Jolley, Ellen; Dang, TD; Smith, Frank; (2024) Melting of wall-mounted ice in shear flow. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , 480 (2283) , Article 20230688. 10.1098/rspa.2023.0688.

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Abstract

The melting of wall-mounted ice deep inside a water layer flow is investigated, the ice being initially in the form of a slender hump or step-up and the oncoming water upstream near the wall being warmer than the ice. The wall is at the same temperature as the oncoming water except beneath the ice where the wall temperature is the same as that of the ice. The unsteady interaction of the flow, heat transfer and phase change is studied analytically and computationally for a basic pure-ice model in two spatial dimensions at high flow rates. In-flow predictions of ice-shape evolution are presented along with the complete melting times and the vanishing points where melting is completed on the solid surface. This is for a range of initial conditions and background heat transfers. The unsteady movement of the contact points at the edges of the ice formation is determined explicitly for the cases of humps and steps, together with the ultimate behaviours of both the ice humps and the ice steps. Effects of reducing the sub-ice wall temperature and accretion leading to flow separation are also discussed.

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