TY  - JOUR
AB  - Purpose– The mathematical model of a two-phase Lamé-Clapeyron-Stefan problem for a semi-infinite material with a density jump is considered. The purpose of this paper is to study the analytical solutions of the models and show the performance of several parameters. Design/methodology/approach– To describe the heat conduction, the Caputo type time fractional heat conduction equation is used and a convective term is included since the changes in density give rise to motion of the liquid phase. The similarity variables are used to simplify the models. Findings– The analytical solutions describing the changes of temperature in both liquid and solid phases are obtained. For the solid phase, the solution is given in the Wright function form. While for the liquid phase, since the appearance of the advection term, an approximate solution in series form is given. Based on the solutions, the performance of the parameters is discussed in detail. Originality/value– From the point of view of mathematics, the moving boundary problems are nonlinear, so barely any analytical solutions for these problems can be obtained. Furthermore, there are many applications in which a material undergoes phase change, such as in melting, freezing, casting and cryosurgery.
VL  - 24
IS  - 6
SN  - 0961-5539
DO  - 10.1108/HFF-03-2013-0102
UR  - https://doi.org/10.1108/HFF-03-2013-0102
AU  - Li Xicheng
ED  - Dr Hong-Yan Liu and Dr Ji-Huan He
PY  - 2014
Y1  - 2014/01/01
TI  - Analytical solutions to a fractional generalized two phase Lame-Clapeyron-Stefan problem
T2  - International Journal of Numerical Methods for Heat & Fluid Flow
PB  - Emerald Group Publishing Limited
SP  - 1251
EP  - 1259
Y2  - 2024/04/24
ER  -