Abstract
The Stefan problem in a semi-infinite region with arbitrarily prescribed initial and boundary conditions, subject to a condition of the mixed type at the interface is investigated. To establish the exact solution of the problem, some new basic solutions of the heat equation are offered. Their mathematical properties are also supplied. The exact solutions of the temperatures in both phases and of the interfacial boundary are derived in infinite series. The existence and uniqueness of these series are considered and proved. It is also shown that these series are absolutely and uniformly convergent. Some concluding remarks about the differences between the present problem and the classical Stefan problem are given. Also the effect of a density discontinuity at the interface is discussed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.