Branching Solutions to Inward Melting Problem in a Horizantal Tube

Abstract

Melting process inside a horizontal circular tube is investigated. Governing equations based on enthalpy formulation are solved by pseudo compressibility method of finite volume type. Small perturbations of four different types are given at the very early stage of melting in order to examine dependence of the solution on the initial disturbance. At Rayleigh number, Ra = 1.0 x 10(6), the flow remained unicellular for all the perturbations prescribed. At a higher Rayleigh number, Ra = 8.0 x 10(6), however, two branching solutions(bicellular and tricellular flow) were obtained depending upon type of initial perturbations. This bifurcation phenomenon can explain the seemingly contradictory melting patterns appeared in the earlier reports.