# MAGNETOHYDRODYNAMIC FLOW AND HEAT TRANSFER OF A JEFFREY FLUID TOWARDS A STRETCHING VERTICAL SURFACE

## Main Article Content

## Abstract

This study investigates the steady-mixed convection boundary layer flow near a stagnation point that runs about a linearly stretched vertical surface filled with a Jeffery fluid in the presence of a transverse magnetic field. It is assumed that the external velocity impinges normally to the wall and the wall temperature varies linearly with the distance from the stagnation point. The governing partial differential equations that govern the fluid flow are transformed into a set of coupled ordinary differential equations, which are then solved numerically using a finite-difference scheme. The numerical results are presented for some values of parameters, namely the Deborah number γ, the Prandtl number Pr, the magnetic parameter M and the mixed convection parameter λ, for both assisting and opposing flows.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2093>. Date accessed: 28 july 2017. doi: https://doi.org/10.2298/TSCI141103029A.

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] Crane, L.J., Flow Past a Stretching Plate. Zeitschrift für angewandte Mathematik und Physik ZAMP, 21 (1970), 4, pp. 645-647

[3] Hiemenz, K., Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder, Dinglers Polytechn J, 326 (1911), pp. 321–324

[4] Ishak, A., et al., Mixed Convection Boundary Layers in the Stagnation-Point Flow Toward a Stretching Vertical Sheet, Meccanica, 41 (2006), 5, pp. 509–518

[5] Ishak, A., et al., Unsteady Mixed Convection Boundary Layer Flow due to a Stretching Vertical Surface, Arabian Journal for Science and Engineering, 31 (2006), 2B, pp. 165-182

[6] Ishak, A., et al., MHD Mixed Convection Boundary Layer Flow towards a Stretching Vertical Surface With Constant Wall Temperature, International Journal of Heat and Mass Transfer, 53 (2010), 23-24, pp. 5330–5334

[7] Pal, D., Heat and Mass Transfer in Stagnation-Point Flow towards a Stretching Surface in the Presence of Buoyant Force and Thermal Radiation, Meccanica, 44 (2009), 44, pp. 145-158

[8] Ali, F.M., et al., MHD Mixed Convection Boundary Layer Flow toward a Stagnation Point on a Vertical Surface with Induced Magnetic Field, ASME Journal of Heat Transfer, 133 (2010), 2, p. 022502

[9] Chen, C.H., Mixed Convection Unsteady Stagnation-Point Flow towards a Stretching Sheet with Slip Effects, Mathematical Problems in Engineering, 2014 (2014), Article ID 435697, 7 pages

[10] Saleh, S.H.M., et al., Mixed Convection Stagnation-Flow towards a Vertical Shrinking Sheet, International Journal of Heat and Mass Transfer, 73 (2014), pp. 839–848

[11] Ellahi, R., et al., A Study on the Mixed Convection Boundary Layer Flow and Heat Transfer over a Vertical Slender Cylinder, Thermal Science, 18 (2014), 4, pp. 1247-1258

[12] Rashidi, M.M., Mehr, N.F., Series Solutions for the Flow in the Vicinity of the Equator of an Magnetohydrodynamic Boundary-Layer over a Porous Rotating Sphere with Heat Transfer, Thermal Science, 18 (2014), pp. S527-S537

[13] Rashidi, S., et al. Study of Stream Wise Transverse Magnetic Fluid Flow with Heat Transfer Around a Porous Obstacle, Journal of Magnetism and Magnetic Materials, 378 (2015), pp. 128–137

[14] Boricic, A.Z., et al., Magnetohydrodynamic Effects on Unsteady Dynamic, Thermal and Diffusion Boundary Layer Flow over a Horizontal Circular Cylinder, Thermal Science, 16 (2012), pp. S311-S321

[15] Lok, Y., et al., Unsteady Mixed Convection Flow of a Micropolar Fluid Near the Stagnation- Point on a Vertical Surface, International Journal of Thermal Sciences, 45 (2006), 12, pp. 1149–1157

[16] Abbas, Z., et al., Mixed Convection in the Stagnation-Point Flow of a Maxwell Fluid towards a Vertical Stretching Surface, Nonlinear Analysis: Real World Applications, 11 (2010), 4, pp. 3218-3228

[17] Ahmad, K., Nazar, R., Unsteady Magnetohydrodynamic Mixed Convection Stagnation-Point Flow of a Viscoelastic Fluid on a Vertical Surface, Journal of Quality Measurement and Analysis, 6 (2010), 2, pp. 105-117

[18] Das, K., Slip Effects on MHD Mixed Convection Stagnation-Point Flow of a Micropolar Fluid towards a Shrinking Vertical Sheet, Computers & Mathematics with Applications, 63 (2012), 1, pp. 255-267

[19] Makinde, O.D., et al., Buoyancy Effects on MHD Stagnation-Point Flow and Heat Transfer of a Nanofluid Past a Convectively Heated Stretching/Shrinking Sheet, International Journal of Heat and Mass Transfer, 62 (2013), pp. 526-533

[20] Ellahi, R.,The Effects of MHD and Temperature Dependent Viscosity on the Flow of Non- Newtonian Nanofluid in a Pipe: Analytical Solutions, Applied Mathematical Modelling, 37 (2013), 3, pp. 1451-1457

[21] Ellahi, R., et al., M., Series Solutions of Magnetohydrodynamic Peristaltic Flow of a Jeffrey Fluid in Eccentric Cylinders, Applied Mathematics & Information Sciences, 7 (2013), pp. 1441- 1449

[22] Singh, V., Agarwal, S., MHD Flow and Heat Transfer for Maxwell Fluid over an Exponentially Stretching Sheet with Variable Thermal Conductivity in Porous Medium, Thermal Science, 18 (2014), pp. S599-S615

[23] Abdel-Rahman, G.M., Effects of Variable Viscosity and Thermal Conductivity on Unsteady MHD Flow of Non-Newtonian Fluid over a Stretching Porous Sheet, Thermal Science, 17 (2013), pp. 1035-1047

[24] Yacob, N.A. et al., Hydromagnetic Flow and Heat Transfer Adjacent to a Stretching Vertical Sheet in a Micropolar Fluid, Thermal Science, 17 (2013), pp. 525-532

[25] Sheikholeslami, M., et al., Effects of MHD on Cu-Water Nanofluid Flow and Heat Transfer by Means of CVFEM, Journal of Magnetism and Magnetic Materials, 349 (2014), pp. 188-200

[26] Zeeshan, A., et al., Magnetohydrodynamic Flow of Water/Ethylene Glycol Based Nanofluids with Natural Convection Through Porous Medium, The European Physical Journal Plus, 129 (2014), pp. 261

[27] Lin, Y., et al. MHD Thin Film and Heat Transfer of Power Law Fluids over an Unsteady Stretching Sheet with Variable Thermal Conductivity, Thermal Science (2015), online first

[28] Hayat, T., et al., An Analysis of Peristaltic Transport for Flow of a Jeffrey Fluid, Acta Mechanica, 193 (2007), 1-2, pp. 101–112

[29] Ramachandran, N., et al., Mixed Convection in Stagnation Flows Adjacent to Vertical Surfaces, ASME Journal of Heat Transfer, 110 (1988), 2, pp. 373–377

[30] Cebeci, T., Convective Heat Transfer, Horizon Publishing, California, USA, 2002.

[31] Cebeci, T., Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer, Springer, New York, USA, 1988.

[32] Mahapatra, T.R., Gupta, A.S., Heat Transfer in Stagnation-Point towards a Stretching Sheet, Heat Mass Transfer, 38 (2002), 6, pp. 517-521

[33] Nazar, R., et al., Unsteady Boundary Layer Flow in the Region of the Stagnation Point on a Stretching Sheet, International Journal of Engineering Science, 42 (2004), 11-12, pp. 1241– 1253

[34] Reiner, M., The Deborah number, Physics Today, 17 (1964), 1, pp. 62

[35] Schlichting, H., Boundary Layer Theory, McGraw-Hill, New York, USA, 1968