The hybrid application of the Laplace transform technique and the finite difference method (FDM) to one-dimensional Stefan problems involving the radiative and convective boundary condition is studied. The radiative term is linearized by Taylor's series approximation, and then the above hybrid method is used. This scheme is obtained by the use of the Laplace transform technique for the time-dependent terms and the fixed-grid FDM for space domain. It can be found from various illustrated examples that excellent agreement is obtained between the present results and those of early works. For the phase-change problem subjected to the nonlinear boundary condition, three or four iterations are required to obtain a convergent result at a specific time. The present analysis also demonstrates that the application of the Laplace transform technique is no longer limited to phase-change problems with the linear boundary condition.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanical Engineering
- Fluid Flow and Transfer Processes