Moving Taylor series for solving one-dimensional one-phase Stefan problem
Alexandria Engineering Journal, 2022 In this work, a modified form of Taylor series is proposed which we call the moving Taylor series. We prove theorems that formulate coefficients of the proposed series along with the formula of its time-derivatives.
A. Elsaid, S.M. Helal
doaj +1 more source
Successive melting of a phase change material bounded in a finned trapezoidal domain
Case Studies in Thermal Engineering, 2021 The storage of thermal energy in a trapezoidal aluminum enclosure via melting of PCM phase change material is studied. Experimental observations and numerical simulation are made to examine the process for the phase change of paraffin wax.
Farooq Ahmad +6 more
doaj +1 more source
On the Two-phase Fractional Stefan Problem
Advanced Nonlinear Studies, 2020 The classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion.
del Teso Félix +2 more
doaj +1 more source
An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems [PDF]
, 1995 In the context of analyzing a new model for nonlinear diffusion in polymers, an unusual condition appears at the moving interface between the glassy and rubbery phases of the polymer.
Cohen, D. S., Edwards, D. A.
core +1 more source
Controlled Drug Release Asymptotics [PDF]
, 1998 The solution of Higushi's model for controlled release of drugs is examined when the solubility of the drug in the polymer matrix is a prescribed function of time. A time-dependent solubility results either from an external control or from a change in pH
Cohen, Donald S., Erneux, Thomas
core +1 more source
A new equivalence of Stefan's problems for the Time-Fractional-Diffusion Equation [PDF]
, 2014 A fractional Stefan problem with a boundary convective condition is solved, where the fractional derivative of order $ \alpha \in (0,1) $ is taken in the Caputo sense.
Marcus, Eduardo Santillan +1 more
core +2 more sources
Convective stabilization of a Laplacian moving boundary problem with kinetic undercooling [PDF]
, 2007 We study the shape stability of disks moving in an external Laplacian field in two dimensions. The problem is motivated by the motion of ionization fronts in streamer-type electric breakdown.
Bernard Meulenbroek +3 more
core +5 more sources
Two equivalent Stefan's problems for the Time Fractional Diffusion Equation [PDF]
, 2013 Two Stefan's problems for the diffusion fractional equation are solved, where the fractional derivative of order $ \al \in (0,1) $ is taken in the Caputo's sense.
Marcus, Eduardo A. Santillan +1 more
core +2 more sources
A new mathematical formulation for a phase change problem with a memory flux [PDF]
, 2018 A mathematical formulation for a one-phase change problem in a form of Stefan problem with a memory flux is obtained. The hypothesis that the integral of weighted backward fluxes is proportional to the gradient of the temperature is considered. The model
Bollati, Julieta +2 more
core +2 more sources
Cahn–Hilliard equation on the boundary with bulk condition of Allen–Cahn type
Advances in Nonlinear Analysis, 2018 The well-posedness of a system of partial differential equations with dynamic boundary conditions is discussed. This system is a sort of transmission problem between the dynamics in the bulk Ω and on the boundary Γ.
Colli Pierluigi, Fukao Takeshi
doaj +1 more source