## THERMAL SCIENCE

International Scientific Journal

### MIXED CONVECTION BOUNDARY-LAYER FLOW OF A VISCOELASTIC FLUID DUE TO HORIZONTAL ELLIPTIC CYLINDER WITH CONSTANT HEAT FLUX

**ABSTRACT**

This article presents numerical analysis of mixed convection laminar flow of a second grade viscoelastic fluid due to cylinder of elliptic cross-section with prescribed surface heat flux. Dimensionless non-linear analysis is computed employing Keller-box method. Skin friction coefficient and Nusselt number are emphasized specifically. These quantities are displayed graphically to examine their behavior along the surface of cylinder. The flow and heat transfer rates are carefully judged while varying the important resulting parameters (mixed convection parameter, viscoelastic parameter aspect ratio, etc.) through sketched graphs keeping major axis of ellipse along and perpendicular to the horizontal. These two positions of major axis are termed as blunt and slender orientations, respectively. The values of skin friction and Nusselt number increase with rise in mixed convection parameter. On the other hand, these quantities lessen by increasing the value of viscoelastic parameter.

**KEYWORDS**

PAPER SUBMITTED: 2015-01-20

PAPER REVISED: 2016-12-08

PAPER ACCEPTED: 2016-12-11

PUBLISHED ONLINE: 2017-01-14

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**Issue 1**, PAGES [519 - 531]

- Merkin, J.H., Free convection boundary layers on cylinders of elliptic cross section, J. Heat Transfer 99 (1977), pp. 453-457.
- Merkin, J.H., Mixed convection from a horizontal circular cylinder, Int. J. Heat Mass Transfer 20 (1977), pp. 73-77.
- Bhatacharyya, S. and Pop, I., Free convection from cylinder of elliptic cross section in micropolar fluids, Int. J. Eng. Sci. 34 (1996), pp.1301-1310.
- M.A. Hossain, M.A. Alim, D. Rees, Effect of thermal radiation on natural convection over cylinders of elliptic cross section, Acta Mech. 42 (1998), pp. 177-186.
- S. Ahmad, N.M. Arifin, R. Nazar and I. Pop, Free convection boundary layer flow over cylinders of elliptic cross section with constant surface heat flux, Eur. J. Sci. Res. 23 (2008), pp. 613-625.
- T. Javed, I. Mustafa, H. Ahmad, Effect of thermal radiation on unsteady mixed convection flow near forward stagnation point over a cylinder of elliptic cross section, Thermal science, doi: 10.2298/tsci140926027j (2015).
- T. Javed, H. Ahmad, A. Ghaffari, Mixed convection boundary layer flow over a horizontal elliptic cylinder with constant heat flux, Z. Angew. Math. Phys., 66 (2015), 6, pp. 3393-3403.
- Rashidi, M. M., et al. Mixed convective heat transfer for MHD viscoelastic fluid flow over a porous wedge with thermal radiation, Advances in Mechanical Engineering 6 (2014), pp. 735939.
- Garoosi F., et al., Two-phase mixture modeling of mixed convection of nanofluids in a square cavity with internal and external heating, Powder Technology 275 (2015), pp. 304-321
- Bég, O. A, et al. Double-diffusive radiative magnetic mixed convective slip flow with Biot and Richardson number effects, Journal of Engineering Thermophysics, 23 (2014), 2, pp. 79-97.
- Rashidi, M. M., et al. Group theory and differential transform analysis of mixed convective heat and mass transfer from a horizontal surface with chemical reaction effects, Chemical Engineering Communications, 199 (2012), 8, pp. 1012-1043.
- J.E. Dunn, K.R. Rajagopal, Fluids of differential type: critical review and thermodynamic analysis, Int. J. Eng. Sci. 33 (1995), pp. 689-729.
- P.D. Ariel, Stagnation point flow of a viscoelastic fluid towards a moving plate, Int. J. Eng. Sci. 33 (1995), pp. 1679-1687.
- K.R. Rajagopal, M. Renardy, Y. Renardy, A.S. Wineman, Flow of viscoelastic fluids between plates rotating about distinct axes, Rheol.Acta 25 (1986), pp. 459-467.
- R.A. Cortell, Note on flow and heat transfer of a viscoelastic fluid over a stretching sheet, Int. J. Non- Linear Mech. 41 (2006), pp. 78-85.
- M.S. Abel, S.K. Khan, K.V. Prasad, Study of visco-elastic fluid flow and heat transfer over a stretching sheet with variable viscosity, Int. J. Non-Linear Mech. 37 (2002), pp. 81-88.
- T. Hayat, Z. Abbas, T. Javed, Mixed convection flow of a micropolar fluid over a nonlinear stretching sheet, Physics Letters A372 (2008), pp. 637-647.
- M. Sajid, Z. Abbas, T. Javed, N. Ali, Boundary layer flow of an Oldroyed B fluid in the Region of stagnation point over a stretching sheet, Canadian J. of Physics, 88 (2010), pp. 635-640.
- Abbas, Z., et al., Mass transfer in two MHD viscoelastic fluids over a shrinking sheet in porous medium with chemical reaction species, J. Porous Media 16 (2013), 7, pp. 619-636
- Abbas, Z., et al., Hydromagnetic stagnation point flow of a micropolar viscoelastic fluid towards a stretching/shrinking sheet in the presence of heat generation, Can. J. Phys. 92 (2014), 10, pp. 1113-1123
- Abbas, Z., et al., Chemically reactive hydromagnetic flow of a second grade fluid in a semi-porous channel, J. Appl. Mech. Tech. Phys. 56 (2015), 5, pp. 878-888
- Anwar, I. et al., Mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder, Int. J. Non-Linear Mech. 43 (2008), pp. 814-821.
- Kasim, A.R.M et al., Constant heat flux solution for mixed convection boundary layer viscoelastic fluid, Heat Mass Transfer, 49(2013), pp. 163-171.
- Ahmad, H., Javed, T., Ghaffari, A., Radiation effect on mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder with constant heat flux, Journal of Applied Fluid Mechanics, 9(2016), 3, pp. 1167-1174.
- Garg, V.K. and Rajagopal, K.R., Stagnation point flow of a non-Newtonian fluid, Mech. Res. Commun. 17 (1990), pp. 415-421.
- Keller, H.B. and Cebeci, T., Numerical methods in boundary layer theory, Annual Rev. Fluid Mech. Vol. 10 (1978), pp. 417-33.
- Cebeci, T. and Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer, Springer New York (1984).
- Nazar, R. et al., Mixed convection boundary layer flow from a horizontal circular cylinder with a constant surface heat flux, Int. J. Heat Mass Transfer 40(2004), pp. 219-227.