zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Phase changes following the initiation of a hot turbulent flow over a cold solid surface. (English) Zbl 0662.76072
We analyse the melting and/or freezing that can occur when a very large layer of hot fluid begins to flow turbulently over a cold solid retaining boundary. This is a form of Stefan problem and the response is determined by the balance between the turbulent heat flux from the fluid, H, and the (initially infinite) conductive flux into the solid. We show that solidification of the flow at the boundary must always occur initially, unless the freezing temperature of the fluid, T f , is less than the initially uniform temperature, T 0 , of the semi-infinite solid. We determine the evolution of the solidified region and show that with time it will be totally remelted. Melting and ablation of the solid retaining boundary will then generally follow, unless its melting temperature exceeds that of the turbulent flow. The maximum thickness of the solidified crust is shown to scale with k 2 (T f -T 0 ) 2 /ρκHL and its evolution takes place on a timescale of k 2 (T f -T 0 ) 2 /κH 2 , where k is the thermal conductivity, κ the thermal diffusivity, ρ the density and L the latent heat, with all these material properties assumed to be equal for fluid and solid.

MSC:
76F99Turbulence
76T99Two-phase and multiphase flows
80A20Heat and mass transfer, heat flow
76M99Basic methods in fluid mechanics