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)
Mixed convection boundary layer similarity solutions: Prescribed wall heat flux. (English) Zbl 0667.76126
The similarity solutions for mixed convection boundary-layer flow when the wall heat flux is prescribed are analysed in detail in terms of a buoyancy parameter $\alpha$ and m the exponent of the free stream flow. It is shown that for $\alpha >0$ the solution approaches the free convection limit, and for $\alpha <0$, there is a range of $\alpha$, $\alpha\sb s<\alpha <0$, over which dual solutions exist. The nature of the bifurcation at $\alpha =\alpha\sb s$ and how the lower branch of solutions behaves as $\alpha \to 0\sp-$ are also considered. It is established that the solution becomes singular as $m\to 1/5$ and the nature of this singularity is also discussed, where it is shown that two separate cases have to be treated, namely when $\alpha$ is of O(1) and when $\alpha$ is small. Finally it is shown that for m large the solution approaches that corresponding to exponential forms for the free stream and prescribed wall heat flux. Taken all together this information enables a complete description of how the solution behaves over all possible ranges of the parameters $\alpha$ and m to be deduced.

76R05Forced convection (fluid mechanics)
76R10Free convection (fluid mechanics)
35Q99PDE of mathematical physics and other areas
76M99Basic methods in fluid mechanics
Full Text: DOI
[1] E. M. Sparrow, R. Eichhorn and J. L. Gregg,Combined forced and free convection in boundary layer flow. Phys. Fluids2, 319-328 (1959). · Zbl 0086.40601 · doi:10.1063/1.1705928
[2] C. B. Cohen and E. Reshotko,Similar solutions for the compressible boundary layer with heat transfer and pressure gradient. NACA Report 1293 (1956).
[3] G. Wilks and J. S. Bramley,Dual solutions in mixed convection. Proc. Roy. Soc. Edinburgh87A, 349-358 (1981). · Zbl 0449.76074
[4] W. H. H. Banks and P. G. Drazin,Perturbation methods in boundary-layer theory. J. Fluid Mech.58, 763-775 (1973). · Zbl 0263.76026 · doi:10.1017/S002211207300248X
[5] T. Mahmood and J. H. Merkin,Similarity solutions in axisymmetric mixed convection boundary-layer flow. J. Eng. Math.22, 73-92 (1988). · Zbl 0656.76073 · doi:10.1007/BF00044366
[6] R. Eichhorn and M. M. Hasan,Mixed convection about a vertical surface in cross-flow: a similarity solution. J. Heat Transfer102, 775-777 (1980). · doi:10.1115/1.3244391
[7] E. M. Sparrow and J. L. Gregg,Laminar free convection from a vertical plate with uniform surface heat flux. Trans. ASME78, 435-440 (1956).
[8] J. H. Merkin,A note on the similarity solutions for free convection on a vertical plate. J. Eng. Math.19, 189-201 (1985). · Zbl 0577.76083 · doi:10.1007/BF00042533
[9] C. W. Jones and E. J. Watson,Two-dimensional boundary layers, InLaminar boundary layers, (Ed L. Rosenhead). Clarendon Press, Oxford (1963).