Optimization of thermocapillary-driven melting in trapezoidal and triangular geometry in microgravity

Abstract

A numerical analysis of thermocapillary-driven melting in trapezoidal and triangular geometry in microgravity is presented. The phase change transition is modelled using an enthalpy-porosity-based formulation of the Navier-Stokes equations, where the solid and liquid phases are treated as a single layer with physical properties depending on the local temperature, and analyzed for the organic phase change material (PCM) n-octadecane, due to its relevance to recent and upcoming microgravity research. We describe first the melting process in rectangular geometry, which is characterized by a final diffusive stage that largely determines the melting time τM, where the solid PCM near the cold boundary melts slowly. Other geometries are proposed to optimize the process and minimize τM. By inclining the cold lateral wall, melting can be accelerated substantially. We find a maximum reduction in τM by a factor of 3 in the limiting case of a right triangle — the optimal geometry within the scope of the present work. For completeness, the process is analyzed in the symmetric trapezoids that result from inclining the hot lateral wall. An increase (reduction) of the overall melting time (rate) is observed at moderate inclination angles, associated with a PCM region dominated by weak thermal diffusion. Finally, the effect of Γ is presented in both rectangular geometry and the optimal triangular geometry, suggesting a general scaling τM∝Γ−1.25.