## A Conduction-radiation Fixed Grid Model for Melting of Semitransparent Material
## 摘要This article presents a mathematical model to capture the melt front during melting of two-dimensional semitransparent material. The medium is considered absorbing, emitting and scattering. The radiation field is obtained by solving the equation of transfer. The temperature field is predicted by solving the energy equation with a volumetric radiation source. The finite volume method is adopted to discretize both the equations: the equation of transfer and the energy equation. The enthalpy formulation is used to capture the continuously evolving solid-liquid interface during phase change. The thermo physical properties are taken different for different phases. The inclusion of internal radiation heat transfer makes the problem highly non-linear when the conduction-radiation parameter has a lower value. Most of the studies dealt with constant temperature boundary condition at the wall and the results are discussed at high value of conduction-radiation parameter and thus the nonlinearity effect is not so significant. In reality, the boundary conditions would be either insulated or convective where the temperature at the wall will be unknown priori and will have to be iteratively calculated in the coupled conduction-radiation formulation. As the problem is highly non-linear and thus the numerical solution is prone to be diverged if the non-linear term will not be linearized properly. Further, most of the authors have not considered the volumetric radiative heat flux at the boundary while solving for the temperature at the boundary walls. Rather, they have treated the walls as opaque. So, the present numerical model is made capable of handling all these limitations. The results are validated with those available in the literature. Then, the effect of different parameters such as optical thickness, scattering albedo and the conduction-radiation parameter on the liquid fractions and temperature distribution in the medium are studied. It is observed that when the radiation is dominant, the temperature in the medium is high and hence the liquid fraction is more in contrast to conduction dominated phase change. |

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