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Thermal free convection from a solid sphere

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Summary

Thermal free convection from a sphere has been studied by melting solid benzene spheres in excess liquid benzene (Pr=8,3; 108<Gr<109). Overall heat transfer as well as local heat transfer were investigated. For the effect of cold liquid produced by the melting a correction has been applied. Results are compared with those obtained by other workers who used alternative experimental methods.

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Abbreviations

α :

coefficient of heat transfer

d :

characteristic length, here diameter of sphere

λ :

thermal conductivity

g :

acceleration of free fall

β :

cubic expansion coefficient

ΔT :

temperature difference between wall and fluid at infinity

ν :

kinematic viscosity

ρ :

density

c :

specific heat capacity

a :

thermal diffusivity (=λ/ρc)

D :

diffusion coefficient

Nu :

dimensionless Nusselt number (=αd/λ)

Nu*:

the analogous number for mass transfer (=kd/D)

\(\overline {Nu} \) :

mean value of Nusselt number

Gr :

dimensionless Grashof number (=gβd 3ΔT/ν 2)

Gr*:

the analogous number for mass transfer (=gβd 3Δx/ν 2)

Pr :

dimensionless Prandtl number (=ν/a)

Sc :

dimensionless Schmidt number (=ν/D)

References

  1. Dumoré, J. M., H. J. Merk and J. A. Prins, Nature 172 (1953) 460; Van der Burgh, J., Appl. sci. Res. A 9 (1960) 293; Frederikse, J. W., unpublished work.

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  2. Schütz, G., Int. J. Heat Mass Transfer 6 (1963) 873.

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  3. Garner, F. H. and R. B. Keey, Chem. Engng Sci. 9 (1959) 218. Garner, F. H. and J. M. Hoffman, A.I.Ch. E. J. 7 (1961) 148.

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  4. Merk, H. J. and J. A. Prins, Appl. sci. Res. A 4 (1954) 207 (particularly fig. 4).

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  5. Merk, H. J., Appl. sci. Res. A 4 (1954) 435.

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  6. Kranse, A. A., Internal report, Technische Hogeschool Delft 1965. Contains the complete experimental material that could not be presented in full in fig. 1 and 2 of this paper.

  7. Pei, D. C. T. and W. H. Gauvin, A.I.Ch. E. J. 9 (1963) 375.

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Authors and Affiliations

  1. Laboratorium voor Technische Natuurkunde der Technische Hogeschool, Delft, Netherlands

    A. A. Kranse & J. Schenk

Authors
  1. A. A. Kranse
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  2. J. Schenk
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Kranse, A.A., Schenk, J. Thermal free convection from a solid sphere. Appl. sci. Res. 15, 397–403 (1966). https://doi.org/10.1007/BF00411573

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  • DOI: https://doi.org/10.1007/BF00411573

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