zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones. (English) Zbl 1101.76056
Summary: We revisit the boundary value problem for similar stream function $f = f (\eta;\lambda)$ of the Cheng-Minkowycz free convection flow over a vertical plate with power law temperature distribution $T_{w}(x) = T_{\infty} + Ax^{\lambda}$ in a porous medium. It is shown that in the $\lambda$-range $-1/2 < \lambda < 0$, the well-known exponentially decaying “first branch” solutions for velocity and temperature fields are not isolated solutions as one has believed until now, but limiting cases of families of algebraically decaying multiple solutions. For these multiple solutions we give well-converging analytical series. This result yields a bridging to the historical quarreling concerning the feasibility of exponentially and algebraically decaying boundary layers. Owing to a mathematical analogy, our results also hold for similar boundary layer flows induced by continuous surfaces stretched in viscous fluids with power-law velocities $u_w(x) \sim x^\lambda$.

76R10Free convection (fluid mechanics)
76M55Dimensional analysis and similarity (fluid mechanics)
76S05Flows in porous media; filtration; seepage
76D10Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids)
80A20Heat and mass transfer, heat flow
Full Text: DOI