Periodic melting within a square enclosure with an oscillatory surface temperature

Abstract

This paper presents a numerical study dealing with the natural convection-dominated melting process of a pure metal (tin) from a hot vertical wall, having a uniform surface temperature with a timedependent sinusoidally varying perturbation, of a square enclosure. The enthalpy method is adopted to model the latent heat absorption/release at the moving solid-liquid interface and the Boussinesq approximation is adhered to to simulate the natural convection flow in the melt region. Parametric simulations via a finite difference method have been directed towards the response of the melting process in the enclosure to the imposed oscillatory wall temperature. The ranges of the relevant parameters covered in the present study are Ra = 10 3−5 × 10 5, Sie = 0.007 and 0.07, Sc = 0.2–0.5, p = 0.5—8, and A = 0–0.69. Results clearly demonstrate that a steady periodic melting regime arises following a period of transient oscillatory melting. The heat transfer rates at the vertical hot and cold walls as well as the melting rate exhibit a regular temporal oscillation at a frequency equal to that of the imposed wall temperature perturbation but with phase difference. The effects of relevant parameters on the oscillatory melting behavior are investigated.