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
Corresponding Author:irina.alexanderova@urfu.ru
Author ProfileAlexander Ivanov
Ural Federal University named after the first President of Russia B N Yeltsin
Author ProfileDmitri Alexandrov
Ural Federal University named after the first President of Russia B N Yeltsin
Author ProfileAbstract
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.21 Feb 2021Submitted to Mathematical Methods in the Applied Sciences 23 Feb 2021Submission Checks Completed
23 Feb 2021Assigned to Editor
28 Feb 2021Reviewer(s) Assigned
11 Mar 2021Review(s) Completed, Editorial Evaluation Pending
10 Apr 2021Editorial Decision: Accept
15 Sep 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 13 on pages 7954-7961. 10.1002/mma.7560