Abstract
The mixed convection flow near an axisymmetric stagnation point on a vertical cylinder is considered. The equations for the fluid flow and temperature fields reduce to similarity form that involves a Reynolds number R and a mixed convection parameter λ, as well as the Prandtl number σ. Numerical solutions are obtained for representative values of these parameters, which show the existence of a critical value λ c = λ c (R, σ) for the existence of solutions in the opposing (λ < 0) case. The variation of λ c with R is considered. In the aiding (λ > 0) case solutions are possible for all λ and the asymptotic limit λ → ∞ is obtained. The limits of large and small R are also treated and the nature of the solution in the asymptotic limit of large Prandtl number is briefly discussed.
Authors
C. Revnic
Tiberiu Popoviciu Institute of Numerical Analysis Cluj, Romanian Academy
T. Grosan
Applied Mathematics, Babes-Bolyai University Cluj, Romania
J. Merkin
Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK
I. Pop
Applied Mathematics, Babes-Bolyai University, Cluj, Romania
Keywords
Asymptotic solutions; Axisymmetric stagnation flow; Boundary layers; Dual solutions; Mixed convection
References
Paper coordinates
C. Revnic, T. Grosan, J. Merkin, I. Pop, Mixed convection flow near an axisymmetric stagnation point on a vertical cylinder, Journal of Engineering Mathematics, 64 (2009), pp. 1–13,
doi: 10.1007/s10665-008-9248-9
soon
About this paper
Publisher Name
Springer
Print ISSN
0022-0833
Online ISSN
1573-2703
Google Scholar Profile
soon
[1] Hiemenz K (1911) Die Grenzschicht an einem in den gleich formigen Flussigkeitsstrom eingetacuhten geraden Kreisszylinder. Dinglers Polytech J 326: 321–324
Google Scholar
[2] Eckert ERG (1942) Die Berechnung des Wärmeüberganges in der laminaren Grenzschicht um stromter Korper. VDI – Forchungsheft 416: 1–24
MathSciNet Google Scholar
[3] Gorla RSR (1976) Heat transfer in an axisymmetric stagnation flow on a cylinder. Appl Sci Res 32: 541–553
Article Google Scholar
[4] Hommann F (1936) Der Einfluss grosser Zähigkeit bei der Stromung um den Cylinder und um die Kugel. J Appl Math Phys (ZAMP) 16: 153–164
Google Scholar
[5] Smith FT (1974) Three dimensional stagnation point flow in a corner. Proc R Soc Lond A 344: 489–507
ADS Google Scholar
[6] Wang CY (1974) Axisymmetric stagnation flow on a cylinder. Quart Appl Math 32: 207–213
MATH Google Scholar
[7] Gorla RSR (1978) Nonsimilar axisymetric stagnation flow on a moving cylinder. Int J Eng Sci 16: 392–400
Article Google Scholar
[8] Weidman PD, Putkaradze V (2003) Axisymmetric stagnation flow obliquely impinging on a circular cylinder. Eur J Mech B/Fluids 22: 123–131
Article Google Scholar
[9] Weidman PD, Mahalingam S (1997) Axisymmetric stagnation-point flow impinging on a transversely oscillating plate with suction. J Eng Math 31: 305–318
MATH Article MathSciNet Google Scholar
[10] Gorla RSR (1979) Unsteady viscous flow in the vicinity of an axisymmetric stagnation point on a circular cylinder. Int J Eng Sci 17: 87–93
Article Google Scholar
[11] Ramachandran N, Chen TS, Armaly BF (1988) Mixed convection in stagnation flows adjacent to vertical surface. J Heat Trans 110: 173–177
Google Scholar
[12] Gorla RSR (1993) Mixed convection in an axisymmetric stagnation flow on a vertical cylinder. Acta Mech 99: 113–123
MATH Article Google Scholar
[13] Kuiken HK (1974) The thick free-convective boundary-layer along a semi-infinite isothermal vertical cylinder. J Appl Math Phys (ZAMP) 25: 497–514
MATH Article Google Scholar
[14] Naraian IP, Uberoi MS (1972) Combined forced and free convection heat transfer from thin needles in a uniform stream. Phys Fluids 15: 1879–1882
Article ADS Google Scholar
[15] Naraian IP, Uberoi MS (1973) Combined forced and free convection over thin needles. Int J Heat Mass Trans 16: 1505–1511
Article Google Scholar
[16] Chen ILS (1987) Mixed convection flow about slender bodies of revolution. J Heat Trans 109: 1033–1036
Article Google Scholar
[17] Wang CY (1990) Mixed convection on a vertical needle with heated tip. Phys Fluids A 2: 622–625
Article ADS Google Scholar
[18] Merkin JH (1985) On dual solutions occurring in mixed convection in a porous medium. J Eng Math 20: 171–179
Article MathSciNet Google Scholar
[19] Merkin JH, Mahmood T (1989) Mixed convection boundary layer similarity solutions: prescribed wall heat flux. J Appl Math Phys (ZAMP) 40: 51–68
MATH Article MathSciNet Google Scholar
[20] Stewartson K, Jones LT (1957) The heated vertical plate at high Prandtl number. J Aeronaut Sci 24: 379–380
Google Scholar
[21] Kuiken HK (1968) The heated vertical plate at high Prandtl number free convection. J Eng Math 2: 355–371
MATH Article Google Scholar
[22] Slater LJ (1960) Confluent hypergeometric functions. Cambridge University Press, Cambridge
Google Scholar
[23] Wilks G, Bramley JS (1981) Dual solutions in mixed convection. Proc R Soc Edinb 87A: 349–358
MathSciNet Google Scholar