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

## Main Article Content

## 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.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2089>. Date accessed: 24 june 2017. doi: https://doi.org/10.2298/TSCI140926027J.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright of the published article and have the right to use the article in the ways permitted to third parties under the - Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence. Full bibliographic information (authors, article title, journal title, volume, issue, pages) about the original publication must be provided and a link must be made to the article's DOI.

The authors and third parties who wish use the article in a way not covered by the the -Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence must obtain a written consent of the publisher. This license allows others to download the paper and share it with others as long as they credit the journal, but they cannot change it in any way or use it commercially.

Authors grant to the publisher the right to publish the article, to be cited as its original publisher in case of reuse, and to distribute it in all forms and media.

Accepted 2017-03-13

Published 2017-03-13

## References

[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