# MHD FLOW OF POWELL-EYRING FLUID BY A STRETCHING CYLINDER WITH NEWTONIAN HEATING

## Main Article Content

## Abstract

This paper examines magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder with thermal radiation. Analysis has been presented through inclined magnetic field. Characteristics of heat transfer are analyzed with advanced boundary condition (i.e., Newtonian heating). Suitable transformations convert the nonlinear partial differential equations to the nonlinear ordinary differential equations. Convergent series solutions of momentum and energy equations are developed. Effects of different pertinent parameters on the velocity and temperature distributions are shown graphically. Numerical values of the skin friction coefficient and Nusselt number are also computed and analyzed. Comparison of the present study with the previous published work is also examined. Higher values of fluid M and curvature parameters show enhancement in the fluid velocity while opposite behavior is observed for Hartman number and Suction parameter. Conjugate and radiation parameters lead to an increase in temperature.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2187>. Date accessed: 14 dec. 2017. doi: https://doi.org/10.2298/TSCI150717162H.

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] Patel, M., Timol, M. G., Numerical Treatment of MHD Powell-Eyring Fluid Flow Using the Method of Satisfaction of Asymptotic Boundary Conditions, International Journal of Mathematics and computation, 2 (2011), pp. 71-78

[3] Hayat, T., Awais, M., Asghar, S., Radiative Effects in a Three-dimensional Flow of MHD Eyring- Powell Fluid, Journal of the Egyptian Mathematical Society, 21 (2013), 3, pp. 379-384

[4] Ara, A., Khan, N. A., Khan, H., Sultan, F., Radiation Effect on Boundary Layer Flow of an Eyring- Powell Fluid over an Exponentially Shrinking Sheet, Ain Shams Engineering Journal, 5 (2014), 4, pp. 1337-1342

[5] Hayat, T., Farooq, M., Alsaedi, A., Iqbal, Z., Melting Heat Transfer in the Stagnation Point Flow of PowellEyring fluid, Journal of Thermophysics and Heat Transfer, 27 (2013), 4, pp. 761-766

[6] Ishak, A., MHD Boundary Layer Flow due to an Exponentially Stretching Sheet with Radiation Effect, Sains Malaysiana, 40 (2011), 4, pp. 391-395

[7] Noor, N. F. M., Hashim, I., MHD Flow and Heat Transfer Adjacent to a Permeable Shrinking Sheet Embedded in a Porous Medium, Sains Malaysiana, 38 (2009), 4, pp. 559-565

[8] Turkyilmazoglu, M., MHD Fluid Flow and Heat Transfer due to a Shrinking Rotating Disk, Computers and Fluids, 90 (2014) pp. 51-56

[9] Hayat, T., Anwar, M. S., Farooq, M., Alsaedi, A., MHD Stagnation Point Flow of Second Grade Fluid over a Stretching Cylinder with Heat and Mass Transfer, International Journal of Nonlinear Sciences and Numerical Simulation, 15 (2014), 6, pp. 365-376

[10] Sheikholeslami, M., Ganji, D. D., Gorji-Bandpy, M., Soleimani, S., Magnetic Field Effect on Nanofluid Flow and Heat Transfer using KKL Model, Journal of the Taiwan Institute of Chemi- cal Engineers, 45 (2014), 3, pp. 795-807

[11] Rashidi, M. M., Ferdows, M., Parsa, A. B., Abelman, S., MHD Natural Convection with Con- vective Surface Boundary Condition over a Flat Plate, In Abstract and Applied Analysis Hindawi Publishing Corporation, (2014) 923487

[12] Merkin, J. H., Natural-Convection Boundary-Layer Flow on a Vertical Surface with Newtonian Heating, International Journal of Heat and Fluid Flow, 15 (1994), 5, pp. 392-398

[13] Ramzan, M., Farooq, M., Alsaedi, A., Hayat, T., MHD Three-dimensional Flow of Couple Stress Fluid with Newtonian Heating, The European Physical Journal Plus, 128 (2013), 5, pp. 1-15

[14] Salleh, M. Z., Nazar, R., Free Convection Boundary Layer Flow over a Horizontal Circular Cylin- der with Newtonian Heating, Sains Malaysiana, 39 (2010), 4, pp. 671-676

[15] Salleh, M. Z., Nazar, R., Pop, I., Numerical Solutions of Free Convection Boundary Layer Flow on a Solid Sphere with Newtonian Heating in a Micropolar Fluid, Meccanica, 47 (2012), 5, pp. 1261-1269

[16] Narahari, M., Dutta, B. K., Effects of Thermal Radiation and Mass Diffusion on Free Convection Flow near a Vertical Plate with Newtonian Heating, Chemical Engineering Communications, 199 (2012), 5, pp. 628-643

[17] Javed, T., Ali, N., Abbas, Z., Sajid, M., Flow of an Eyring-Powell Non-Newtonian fluid over a Stretching Sheet, Chemical Engineering Communications, 200 (2013), 3, pp. 327-336

[18] Liao, S., Homotopy Analysis Method in Nonlinear Differential Equations, Higher Education Press (2012), pp. 153-165

[19] Sajid, M., Hayat, T., The Application of Homotopy Analysis Method for MHD Viscous Flow due to a Shrinking Sheet, Chaos, Solitons and Fractals, 39 (2009), 3, pp. 1317-1323

[20] Abbasbandy, S., Shirzadi, A., Homotopy Analysis Method for Multiple Solutions of the Frac- tional Sturm-Liouville Problems, Numerical Algorithms, 54 (2010), 4, pp. 521-532

[21] Liao, S. J., On the Homotopy Multiple-Variable Method and its Applications in the Interactions of Nonlinear Gravity Waves, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), 3, pp. 1274-1303

[22] Abbasbandy, S., Lpez, J. L., Lpez-Ruiz, R., The Homotopy Analysis Method and the Linard Equation, International Journal of Computer Mathematics, 88 (2011), 1, pp. 121-134

[23] Rashidi, M. M., Rastegari, M. T., Asadi, M., Bg, O. A., A Study of Non-Newtonian Flow and Heat Transfer over a Non-Isothermal Wedge Using the Homotopy Analysis Method, Chemical Engineering Communications, 199 (2012), 2, pp. 231-256

[24] Shahzad, A., Ali, R., Approximate Analytic Solution for Magneto-Hydrodynamic Flow of a Non-Newtonian Fluid over a Vertical Stretching Sheet, Can J Appl Sci, 2 (2012), pp. 202-215

[25] Sheikholeslami, M., Ashorynejad, H. R., Domairry, D., Hashim, I., Investigation of the Lami- nar Viscous Flow in a Semi-Porous Channel in the Presence of Uniform Magnetic Field Using Optimal Homotopy Asymptotic Method, Sains Malaysiana, 41 (2012), 10, pp. 1177-1229

[26] Masood, K., Ramzan, A., Shahzad, A., MHD Falkner-Skan Flow with Mixed Convection and Convective Boundary Conditions, Walailak Journal of Science and Technology (WJST), 10 (2013), 5, pp. 517-529

[27] Khan, J. A., Mustafa, M., Hayat, T., Farooq, M. A., Alsaedi, A., Liao, S. J., On Model for Three- dimensional Flow of Nanofluid: An Application to Solar Energy, Journal of Molecular Liquids, 194 (2014) pp.41-47

[28] Aziz, T., Mahomed, F. M., Shahzad, A., Ali, R., Travelling Wave Solutions for the Unsteady Flow of a Third Grade Fluid Induced due to Impulsive Motion of Flat Porous Plate Embedded in a Porous Medium, Journal of Mechanics, 30 (2014), 5, pp. 527-535

[29] Hayat, T., Hussain, Z., Farooq, M., Alsaedi, A., Obaid, M., Thermally Stratified Stagnation Point Flow of an Oldroyd-B Fluid, International Journal of Nonlinear Sciences and Numerical Simulation, 15 (2014), 1, pp. 77-86

[30] Ali, R., Shahzad, A., Khan, M., Ayub, M., Analytic and Numerical Solutions for Axisymmetric Flow with Partial Slip, Engineering with Computers, 32 (2016), 1, pp. 149-154

[31] Hayat, T., Hussain, Z., Alsaedi, A., Farooq, M., Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions PloS one, 11 (2016), 6, p.e0156955

[32] Hayat, T., Hussain, Z., Alsaedi, A., Ahmad, B., Heterogeneous-Homogeneous Reactions and Melting Heat Transfer Effects in Flow with Carbon Nanotubes, Journal of Molecular Liquids, 220 (2016), pp. 200-207

[33] Hayat, T., Khan, M. I., Farooq, M., Yasmeen, T., Alsaedi, A., Stagnation Point Flow with Cattaneo-Christov Heat Flux and Homogeneous-Heterogeneous ReactionsL, Journal of Molec- ular Liquids, 220 (2016), pp. 49-55

[34] Hayat, T., Khan, M. I., Farooq, M., Alsaedi, A., Waqas, M., Yasmeen, T., Impact of CattaneoChris- tov Heat Flux Model in Flow of Variable Thermal Conductivity Fluid over a Variable Thicked Surface, International Journal of Heat and Mass Transfer, 99 (2016), pp. 702-710

[35] Hayat, T., Hussain, Z., Alsaedi, A., Asghar, S., Carbon nanotubes effects in the stagnation point flow towards a nonlinear stretching sheet with variable thickness, Advanced Powder Technology, (2016)

[36] Khan, M. I., Kiyani, M. Z., Malik, M. Y., Yasmeen, T., Khan, M .W .A., Abbas, T., Numerical In- vestigation of Magnetohydrodynamic Stagnation Point Flow with Variable Properties, Alexan- dria Engineering Journal, (2016)