Exact solution for a Stefan problem with latent heat a power function of position

Moving boundary problems for the Harry Dym equation and its reciprocal associates

“…Thus, in [31], the latent heat varies inversely withṠ(t), where S(t) ∼ t 1/2 . Indeed, Stefan problems with variable latent heat leading to i = 0 have been extensively studied (see, for example, [32][33][34][35][36] and literature cited therein). It will be seen that for the present class of moving boundary problems (2.6), the similarity reduction requires that i = j.…”

One-dimensional non-Darcy flow in a semi-infinite porous media: a multiphase implicit Stefan problem with phases divided by hydraulic gradients

“…In most situations, the Stefan problem can only be solved numerically; however, finding analytical solutions for the problem has always been of great interest to the researchers. It is encouraging to see that many analytical solutions, which take into account complicated conditions such as nonlinear thermal properties, variable latent heat, and different types of boundaries, have been developed [17][18][19][20][21][22][23][24][25][26][27].…”

Exact solution for Stefan problem with general power-type latent heat using Kummer function

“…Recently, a Stefan problem with space-dependent latent heat has attracted much attention [10][11][12][13][14][15]. Voller et al [12] presented an exact solution for a one-phase Stefan problem with latent heat a linear function of position.…”

“…Lorenzo-Trueba and Voller [13], Salva and Tarzia [14] made some extensions of Voller's solution, and they also considered the linearly distributed latent heat. Zhou et al [15] investigated a Stefan problem in which the latent heat is a power function of position with an integer exponent (positive integer), and they constructed an exact solution using functions of the error integral family.…”