Numerical solution to N-S equations in the case of unsteady axisymmetric stagnation-point flow on a vertical circular cylinder with mixed convection heat transfer

Document Type : Article

Authors

1 Mechanical Engineering

2 Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box No. 91775-1111, Mashhad, Iran

Abstract

The unsteady problem of impulsive stagnation-point flow on a vertical circular cylinder along with mixed convection heat transfer is solved numerically for the first time. This is because of limitations of similarity solution techniques when we encounter various physical conditions such as time-dependent states. Initially, the fluid is considered to be at rest and with a uniform temperature .  At t=0 this fluid starts flowing toward a vertical cylinder at the strength rate of  and the cylinder surface's temperature rises to Tw, simultaneously. The Navier-Stokes and energy equations in cylindrical coordinate system have been descritized and solved in a 2-D domain by using a SIMPLE based algorithm. The solution has been obtained in three cases. Firstly, when cylinder's wall temperature Tw is constant. Secondly, when Tw varies linearly along cylinder's axis. And thirdly, when it has parabolic variations. Considering a sample case of incompressible flow with Re=1 and ,  the results of Nusselt number, wall shear- stress and dimensionless velocity and temperature have been obtained at different states of cylinder's wall temperature and for some selected values of Grashof numbers. An entropy generation analysis for the case of constant wall temperature is performed which is also for the first time in this subject.

Keywords

Main Subjects


References
1. Hiemenz, K. Axisymmetric stagnation-point
ow on
a cylinder" [Die Grenzchicht an einem in den gleichformingen
Flussigkeitsstrom eingetauchten graden
Kreiszylinder], Dinglers Polytech. J., 236, pp. 321-410
(1911).
2. Wang, C. Axisymmetric stagnation
ow on a cylinder",
Quarterly of Applied Mathematics, 10, pp. 207-
213 (1974).
3. Gorla, R.S.R. Heat transfer in an axisymmetric stagnation

ow on a cylinder", Applied Scienti c Research,
32(5), pp. 541-553 (1976).
4. Gorla, R.S.R. Transient response behavior of an
axisymmetric stagnation
ow on a circular cylinder due
to time dependent free stream velocity", International
Journal of Engineering Science, 16(7), pp. 493-502
(1978).
5. Gorla, R.S.R. Unsteady viscous
ow in the vicinity of
an axisymmetric stagnation point on a circular cylinder",
International Journal of Engineering Science,
17(1), pp. 87-93 (1979).
6. Ramachandran, R., Chen, T.S., and Armaly, B.F.
Mixed convection in stagnation
ows adjacent to
vertical surfaces", ASME J. Heat Transf., 110, pp.
373-377 (1988).
7. Gorla, R. Mixed convection in an axisymmetric stagnation

ow on a vertical cylinder", Acta Mechanica,
99(1-4), pp. 113-123 (1993).
R. Bayat and A.B. Rahimi/Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 2130{2143 2143
8. Takhar, H., Chamkha, A., and Nath, G. Unsteady
axisymmetric stagnation-point
ow of a viscous
uid
on a cylinder", International Journal of Engineering
Science, 37(15), pp. 1943-1957 (1999).
9. Rahimi, A. Heat transfer in an axisymmetric stagnation

ow at high Reynolds numbers on a cylinder using
perturbation techniques", Scientia Iranica, 10(1), pp.
116-121 (2003).
10. Saleh, R. and Rahimi, A.B. Axisymmetric stagnation
point
ow of a viscous
uid on a moving cylinder with
time dependent axial velocity", International Journal
of Engineering, 17(1), p. 8 (2004).
11. Saleh, R. and Rahimi, A. Axisymmetric stagnationpoint

ow and heat transfer of a viscous
uid on a moving
cylinder with time-dependent axial velocity and
uniform transpiration", Journal of Fluids Engineering,
126(6), pp. 997-1005 (2004).
12. Saleh, R. and Rahimi, A. Axisymmetric radial
stagnation-point
ow of a viscous
uid on a rotating
cylinder with time-dependent angular velocity", Scientia
Iranica, 12(4), pp. 329-337 (2005).
13. Rahimi, A.B. and Saleh, R. Axisymmetric stagnation
point
ow and heat transfer of a viscous
uid on a rotating
cylinder with time dependent angular velocity",
Journal of Fluids Engineering, 129, pp. 106-115 (Jan.
2007).
14. Rahimi, A. and Saleh, R. Unaxisymmetric heat
transfer in the axisymmetric Stagnation point
ow of
a viscous
uid on a cylinder with simultaneous axial
and rotational movement along with transpiration",
Scientia Iranica, 15(3), pp. 366-377 (2008).
15. Revnic, C., Grosan, T., Merkin, J., and Pop, I. Mixed
convection
ow near an axisymmetric stagnation point
on a vertical cylinder", Journal of Engineering Mathematics,
64(1), pp. 1-13 (2009).
16. Mohammadiun, H. and Rahimi, A.B. Stagnationpoint

ow and heat transfer of a viscous, compressible

uid on a cylinder", Journal of Thermophysics and
Heat Transfer, 26(3), pp. 494-502 (2012).
17. Lok, Y.Y., Merkin, J.H., and Pop, I. Mixed convection

ow near the axisymmetric stagnation point
on a stretching or shrinking cylinder", International
Journal of Thermal Sciences, 59, pp. 186-194 (2012).
18. Mohammadiun, H., Rahimi, A.B., and Kianifar, A.
Axisymmetric stagnation-point
ow and heat transfer
of a viscous, compressible
uid on a cylinder with
constant heat
ux", Scientia Iranica, 20(1), pp. 185-
194 (2013).
19. Bayat, R. and Rahimi, A.B. Unsteady impulsive
oblique stagnation-point
ow impinging axisymmetrically
on a vertical circular cylinder with mixed
convection heat transfer", Scientia Iranica, 24(4), pp.
1966-1974 (2017).
20. Bejan, A., Entropy Generation Through Heat and
Fluid Flow, New York, Wiley (1994).