On the solutions of a phase change problem with temperature-dependent thermal conductivity and specific heat

An Analysis of the One-Phase Stefan Problem with Variable Thermal Coefficients of Order p

“…These problems are known as "Stefan problems". The revolutionary technological development of recent years has led to an increase in interest in this type of problem among researchers; see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. In classical Stefan problems, the substance's specific heat and thermal conductivity are both constants.…”

A Nonclassical Stefan Problem with Nonlinear Thermal Parameters of General Order and Heat Source Term

“…These problems have a deep connection with heat transfer theory since they tend to model phase-change problems due to melting or liquidation processes. The scientific studies concerning these problems have significantly increased in the last two decades due to the high importance and demands of describing and analyzing many industrial and physical processes, see, for example, [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The classical Stefan problems deal with constant thermal parameters (thermal conductivity and specific heat) for the substances, but due to the recent developments in technology and science, researchers realized that models that described temperature-dependent parameters would be more realistic.…”

A Stefan problem with nonlinear thermal conductivity

“…1,2 This has motivated many researchers to develop existence and uniqueness theorems for the solutions of this problem which has been ever since the subject of many research papers; see, for example previous research. [3][4][5][6][7][8][9][10][11][12][13][14] The authors in Ceretani et al 3 proved the existence and uniqueness of the modified error function for small values of 𝛿 > 0, and the general case 𝛿 > −1 was proved in Bougoffa et al 4 The purpose of this paper is to provide an existence and uniqueness theorem for the solution of (1.4) that was proposed in Cho and Sunderland, 1 which represents a Stefan problem with a nonlinear thermal conductivity of the form (1 + 𝛿𝑦 + 𝛾𝑦 2 ) n , where 𝛿 > −1 and 𝛾 > −1. To the best of our knowledge, the question of existence and uniqueness of the solution of Problem (1.4) has not been answered since proposing the problem in 1974.…”

“…No existence and uniqueness theorems have been established in earlier studies 1,2 . This has motivated many researchers to develop existence and uniqueness theorems for the solutions of this problem which has been ever since the subject of many research papers; see, for example previous research 3–14 . The authors in Ceretani et al 3 proved the existence and uniqueness of the modified error function for small values of $$$ \delta >0 $$$, and the general case $$$ \delta >-1 $$$ was proved in Bougoffa et al 4 …”