An analytical method for the solution of two phase Stefan problem in cylindrical geometry

Abstract

Two phase Stefan problem was solved using analytical method in cylindrical domain. To solve governing equations Eigen conditions were formulated by using separation of variable technique. Eigenvalues of the eigencondition were obtained by applying corresponding boundary conditions for liquid and solid phase. Eigenvalues are graphically validated by using window size method in Mathematica. It is noted radial eigenvalues are free from imaginary values. Interface equation obtained from this method were solved and analyzed by varying the Stefan number and introducing the forced and natural convection. Conduction and convection heat transfer mechanism was studied and results obtained by varying thermal diffusivity, thermal conductivity and Stefan number were discussed. Natural convection effects were studied by introducing Rayleigh number and results showed Stefan number has significant effect than Rayleigh number during Phase transition process. Furthermore, eigen function expansion Method was compared with exact solution of Exponential Integral function method and results showed good agreement for Q = 1.