Analytical solution of integro‐differential equations describing the process of intense boiling of a superheated liquid

In this article, an approximate analytical solution of an integro‐differential system of equations is constructed, which describes the process of intense boiling of a superheated liquid. The kinetic and balance equations for the bubble‐size distribution function and liquid temperature are solved ana...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 45; no. 13; pp. 7954 - 7961
Main Authors Alexandrova, Irina V., Ivanov, Alexander A., Alexandrov, Dmitri V.
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 15.09.2022
Subjects
applied mathematical modeling
Boiling
Differential equations
Distribution functions
Exact solutions
integro‐differential model
intense boiling
Mathematical analysis
Nucleation
phase transitions
Size distribution
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Summary:In this article, an approximate analytical solution of an integro‐differential system of equations is constructed, which describes the process of intense boiling of a superheated liquid. The kinetic and balance equations for the bubble‐size distribution function and liquid temperature are solved analytically using the Laplace transform and saddle‐point methods with allowance for an arbitrary dependence of the bubble growth rate on temperature. The rate of bubble appearance therewith is considered in accordance with the Dering–Volmer and Frenkel–Zeldovich–Kagan nucleation theories. It is shown that the initial distribution function decreases with increasing the dimensionless size of bubbles and shifts to their greater values with time.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7560