An Inverse Stefan Problem Relevant to Boilover: Heat Balance Integral Solutions and Analysis

TL;DR

This paper formulates Stefan problems related to oil-water burning systems, solving inverse problems using heat balance integral methods to analyze heat transfer and boundary movements in such systems.

Contribution

It introduces a semi-analytical approach for inverse Stefan problems in oil-water systems, incorporating internal heat generation and boundary dynamics.

Findings

Semi-analytical solutions for inverse Stefan problems

Application of heat balance integral method to burning oil-water systems

Analysis of boundary movement and heat transfer in fuel layers

Abstract

Stefan problems relevant to burning oil-water systems are formulated. Two moving boundary sub-problems are defined: burning liquid surface and formation of a distillation ("hot zone") layer beneath it. The basic model considers a heat transfer equation with internal heat generation due to radiation flux absorbed in the fuel depth. In verse Stefan problem corresponding to the first case solved by the heat balance integral method and dimensionless scaling of semi-analytical solutions are at issue.