ME812 – Conductive Heat Transfer Homework #9 (due 12/11/22 11:59pm) Problem 1 Solve a similar Neumann’s problem for the case of melting. A solid in x > 0 is initially at a uniform temperature Ti which is lower than the melting temperature Tm. For times t > 0 the boundary surface at x = 0 is raised to a temperature T0 (> Tm), and kept at that temperature. As a result, melting starts at the surface x = 0 and the solid-liquid interface moves in the positive x direction. Determine the temperature distribution in the liquid and solid phases, and the location of the solid-liquid interface as a function of time. Problem 2 A liquid at the melting temperature Tm is confined to a half-space x > 0. At time t = 0 the boundary at x = 0 is lowered to a temperature T0, which is lower than Tm, and maintained at that temperature for times t > 0. As a result, solidification starts at x = 0 and the solid-liquid interface moves in the positive x direction. Using the integral method of solution, solve this problem and obtain an expression for the temperature distribution in the solid, and for the location of the solid-liquid interface. (Note: the liquid phase remains at a constant temperature Tm throughout; the temperature is unknown only in the solid phase.)
