to its melting point

V :

velocity (ms−1)

SPH:

liquid metal supeheat (T bath − T melting)

β :

coefficient of thermal expansion (K−1)

ρ :

density (kg m−3)

μ :

viscosity (kg s−1 m−1)

\(\overline {Nu_D } \) :

average Nusselt number \(\frac{{h_D \bar D}}{k}\)

Re D :

average Reynolds Number \(\frac{{\bar DV\rho }}{\mu }\)

Pr:

Prandtl number C p μ/k

Gr D :

Grashof number \(\frac{{\beta g(\bar D)^3 \rho ^2 SPH}}{{\mu ^2 }}\)

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Author notes

  1. Anthony C. Mikrovas (Independent Engineering Consultant)

    Present address: Cominco Ltd., V1R 4S4, Trail, BC, Canada

Authors and Affiliations

  1. the Department of Metallurgy and Materials Science, University of Toronto, M5S 3E4, Toronto, ON, Canada

    Stavros A. Argyropoulos (Professor)

  2. Athens, Greece

    Anthony C. Mikrovas (Independent Engineering Consultant)

  3. the Kingston Research and Development Centre, Alcan International Ltd., K7L 5L9, Kingston, ON, Canada

    Don A. Doutre (Senior Research Scientist)

Authors
  1. Stavros A. Argyropoulos
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  2. Anthony C. Mikrovas
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  3. Don A. Doutre
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Argyropoulos, S.A., Mikrovas, A.C. & Doutre, D.A. Dimensionless correlations for forced convection in liquid metals: Part I. single-phase flow. Metall Mater Trans B 32, 239–246 (2001). https://doi.org/10.1007/s11663-001-0047-1

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  • DOI: https://doi.org/10.1007/s11663-001-0047-1

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