Technical Papers
Jul 28, 2015

Magnetohydrodynamic Stagnation Point Flow and Heat Transfer of Casson Nanofluid Past a Stretching Sheet with Slip and Convective Boundary Condition

Publication: Journal of Aerospace Engineering
Volume 29, Issue 2

Abstract

The present study examines the effect of slip and convective boundary condition on magnetohydrodynamic (MHD) stagnation point flow and heat transfer due to Casson nanofluid past a stretching sheet. Similarity transformation is used to convert the nonlinear governing equations and their associated boundary conditions into dimensionless form. The resulting system of ordinary differential equations is then solved numerically using the Runge-Kutta-Fehlberg method along with shooting technique. Numerical results are obtained for velocity, temperature, and concentration distribution as well as for the skin friction coefficient, the local Nusselt number, and Sherwood number. It is found that the local Nusselt number and Sherwood number decrease with an increase in Casson parameter γ. However, the skin friction coefficient -f(0) increases with an increase in Casson parameter γ and decreases with an increase in velocity ratio parameter A. The results are displayed both in graphical and tabular form to illustrate the effect of the governing parameters on the dimensionless velocity, temperature, and concentration. Then, comparison has been made and found to be in good agreement with a previous published result on special cases of the problem.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

The authors wish to express their very sincere thanks to the referees for their valuable comments and suggestions.

References

Aminreza, N., Rashid, P., and Mohammed, G. (2012). “Effect of partial slip boundary condition on the flow and heat transfer of nanofluid past a stretching sheet prescribed constant wall temperature.” Int. J. Therm. Sci., 54, 253–261.
Andersson, H. (2002). “Slip flow past a stretching surface.” Acta Mech., 158(1–2), 121–125.
Attia, H. A., and Sayed, M. E. (2010). “Transient MHD Couette flow of a Casson fluid between parallel plates with heat transfer.” Ital. J. Pure Appl. Math., N-27, 19–38.
Aziz, A. (2009). “Similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition.” Commun. Non-Linear Sci. Numer. Simul., 14(4), 1064–1068.
Aziz, A. (2010). “Hydrodynamic and thermal slip flow boundary layer over a flat plate with constant heat flux boundary condition.” Commun. Non-Linear Sci. Numer. Simul., 15(3), 573–580.
Bachok, N., Ishak, A., Nazar, R., and Pop, I. (2010). “Flow and heat transfer at a general three-dimensional stagnation point in nanofluid.” J. Phys. B, 405(24), 4914–4918.
Bataller, C. (2008). “Radiation effect for the Blasius and Sakiadis flows with convective surface boundary condition.” Appl. Math. Comput., 206(2), 832–840.
Bhattacharyyaa, K., Hayat, T., and Alsaedic, A. (2013). “Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer.” Chin. Phys. B, 22(2), 024702.
Crane, L. J. (1970). “Flow past a stretching plate.” J. Appl. Math. Phys., 21(4), 645–647.
Haq, R. U., Nadeem, S., Khan, Z. H., and Okedayo, T. G. (2014). “Convective heat transfer and MHD effects on Casson nanofluod flow over a shrinking sheet.” Cent. Eur. J. Phys., 12(12), 862–871.
Hayat, T., Qasim, M., and Mesloub, S. (2011). “MHD flow and heat transfer over permeable stretching sheet with slip conditions.” Int. J. Numer. Methods Fluids, 66(8), 963–975.
Hayat, T., Shehzad, S. A., and Alsaedi, A. (2012). “Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid.” Appl. Math. Mech., 33(10), 1301–1312.
Hiemenz, K. (1911). “Die Grenzschicht an Einem in den Gleichformingen Flussigkeitsstrom Eingetauchten Geraden Kreiszylinder.” Dingler Polytech. J., 326, 321–410.
Ibrahim, W., and Shankar, B. (2013). “MHD boundary layer flow and heat transfer of a nanofluid past a permeable stretching sheet with velocity, thermal and solutal slip boundary conditions.” J. Comput. Fluids, 75, 1–10.
Ibrahim, W., Shankar, B., and Mahantesh, M. (2013). “MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet.” Int. J. Heat Mass Transfer, 56(1–2), 1–9.
Ibrahim, W., and Shanker, B. (2012). “Boundary-layer flow and heat transfer of nanofluid over a vertical plate with convective surface boundary condition.” J. Fluids Eng.-Trans., 134(8), 081203.
Ishak, A. (2010). “Similarity solution for flow and heat transfer over a permeable surface with convective boundary condition.” Appl. Math. Comput., 217(2), 837–842.
Ishak, A., Bachok, N., Nazar, R., and Pop, I. (2010). “MHD mixed convection flow near the stagnation-point on a vertical permeable surface.” Phys. A, 389(1), 40–46.
Ishak, A., Jafar, K., Nazar, R., and Pop, I. (2009). “MHD stagnation point flow towards a stretching sheet.” Phys. A, 388(17), 3377–3383.
Ishak, A., Yacob, A., and Bachok, N. (2011). “Radiation effect on the thermal boundary layer flow over a moving plate with convective condition.” Meccanica, 46(4), 795–801.
Khan, W. A., and Aziz, A. (2011). “Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux.” Int. J. Thermal Sci., 50(7), 1207–1214.
Khan, W. A., and Pop, I. (2010). “Boundary layer flow of a nanofluid past a stretching sheet.” Int. J. Heat Mass Transfer, 53(11–12), 2477–2483.
Kuznetsov, A. V., and Nield, D. A. (2010). “Natural convective boundary-layer flow of a nanofluid past a vertical plate.” Int. J. Thermal Sci., 49(2), 243–247.
Mahapatra, T. R., and Gupta, A. S. (2001). “Magnetohydrodynamics stagnation-point flow towards a stretching sheet.” Acta Mech., 152(1–4), 191–196.
Mahapatra, T. R., Nandy, S. K., and Gupta, A. S. (2009). “Magnetohydrodynamic stagnation point flow of a power-law fluid towards a stretching sheet.” Int. J. Non-Linear Mech., 44(2), 124–129.
Makinde, O. D., and Aziz, A. (2011). “Boundary layer flow of a nanofluid past a stretching sheet with convective boundary condition.” Int. J. Thermal Sci., 50(7), 1326–1332.
Mostafa, M., Hayat, T., Pop, I., Ashar, S., and Obaidat, S. (2011). “Stagnation point flow of a nanofluid towards a stretching sheet.” Int. J. Heat Mass Transfer, 54(25–26), 5588–5594.
Mukhopadhyay, S., Chandra Mondal, I., and Chamkha, A. J. (2013). “Casson fluid flow and heat transfer past a symmetric wedge.” Heat Transfer Asian Res., 42(8), 665–675.
Nadeem, S., Haq, R. U., and Akbar, N. S. (2014). “MHD three dimensional boundary layer flow of Casson nanofluid past a linearly stretching sheet with convective boundary condition.” IEEE Trans. Nonotechnol., 13(1), 109–115.
Nadeem, S., Haq, R. U., and Lee, C. (2012). “MHD flow of a Casson fluid over an exponentially shrinking sheet.” Sci. Iranica B, 19(6), 1550–1553.
Olanrewaju, A. M., and Makinde, O. D. (2013). “On boundary layer stagnation point flow of a nanofluid over a permeable flat surface with Newtonian heating.” Chem. Eng. Comm., 200(6), 836–852.
Pavlov, K. B. (1974). “Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface.” Magnitnaya Gidrodinamika, 10(4), 146–148.
Sakiadis, B. C. (1961a). “Boundary layer behaviour on continuous solid surface: II. The boundary layer on a continuous flat surface.” J. Am. Inst. Chem. Eng., 7(2), 221–225.
Tsou, F. K., Sparrow, E. M., and Goldstein, R. J. (1967). “Flow and heat transfer in the boundary layer on a continuous moving surface.” Int. J. Heat Mass Transfer, 10(2), 219–235.
Yacob, A., Ishak, A., Pop, I., and Vajavelu, K. (2011). “Boundary layer flow past a stretching/shrinking surface beneath an external uniform shear flow with convective surface boundary condition in a nanofluid.” Nanoscale Res. Lett., 6(314), 1–7.
Yao, S., Fang, T., and Zhong, Y. (2011). “Heat transfer of a generalized stretching/shrinking wall problem with convective boundary condition.” Commun. Nonlinear Sci. Numer. Simul., 16(2), 752–760.

Information & Authors

Information

Published In

Go to Journal of Aerospace Engineering
Journal of Aerospace Engineering
Volume 29Issue 2March 2016

History

Received: Sep 5, 2014
Accepted: May 28, 2015
Published online: Jul 28, 2015
Discussion open until: Dec 28, 2015
Published in print: Mar 1, 2016

Permissions

Request permissions for this article.

Authors

Affiliations

Wubshet Ibrahim [email protected]
Assistant Professor, Dept. of Mathematics, Ambo Univ., Ambo, P.O. Box 19, Ambo, Ethiopia (corresponding author). E-mail: [email protected]
O. D. Makinde
Professor, Faculty of Military Science, Stellenbosch Univ., Saldanha 7395, South Africa.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share