Abstract
Logistic versions of the heat balance integral and refined integral methods are introduced. A benchmark with a one-phase Stefan problem under constant and time-dependent boundary conditions shows remarkable accuracy at estimating temperature distribution and position of the moving front.
Highlights
We introduce a logistic variant of the heat balance integral method HBIM and its refinement, the refined integral method RIM for the solution of a 1 1 dimensional one-phase Stefan melting problem
It relies a bit on the geometry of the error function, which is sigmoid, and more on the fact that given limited resources, growth for many dynamical systems is better modeled by logistic functions rather than the exponential ones 21
Based on 2.10, error comparison with the Gaussian HBIM of temperature and moving front estimates obtained through the Logistic Heat Balance Integral Method (LHBIM) for β ∈ K values are given, respectively, in Tables 2 and 3
Summary
We introduce a logistic variant of the heat balance integral method HBIM and its refinement, the refined integral method RIM for the solution of a 1 1 dimensional one-phase Stefan melting problem. It is known that the Gaussian variant by Mosally et al 14 and Mitchell and Myers 17 is prescriptively one of the most accurate variants in current literature for obtaining approximate solutions of the 1 1 -dimensional one-phase Stefan melting problem. It relies a bit on the geometry of the error function, which is sigmoid, and more on the fact that given limited resources, growth for many dynamical systems is better modeled by logistic functions rather than the exponential ones 21.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
