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.)