On a mixed boundary value problem of diffusion type

Fluid arriving at the surface of an unevenly heated solid (such as a reactor rod) may initially be converted to steam on the higher temperature portion of the surface; and the extent of the steam covered portion shrinks when there is a continual supply of cooling fluid. A two-dimensional model diffusion problem, involving linear specifications and intended for a determination of the steady advance of the (quench) front which separates the fluid and steam covered parts of a slab face, is resolved in exact fashion and the estimates of a prior approximate calculation (Caflisch and Keller, 1981) are thereby extended.