Document Type : Research Paper


1 SJM Institution of Technology CHitradurga-577502, Karnataka,

2 Presidency University, Bangalore

3 COMSATS Institute of Information Technology, Pakisthan

4 Department of Studies and Research in Mathematics, Kuvempu University,Shankaraghatta-577 451, Shimoga, Karnataka, INDIA


In this article, we examined the behavior of chemical reaction effect on a magnetohydrodynamic Prandtl nanofluid flow due to stretchable sheet. Non-linear thermally radiative term is accounted in energy equation. Constructive transformation is adopted to formulate the ordinary coupled differential equations system. This system of equations is treated numerically through Runge Kutta Fehlberg-45 method based shooing method. The role of physical constraints on liquid velocity, temperature and concentration are discussed through numerical data and plots. Also, the skin friction co-efficient, local Nusselt number and local Sherwood numbers are calculated to study the flow behavior at the wall, which is also presented in tabular form. A comparative analysis is presented with the previous published data in special case for the justification of the present results. The output reveals that for larger values of elastic and Prandtl parameter, the thickness of momentum layer enhanced and the rates of both heat and mass transport reduced. Also, increment of slip parameter decelerated both temperature and concentration filed while nonlinear form thermal radiation rapidly increases the temperature.  

Graphical Abstract

Magneto Prandtl nanofluid past a stretching surface with non-linear radiation and chemical reaction


Main Subjects

[1] S. U. S. Choi and J. A. Eastman, “Enhancing thermal conductivity of fluids with nanoparticles”, Proceedings of the ASME Int. Mech. Eng. Congress and Exposition, Vol. 66, pp. 99–105, (1995).
[2] J. Buongiorno, “Convective transport in nanofluids”, ASME J. Heat. Trans., Vol. 128, No. 3, pp. 240–250, (2005).
[3] W. A. Khan and I. Pop, “Boundary-layer flow of a nanofluid past a stretching sheet”, Int.J. Heat and Mass Transfer, Vol. 53, No. 11–12, pp. 2477–2483, (2010).
[4] O. D. Makinde, W. A. Khan and Z. H. Khan, “Buoyancy effects on MHD stagnation point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet”, Int. J. of Heat and Mass Transfer, Vol. 6, No. 2, pp. 526–533, (2013).
[5] M. Sheikholeslami, S. Abelman and D. D. Ganji, “Numerical simulation of MHD nanofluid flow and heat transfer considering viscous dissipation”, Int. J. Heat Mass Transfer, Vol. 79, pp. 212-222, (2014).
[6] G. K. Ramesh, “Numerical study of the influence of heat source on stagnation point flow towards a stretching surface of a Jeffrey nanoliquid”, Journal of Engineering. Vol. 2015, 10 pages, (2015).
[7] G. K. Ramesh, S. A. Shehzad ,T. Hayat and A. Alsaedi, “Activation energy and chemical reaction in Maxwell magneto-nanoliquid with passive control of nanoparticle volume fraction”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 40, pp. 422, (2018).
[8] B. J. Gireesha, K. Ganesh Kumar, G. K. Ramesh, and B. C. Prasannakumara, “Nonlinear convective heat and mass transfer of Oldroyd-B nanofluid over a stretching sheet in the presence of uniform heat source/sink”, Results in Physics, Vol. 9, pp. 1555-1563 (2018).
[9] K. Govardhan, G. Nagaraju, K. Kaladhar and M. Balasiddulu, “MHD and radiation effects on mixed convection unsteady flow of micropolar fluid over a stretching sheet”, Procedia Comp. Sci., Vol. 57, pp. 65–76, (2015).
[10] R. Cortell, “A note on magnetohydrodynamic flow of a power-law fluid over a stretching sheet”, Appl. Math. Comput. Vol. 168, pp. 557–566, (2005).
[11] M. Y. Malik, T. Salahuddin, A. Hussain and S. Bilal, “MHD flow of tangent hyperbolic fluid over a stretching cylinder: Using Keller box method”, J. of Magnetism and Magnetic Materials, Vol. 395, pp. 271–276, (2015).
[12] R. Nasrin, S. Parvin and M. A. Alim, “Prandtl number effect on assisted convective heat transfer through a solar collector”, Applications and Applied Mathematics: An Int. J., Vol. 2, pp. 22-36, (2016).
[13] N. S. Akbar, S. Nadeem, R. Ul Haq and Z. H. Khan, “Numerical solutions of Magneto hydrodynamic boundary layer flow of tangent hyperbolic fluid flow towards a stretching sheet with magnetic field”, Indian J. Phys., Vol. 87, No. 11, pp. 1121–1124, (2013).
[14] R. Nasrin and M. A. Alim, “Prandtl number effect on free convective flow in a solar collector utilizing nanofluid”, Engg. Transac., Vol. 7, No. 2, pp. 62-72, (2012).
[15] S. Nadeem, S. Ijaz and N. S. Akbar, “Nanoparticle analysis for blood flow of Prandtl fluid model with stenosis”, Int. Nano Letters, Vol. 3, No. 35, pp. 2-13, (2013).
[16] S. A. Shehzad, T. Hayat, A. Alsaedi and A. O. Mustafa, “Nonlinear thermal radiation in three-dimensional flow of Jeffrey nanofluid: A model for solar energy”, Appl. Math. And Compu., Vol. 248, pp. 273–286, (2014).
[17] A. Zaib, M. M. Rashidi, A. J. Chamkha and N. F. Mohammad, “Impact of nonlinear thermal radiation on stagnation-point flow of a Carreau nanofluid past a nonlinear stretching sheet with binary chemical reaction and activation energy”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. Vol. 232, No. 6, pp. 962-972, (2017).
[18] T. Hayat, S. Qayyum, A. Alsaedi and S. A. Shehzad, “Nonlinear thermal radiation aspects in stagnation point flow of tangent hyperbolic nanofluid with double diffusive convection”, Journal of Molecular Liquids, Vol. 223, pp. 969-978, (2016).
[19] T. Hayat, T. Muhammad, A. Alsaedi and M.S. Alhuthali, “Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation”, J. Magnetism and Magnetic Materials, Vol. 385, pp. 222–229, (2015).
[20] G. K. Ramesh and B. J. Gireesha, “Flow over a stretching sheet in a dusty fluid with radiation effect”, ASME J. Heat transfer, Vol. 135, No. 10, pp. 102702(1-6), (2013).
[21] M. Mustafa, A. Mushtaq, T. Hayat,and A. Alsaedi, “Numerical study of the non-linear radiation heat transfer problem for the flow of a second-grade fluid”, J. Bulgarian Chemi. Commun., Vol. 47, No. 2, pp. 725-732, (2015).
[22] G. K. Ramesh, A. J. Chamkha and B. J. Gireesha, “Boundary layer flow past an inclined stationary/moving flat plate with convective boundary condition”, Afrika Matematika, Vol. 27. No. 1-2, pp. 87-95, (2016).
[23] C. Y. Wang, “Flow due to a stretching boundary with partial slip an exact solution of the Navier-Stokes equations”, Chem. Eng. Sci., Vol. 57, pp. 3745–3747, (2002).
[24] S. Mukhopadhyay and R. S. R. Gorla, “Effects of partial slip on boundary layer flow past a permeable exponential stretching sheet in presence of thermal radiation”. Heat Mass Trans., Vol. 45, pp. 1447–1452, (2009).
[25] T. Fang, S. Yao, J. Zhang and A. Aziz, “Viscous flow over a shrinking sheet with a second order slip flow model”. Commun. Nonlinear Sci. and Numerical Simul., Vol. 15, No. 7, pp. 1831–1842, (2010).
[26] K. Bhattacharyya, S. Mukhopadhyay and G. C Layek, “Slip effects on boundary layer stagnation-point flow and heat transfer towards a shrinking sheet”, Int. J. Heat and Mass Tran., Vol. 54, No. 1–3, pp. 308–313, (2011).
[27] S. Das, R. N. Jana and O. D. Makinde, “MHD boundary layer slip flow and heat transfer of nanofluid past a vertical stretching sheet with non-uniform heat generation/absorption”. Int. J. Nanosci., Vol. 13, No. 3, 1450019 (2014).
[28] M. Kezzar and M. Rafik Sari, “Series solution of nanofluid flow and heat transfer between stretchable/shrinkable inclined walls”, International Journal of Applied and Computational Mathematics, Vol.3, No. 3, pp. 2231–2255, (2017).
[29] M. Kezzar, M. Rafik Sari, R. Bourenane, M. M. Rashidi and A. Haiahem, “Heat transfer in hydro-magnetic nano-fluid flow between non parallel plates using DTM”, (2018). DOI: 10.22055/JACM.2018.24959.1221
[30] C.Y. Wang, “Free convection on a vertical stretching surface”, J. Appl. Math. Mech. (ZAMM), Vol. 69, pp. 418–420, (1989).
[31] R. S. R. Gorla and I. Sidawi, “Free convection on a vertical stretching surface with suction and blowing”, Appl. Sci. Res., Vol. 52, pp. 247–257, (1994).