Existence and uniqueness for a convective phase change model with temperature-dependent viscosity

In this article, we consider a class of phase change model with temperature- dependent viscosity, convection and mixed boundary conditions on a bounded domain that reflect melting and solidification in a variety of real-world applications, such as metal casting and crystal growth. The mathematical model, which is based on the enthalpy formulation, takes into consideration the thermophysical differences between the liquid and solid states. The moving liquid-solid interface is explicitly fulfilled as the energy and momentum equations are solved over the full physical domain. Under particular assumptions, we derive various a priori estimates and prove well-posedness results. Numerical simulation of the model employed in the paper is presented as an illustration of an example of a melting problem.& COPY; 2023 Elsevier Inc. All rights reserved.