# Mixed convection boundary-layer flow past a vertical flat plate with a convective boundary condition

M. M. Rahman, J. H. Merkin, I. Pop

Research output: Contribution to journalArticle

17 Citations (Scopus)

The mixed convection boundary-layer flow on a vertical surface with an applied convective boundary condition is considered. Specific forms for the outer flow and surface heat transfer parameter are taken to reduce the problem a similarity system, which is seen to involve three parameters: m, the exponent of the outer flow; λ, the mixed convection parameter and B, the Biot number, as well as the Prandtl number. $${m = \frac{1}{5}}$$m=15 is found to be a transitional case with different behaviour depending on whether $${m > \frac{1}{5}}$$m>15 or $${m <\frac{1}{5}}$$m \frac{1}{5}}$$m>15, there is a critical value λc with solutions only for λ ≥ λc, a range of values of λ where there are dual solutions and the upper solution branch continuing into aiding flow. For$${0 <m <\frac{1}{5}}$$0 \frac{1}{5}}$$m>15 to solutions terminating at a finite value of λ > 0 and continuing to large values of |λ|. For m = 0 (uniform outer flow) only this latter behaviour is seen to arise. When m  \frac{1}{5}}$$m>15. Original language English 2441-2460 20 Acta Mechanica 226 8 https://doi.org/10.1007/s00707-015-1334-2 Published - Mar 20 2015 ### Fingerprint Mixed convection Boundary layer flow Boundary conditions Prandtl number Heat transfer ### ASJC Scopus subject areas • Mechanical Engineering • Computational Mechanics ### Cite this In: Acta Mechanica, Vol. 226, No. 8, 20.03.2015, p. 2441-2460. Research output: Contribution to journalArticle @article{c723ad1ac2fd435ca09fa46eb3ba8092, title = "Mixed convection boundary-layer flow past a vertical flat plate with a convective boundary condition", abstract = "The mixed convection boundary-layer flow on a vertical surface with an applied convective boundary condition is considered. Specific forms for the outer flow and surface heat transfer parameter are taken to reduce the problem a similarity system, which is seen to involve three parameters: m, the exponent of the outer flow; λ, the mixed convection parameter and B, the Biot number, as well as the Prandtl number.$${m = \frac{1}{5}}$$m=15 is found to be a transitional case with different behaviour depending on whether$${m > \frac{1}{5}}$$m>15 or$${m <\frac{1}{5}}$$m \frac{1}{5}}$$m>15, there is a critical value λc with solutions only for λ ≥ λc, a range of values of λ where there are dual solutions and the upper solution branch continuing into aiding flow. For $${0 15 to solutions terminating at a finite value of λ > 0 and continuing to large values of |λ|. For m = 0 (uniform outer flow) only this latter behaviour is seen to arise. When m \frac{1}{5}}$$m>15.",
author = "Rahman, {M. M.} and Merkin, {J. H.} and I. Pop",
year = "2015",
month = "3",
day = "20",
doi = "10.1007/s00707-015-1334-2",
language = "English",
volume = "226",
pages = "2441--2460",
journal = "Acta Mechanica",
issn = "0001-5970",
publisher = "Springer Wien",
number = "8",

}

TY - JOUR

T1 - Mixed convection boundary-layer flow past a vertical flat plate with a convective boundary condition

AU - Rahman, M. M.

AU - Merkin, J. H.

AU - Pop, I.

PY - 2015/3/20

Y1 - 2015/3/20

N2 - The mixed convection boundary-layer flow on a vertical surface with an applied convective boundary condition is considered. Specific forms for the outer flow and surface heat transfer parameter are taken to reduce the problem a similarity system, which is seen to involve three parameters: m, the exponent of the outer flow; λ, the mixed convection parameter and B, the Biot number, as well as the Prandtl number. $${m = \frac{1}{5}}$$m=15 is found to be a transitional case with different behaviour depending on whether $${m > \frac{1}{5}}$$m>15 or $${m <\frac{1}{5}}$$m \frac{1}{5}}$$m>15, there is a critical value λc with solutions only for λ ≥ λc, a range of values of λ where there are dual solutions and the upper solution branch continuing into aiding flow. For$${0 15 to solutions terminating at a finite value of λ > 0 and continuing to large values of |λ|. For m = 0 (uniform outer flow) only this latter behaviour is seen to arise. When m  \frac{1}{5}}$$m>15. AB - The mixed convection boundary-layer flow on a vertical surface with an applied convective boundary condition is considered. Specific forms for the outer flow and surface heat transfer parameter are taken to reduce the problem a similarity system, which is seen to involve three parameters: m, the exponent of the outer flow; λ, the mixed convection parameter and B, the Biot number, as well as the Prandtl number.$${m = \frac{1}{5}}$$m=15 is found to be a transitional case with different behaviour depending on whether$${m > \frac{1}{5}}$$m>15 or$${m <\frac{1}{5}}$$m \frac{1}{5}}$$m>15, there is a critical value λc with solutions only for λ ≥ λc, a range of values of λ where there are dual solutions and the upper solution branch continuing into aiding flow. For $${0 15 to solutions terminating at a finite value of λ > 0 and continuing to large values of |λ|. For m = 0 (uniform outer flow) only this latter behaviour is seen to arise. When m \frac{1}{5}}$$m>15.

UR - http://www.scopus.com/inward/record.url?scp=84931562177&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84931562177&partnerID=8YFLogxK

U2 - 10.1007/s00707-015-1334-2

DO - 10.1007/s00707-015-1334-2

M3 - Article

AN - SCOPUS:84931562177

VL - 226

SP - 2441

EP - 2460

JO - Acta Mechanica

JF - Acta Mechanica

SN - 0001-5970

IS - 8

ER -