MHD free convection flow of Casson fluid over a permeable nonlinearly stretching sheet with chemical reaction


  • Imran Ullah Universiti Teknologi Malaysia
  • Sharidan Shafie Universiti Teknologi Malaysia
  • Ilyas Khan Majmaah University



Casson fluid, MHD, suction/blowing, free convection


The problem of heat and mass transfer free convection flow of Casson fluid over a porous nonlinear stretching sheet in the presence of chemical reaction is investigated. Moreover the effect of magnetic field is also considered. The governing partial differential equations are transformed into ordinary differential equations by making use of suitable transformations and then solved numerically via Keller-box method. The results for skin friction are compared with previous results of the existing literature. The results are also reflected in good agreement. It is noted that concentration of Casson fluid reduces rapidly by increasing Schmidt number and chemical parameter. Also, thermal Grashof number and mass Grashof number enhance the momentum boundary layer thickness, whereas increment in chemical reaction parameter reduces the heat transfer rate. Moreover, both the fluid velocity and wall shear stress are observed to be decreased with increment in suction/blowing parameter.


Casson, N., 1959. A flow equation for pigment-oil suspensions of the printing ink type. In: Mill, C. C., Ed., Rheology of Disperse Systems, Pergamon Press, Oxford, pp.84–104.

Cebeci, T. and Bradshaw, P., 1988. Physical and computational aspects of convective heat transfer 1st ed., Springer-Verlag, New York.

Chamkha, A. J., Takhar, H. S. and Bég, O. A., 2004. Radiative free convective non-Newtonian fluid flow past a wedge embedded in a porous medium. international Journal of Fluid Mechanics Research, 31(2), pp.101–115. doi:


Cortell, R., 2007. Viscous flow and heat transfer over a nonlinearly stretching sheet. Applied Mathematics and Computation, 184(2), pp.864–873.

Gaur, M. and Gupta, M.K., 2014. A Casson fluid model for the steady flow through a stenosed blood vessel 2 mathematical formulation. British Journal of Mathematics & Computer Science, 4(11), pp.1629–1641.

Gupta, P.S. and Gupta, A.S., 1977. Heat and mass transfer on a stretching sheet with suction or blowing. The Canadian Journal of Chemical Engineering, 55(6), pp.744–746.

Hsiao, K.L., 2010. Mixed convection with radiation effect over a nonlinearly stretching sheet. World Academy of Science, Engineering and Technology, 4, pp.338–342.

Hussanan, A., Salleh, M. Z., Khan, I. and Shafie, S., 2016. Analytical solution for suction and injection flow of a viscoplastic Casson fluid past a stretching surface in the presence of viscous dissipation. Neural Computing and Applications. doi:10.1007/s00521-016-2674-0.

Jat, R. N., Chand, G. and Rajotia, D., 2014. MHD heat and mass transfer for viscous flow over nonlinearly stretching sheet in a porous medium. Thermal Energy and Power Engineering, 3(1), pp.191–197.

Kechil, S. A. and Hashim, I., 2009. Flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium. Journal of Porous Media, 12(11), pp.1053–1063.

Kumaran, V. and Ramanaiah, G., 1996. A note on the flow over a stretching sheet. Acta Mechanica, 116(1-4), pp.229–233.

Magyari, E. and Keller, B., 1999. Heat and mass transfer in the

boundary layers on an exponentially stretching continuous surface. Journal of Physics D: Applied Physics, 32(5), pp.577–585.

Mahdy, A., 2014. Natural convection flow of a non-Newtonian Casson fluid past a vertical stretching plane with mass transfer. World Science Research Journals, 2(6), pp.099–107.

Makinde, O. D., 2005. Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate. International Communications in Heat and Mass Transfer, 32(10), pp.1411–1419.

Mangathai, P., Reddy, B. R. and Reddy, G. V. R., 2015. MHD boundary layer flow through a porous medium over a stretching sheet with chemical reaction. International Journal of Mathematical Archive, 6(3), pp.1–10.

Mukhopadhyay, S., 2013. Casson fluid flow and heat transfer over a nonlinearly stretching surface. Chinese Physics B, 22(7), p.074701.

Pramanik, S., 2014. Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation. Ain Shams Engineering Journal, 5(1), pp.205–212.

Prasad, K. V., Vajravelu, K. and Datti, P. S., 2010. The effects of variable fluid properties on the hydro-magnetic flow and heat transfer over a non-linearly stretching sheet. International Journal of Thermal Sciences, 49(3), pp.603–610.

Raju, C. S. K. and Sandeep, N., 2017. Unsteady Casson nano fluid flow over a rotating cone in a rotating frame filled with ferrous nanoparticles : A numerical study. Journal of Magnetism and Magnetic Materials, 421, pp.216–224.

Raptis, A. and Perdikis, C., 2006. Viscous flow over a non-linearly stretching sheet in the presence of a chemical reaction and magnetic field. International Journal of Non-Linear Mechanics, 41(4), pp.527–529.

Reher, E. O., Haroske, D. and Kohler, K., 1969. Chem Technol. Chem Technol, 21(3), pp.137– 143.

Sajid, M. and Hayat, T., 2008. Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet. International Communications in Heat and Mass Transfer, 35(3), pp.347–356.

Sakiadis, B., 1961. Boundary‐layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface. AIChE Journal, 7(2), pp.221–225.

Shehzad, S. A., Hayat, T., Qasim, M. and Asghar, S., 2013. Effects of mass transfer on MHD flow of Casson fluid with chemical reaction and suction. Brazilian Journal of Chemical Engineering, 30(01), pp.187–195.

Singh, S., 2011. Clinical significance of aspirin on blood flow through stenotic blood vessels. Journal of Biomimetics, Biomaterials, and Tissue Engineering, 10, pp.17–24.

Vajravelu, K., 2001. Viscous flow over a nonlinearly stretching sheet. Applied Mathematics and Computation, 124(3), pp.281–288.