EFFECT OF THERMAL RADIATION ON UNSTEADY MIXED CONVECTION FLOW NEAR FORWARD STAGNATION POINT OVER A CYLINDER OF ELLIPTIC CROSS SECTION

Abstract

The effect of thermal radiation on unsteady mixed convection flow near a forward stagnation point over a cylinder of elliptic cross section is investigated in this paper. The governing equations are transformed into dimensionless partial differential equations by using a suitable transformation and then are solved numerically by using an implicit finite difference scheme known as Keller Box method. The accuracy of the results is verified by comparing the obtained results with the previous studies available in the literature. It is shown that the results are highly accurate and are in good agreement. The separation times for both blunt and slender orientations in the presence of thermal radiation are shown in tabular forms. Moreover, the effects of pertinent parameters including Prandtl number Pr, mixed convection parameter λ, thermal radiation parameter Rd, surface temperature parameter θw and blunt/slender orientation parameter ω on the velocity profile, the temperature profile and the Nusselt number are shown graphically. From the present study, it is observed that boundary layer separation occurs early due to thermal radiation and Nusselt number increases for both blunt and slender orientations.

Keywords

Dates

  • Submission Date2014-09-26
  • Revision Date2014-02-02
  • Acceptance Date2015-02-16
  • Online Date2015-03-08

DOI Reference

10.2298/TSCI140926027J

References

  1. Merkin, J. H., Mixed Convection from a Horizontal Circular Cylinder, Int. J. Heat Mass Transfer, 20 (1977), 1, pp. 73-77
  2. Ingham, D. B., Pop, I., Natural Convection about a Heated Horizontal Cylinder in Porous Medium, J. Fluid Mech., 184 (1987), pp. 157-181
  3. Merkin, J. H., Pop, I., A Note on the Free Convection Boundary Layer on a Horizontal Circular Cylinder with Constant Heat Transfer, Warme-und Stoffubert, 22 (1988), 1, pp. 79-81
  4. Nazar, R., et al., Mixed Convection Boundary Layer Flow a Horizontal Circular Cylinder with a Constant Surface Heat Flux, Heat Mass Transfer, 40 (2004), 3, pp. 219-227
  5. Molla, M. M., et al., Natural Convection Flow from an Isothermal Horizontal Circular Cylinder in Presence of Heat Generation, Int. J. Eng. Sci., 44 (2006), 13-14, pp. 949-958
  6. Ahmad, S., et al., Mixed Convection Boundary Layer Flow Past an Isothermal Horizontal Circular Cylinder with Temperature Dependent Viscosity, Int. J. Therm. Sci., 48 (2009), 10, pp. 1943-1948
  7. Hu, H., Koochesfahani, M. M., Thermal Effects on the Wake of a Heated Circular Cylinder Operating in Mixed Convection Regime, J. Fluid Mech., 685 (2011), pp. 235-270
  8. Azim, NHM. A., Chowdhury, M. K., MHD Conjugate Free Convection from an Isothermal Horizontal Circular Cylinder with Joule Heating and Heat Generation, J. Comp. Methods Phys., (2013), Article ID 180516, pp. 11
  9. Nazar, R., et al., Mixed Convection Boundary Layer Flow from a Horizontal Circular Cylinder in Micropolar Fluids: Case of Constant Wall Temperature, Int. J. Numer. Methods Heat Fluid Flow, 13 (2003), 1, pp. 86-109
  10. Anwar, I., et al., Mixed Convection Boundary Layer Flow of a Viscoelastic Fluid over a Horizontal Circular Cylinder, Int. J. Nonlinear Mech., 43 (2008), 9, pp. 814-821
  11. Srinivas, A. T., et al., Mixed Convection Heat Transfer from a Cylinder in Power-Law Fluids: Effect of Aiding Buoyancy, Ind. Eng. Chem. Res., 48 (2009), 21, pp. 9735-9754
  12. Bhowmik, S., et al., Non-Newtonian Mixed Convection Flow from an Isothermal Horizontal Circular Cylinder, Numer. Heat Tr. A-Appl., (2013) (Accepted).
  13. Merkin, J. H., Free Convection Boundary Layers on Cylinders of Elliptic Cross Section, J. Heat Transfer, 99 (1977), pp. 453 - 457
  14. D'Alessio, S. J. D., Dennis, S. C. R., Steady Laminar Forced Convection from an Elliptic Cylinder, J. Eng. Math., 29 (1995), 2, pp. 181 - 193
  15. Hossain, M. A., et al., Effect of Thermal Radiation on Natural Convection over Cylinders of Elliptic Cross Section, Acta Mech., 129 (1998), 3-4, pp. 177- 186
  16. Cheng, C-Y., A Boundary Layer Analysis of Heat Transfer by Free Convection from Permeable Horizontal Cylinders of Elliptic Cross Section in Porous Media using a Thermal Non- Equilibrium Model, Int. Commun. Heat Mass, 34 (2007), 5, pp. 613-622
  17. Ahmad, S., et al., Free Convection Boundary Layer Flow over Cylinders of Elliptic Cross Section with Constant Surface Heat Flux, Eur. J. Sci. Res., 23 (2008), 4, pp. 613-625
  18. Cheng, C-Y., Natural Convection Heat Transfer from a Horizontal Isothermal Elliptical Cylinder with Internal Heat Generation. Int. Commun. Heat Mass, 36 (2009), 4, pp. 346-350
  19. Kaprawi, S., Santoso, D., Convective Heat Transfer from a Heated Elliptic Cylinder at Uniform Wall Temperature, IJEE, 4 (2013), 1, pp. 133-140
  20. Jain, P. C., Goel, B. S., A Numerical Study of Unsteady Laminar Forced Convection from a Circular Cylinder, J. Heat Transfer, 98 (1976), 2, pp. 303-307
  21. Jain, P. C., Lohar, B. L., Unsteady Mixed Convection Heat Transfer from a Horizontal Circular Cylinder, J. Heat Transfer, 101 (1979), 1, pp. 126-131
  22. Ingham, D. B., Merkin, J. H., Unsteady Mixed Convection from an Isothermal Circular Cylinder, Acta Mech., 38 (1981), 1-2, pp. 55-69
  23. Kamrujjaman, et al., Oscillating Free Convection Flow along a Heated Horizontal Circular Cylinder, Proceedings, Applied Mathematics and Mathematical Physics Conf., Sylhet, Ban., 2005
  24. Ali, A., et al., Unsteady Mixed Convection Boundary Layer from a Circular Cylinder in a Micropolar Fluid, Int. J. Chem. Eng., (2010), Article ID 417875
  25. Boricic, A. Z., et al., MHD Effects on Unsteady Dynamic, Thermal and Diffusion Boundary Layer Flow Over a Horizontal Circular Cylinder, Therm. Sci., 16 (2012), 2, pp. 311-321
  26. Chandna, A., Flow Past an Elliptic Cylinder, J. Comput. Appl. Math., 85 (1997), 2, pp. 203- 214
  27. D'Alessio, S. J. D., Steady and Unsteady Forced Convection Past an Inclined Elliptic Cylinder, Acta Mech., 123 (1997), 1-4, pp. 99-115
  28. Williams, M. L., Analytic Study of Unsteady Free Convection from an Inclined Elliptic Cylinder, M. Math. thesis, Waterloo University, Waterloo, Ont., 2004
  29. Jaman, M. K., Hossain, M. A., Effect of Fluctuating Surface Temperature on Natural Convection Flow Over Cylinders of Elliptic Cross section, Int. J. Transp. Phenom., 2 (2010), pp. 35-47
  30. Hiemenz, K., Die Grenzschicht an Einem in den Gleichformingen Flussigkeitsstrom Eingetauch ten Geraden Kreiszylinder, Dingler's Poly. J., 326 (1911), pp. 321-324
  31. Eswara, A. T., Nath, G., Effect of Large Injection Rates on Unsteady Mixed Convection Flow at a Three Dimensional Stagnation Point, Int. J. Non Linear Mech., 34 (1999), 1, pp. 85-103
  32. Nazar, R., et al., Unsteady Mixed Convection Near the Forward Stagnation Point of a Two Dimensional Symmetric Body, Int. Comm. Heat Mass Transfer, 30 (2003), 5, pp. 673-682
  33. Jamaludin, M., et al., Unsteady Mixed Convection Flow over a Cylinder of Elliptic Cross Section near Forward Stagnation Point, Matematika, 28 (2012), 2, pp. 109-125
  34. Siegel, R., Howell, J. R., Thermal Radiation Heat Transfer, McGraw-Hill, New York, 1987
  35. Cebeci, T., Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer, Springer, New York, 1984