Freezing over a cylinder with finite heat transfer at the wall

A simple and straightforward implicit numerical technique for phase change problems in cylindrical geometry is proposed. When implicit schemes are used the moving interface along with the convective or radiative boundary condition pose a problem because of the requirement to calculate the interface location and boundary temperature implicitly. Due to this difficulty some of the methods available in literature used approximations near the wall and the rest used iterative methods. The present technique isolates the nonlinearity associated with the moving interface as well as that of any nonlinear wall boundary condition and permits the simultaneous evaluation of the unknown interface location and the wall temperature at the new time level. Thereafter the temperatures at the other nodes are obtained without nodal iterations. Numerical results are obtained for outward solidification with both finite and infinite heat transfer rates at the wall. Good agreement is obtained between the present numerical results and the results available in literature for the limiting cases.