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Heat and Mass Transfer

, Volume 42, Issue 5, pp 359–363 | Cite as

Temperature distribution in a mixture surrounding a growing vapour bubble

  • S. A. MohammadeinEmail author
  • Sh. A. Gouda
Original

Abstract

The paper presents temperature distribution of superheated liquid during the growth of spherical vapour bubble between two-phase temperatures. The heat equation is resolved by the modification of similarity parameter method of Screven [Chem Engng Sci 10:1-13(1959)] between two finite boundaries. Under these conditions, the growth of vapour bubble and temperature are obtained analytically in an implicit form which are different than that obtained before. The growth rate is obtained as a generalized formula compared with Plesset amd Zwick and Scriven et al. theories [J Appl Phys 25:493-500(1954);Chem Engng Sci 10:1-13(1959)]. The growth and temperature field affected by the initial superheating and thermal diffusivity.

Keywords

Heat conduction equation Scriven theory Growth of spherical vapour bubble Temperature distribution between two finite boundaries 

Nomenclature

a

Thermal diffusivity

A1

Constant given by Eq. 24

C

Constant given by Eq. 35

C

Constant given by Eq.19

D

Constant given in Appendix

Ja

= \(\frac{{C_{{\text{pl}}} \rho _{\text{l}} }} {{C_{{\text{pv}}} L}}\Delta \theta _0 \) Jacob number

k

Liquid thermal conduction (m−1 s−1 °K J)

L

Latent heat of vaporization (kg−1 J)

R

Instantaneous bubble radius (m)

\(\mathop R\limits^. \)

Instantaneous radial velocity of bubble boundary

s

Variable relating distance to penetration depth for heat conduction

t

Time of bubble growth (s)

ti

Instantaneous time of bubble growth (s)

Tl

Temperature of liquid (°K)

Ts

Initial temperature of bubble (°K)

T0

Initial temperature of liquid (°K)

w

Liquid velocity

x, y, z

Integration parameters

β

Value of s at r = R

Cpl Cpv

Specific heat at constant pressure and volume

Δθ0

Initial superheating

ρ

Density

φ0

Initial void fraction

ε

Constant defined by Eq. 4

subscript

l

Liquid

v

Vapour

Infinity

V

Volume

P

Pressure

Notes

Acknowledgements

The authors are grateful to the reviewers for their useful comments.

References

  1. 1.
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    Mohammadein SA (1994) Evaluation of characteristic time in the relaxation model for one-component bubble-flow. Doctoral thesis, PAN. GdanskGoogle Scholar
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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of ScienceTanta UniversityEgypt

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