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Analytical solution of integro-differential equations describing the process of intense boiling of a superheated liquid
  • Irina Alexandrova,
  • Alexander Ivanov,
  • Dmitri Alexandrov
Irina Alexandrova
Ural Federal University named after the first President of Russia B N Yeltsin
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Alexander Ivanov
Ural Federal University named after the first President of Russia B N Yeltsin
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Dmitri Alexandrov
Ural Federal University named after the first President of Russia B N Yeltsin
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Abstract

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.

Peer review status:ACCEPTED

21 Feb 2021Submitted to Mathematical Methods in the Applied Sciences
23 Feb 2021Assigned to Editor
23 Feb 2021Submission Checks Completed
28 Feb 2021Reviewer(s) Assigned
11 Mar 2021Review(s) Completed, Editorial Evaluation Pending
10 Apr 2021Editorial Decision: Accept