Variable Viscosity of Casson Fluid Flow Over A Stretching Sheet in Porous Media with Newtonian Heating

Kartini Ahmad, Syafrina Abdul Halim, Zahir Hanouf

Abstract


Casson fluid flow with variable viscosity in porous media over a heated stretching sheet is investigated. The partial differential equations representing the flow motion are first transformed to ordinary differential equations by similarity transformation before being solved numerically by the finite-difference method. The effects of the viscosity variation parameter \((\Omega)\), the permeability number \((\kappa)\), Prandtl number \((Pr)\), Biot number \((Bi)\) and non-Newtonian fluid parameter \((\beta)\) on the fluid flow and heat transfer, along with the temperature and velocity profiles, are presented graphically for some arbitrary values.

Keywords


Casson fluid; Stretching sheet; Newtonian heating; Variable viscosity

Full Text:

PDF

References


K. Ahmad, Z. Hanouf and A. Ishak, MHD Casson nanofluid flow past a wedge with Newtonian heating, Euro. Phys. J. Plus 132 (2017), 87 – 97.

K. Ahmad, R. Nazar and I. Pop, Boundary layer flows and heat transfer of micropolar fluids near the stagnation point on a stretching vertical surface with prescribed skin friction, International Journal of Minerals, Metallurgy and Materials 18 (2011), 4, 502 – 507.

K. Ahmad and Z.Wahid, Jeffrey fluid flow over a stretching sheet with non-uniform heat source/sink, Australian Journal of Basic and Applied Sciences (special issue) 9 (28) (2015), 32 – 38.

M.E. Ali, The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface, International Journal of Thermal Sciences 45 (2006), 60 – 69.

T. Cebeci and P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer, Springer, New York (1988).

R.C. Chaudhary and P. Jain, Unsteady free convection boundary-layer flow past an impulsively started vertical surface with Newtonian heating, Romanian Journal of Physics 51 (9/10) (2006), 911 – 925.

R.C. Chaudhary and P. Jain, An exact solution to the unsteady free convection boundary-layer flow past an impulsively started vertical surface with Newtonian heating, J. Eng. Phy. Thermophys 80 (2007), 954 – 960.

T.C. Chiam, Micropolar fluid flow over a stretching sheet, ZAMM - Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 62(10) (1982), 565 – 568.

R. Cortell, A note on magnetohydrodynamic flow of a power-law fluid over a stretching sheet, Applied Mathematics and Computation 168(1) (2005), 557 – 566.

L.J. Crane, Flow past a stretching plate, Zeitschrift für angewandte Mathematik und Physik ZAMP 21(4) (1970), 645 – 647.

J. Gary, D.R. Kassory, H. Tadjeran and A. Zebib, The effect of significant viscosity variation on convective heat transport in water-saturated porous media, J. Fluid Mech. 117 (1982), 233 – 249.

H. Herwig and K. Gersten, The effect of variable properties on laminar boundary layer flow, Wärmeund Stoffübertragung 20 (1986), 47 – 57.

L.C. Lai and F.A. Kulacki, The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium, Int. J. Heat Mass Transfer 33 (1990), 1028 – 1031.

A.I. Lare, Casson fluid flow with variable viscosity and thermal conductivity along exponentially stretching sheet embedded in a thermally stratified medium with exponentially heat generation, Journal of Heat and Mass Transfer Research 2(2) (2015), 63 – 78.

M. Lavanya, M. Sreedhar Babu and G. , M., Venkata Ramanaiah, G., 2016, Heat transfer of nanofluid past an exponentially permeable stretching sheet with heat generation and Newtonian heating in a porous medium, International Journal of Innovative Research and Development 5 (1), 318 – 329.

J.X. Ling and A. Dybbs, Forced convection over a flat plate submersed in a porous medium: variable viscosity case, American Society of Mechanical Engineers (1987), 13 – 18.

M.A.A. Mahmoud, The effects of variable fluid properties on MHD Maxwell fluids over a stretching surface in the presence of heat generation/absorption, Chemical Engineering Communications 198(1) (2010), 131 – 146.

O.D. Makinde, Second law analysis for variable viscosity hydromagnetic boundary layer flow with thermal radiation and Newtonian heating, Entropy 13(8) (2011), 1446 – 1464.

M.Y. Malik, M. Khan, T. Salahuddin and I. Khan, Variable viscosity and MHD flow in Casson fluid with Cattaneo-Christov heat flux model: Using Keller box method, Engineering Science and Technology, an International Journal 19(4) (2016), 1985 – 1992.

A. Mastroberardino, Mixed convection in viscoelastic boundary layer flow and heat transfer over a stretching sheet, Adv. Appl. Math. Mech. 6 (2014), 359 – 375.

J.B. McLeod and K.R. Rajagopal, On the uniqueness of flow of a Navier-Stokes fluid due to a stretching boundary, Analysis and Continuum Mechanics 1989 (1989), 565 – 573.

K.N. Mehta and S. Sood, Transient free convection flow with temperature dependent viscosity in a fluid saturated porous medium, Int. J. Engrg. Sci. 30 (1992), 1083 – 1087.

J.H. Merkin, R. Nazar and I. Pop, The development of forced convection heat transfer near a forward stagnation point with Newtonian heating, J. Eng. Math. 74 (2012), 53 – 60.

M.K.A. Mohamed, N.M. Nasir, N.S. Khasi’ie, R. Jusoh, N.H. Moslim, E.M. Zaihidee and M.Z. Salleh, Numerical investigation of stagnation point flow over a stretching sheet with Newtonian heating, AIP Conference Proceedings 1482(1) (2012), 347 – 350.

P.V. Narayana, D. Babu and B. Venkateswarlu, Soret and Dufour effects on MHd radiative heat and mass transfer flow of a Jeffrey fluid over a stretching sheet, Frontiers in Heat and Mass Transfer 8(5) (2017), 1 – 9.

P.O. Olanrewaju, T.A. Anake, O.T. Arulogun, D.A. Ajadi, Further results on the effects of variable viscosity and magnetic field on flow and heat transfer to a continuous flat plate in the presence of heat generation and radiation with a convective boundary condition, American Journal of Computational and Applied Mathematics 2(2) (2012), 42 – 48.

B.N. Rao, Flow of a fluid of second grade over a stretching sheet, International Journal of non-Linear Mechanics 31(4) (1996), 547 – 550.

A. Rasekh, M. Farzaneh-Gord, S.R. Varedi, D.D. Ganji, Analytical solution for magnetohydrodynamic stagnation point flow and heat transfer over a permeable stretching sheet with chemical reaction, Journal of Theoretical and Applied Mechanics 51(3) (2013), 675 – 686.

M. Reza, R. Chahal and N. Sharma, Radiation effect on MHD Casson fluid flow over a power-law stretching sheet with chemical reaction, World Academy of Science, Engineering and Technology, International Journal of Chemical, Molecular, Nuclear, Materials and Metallurgical Engineering 10(5) (2016), 566 – 571.

M.Z. Salleh, R. Nazar and I. Pop, Forced convection boundary layer flow at a forward stagnation point with Newtonian heating, Chem. Eng. Comm. 196 (2009), 987 – 996.

N.M. Sarif, M.Z. Salleh and R. Nazar, Numerical solution of flow and heat transfer over a stretching sheet with Newtonian heating using the Keller-box method, Procedia Engineering 53 (2013), 542 – 554.

M. Uddin, O.A. Bég, W.A. Khan and A.I. Ismail, Effect of Newtonian heating and thermal radiation on heat and mass transfer of nanofluids over a stretching sheet in porous media, Heat Transfer— Asian Research 44(8) (2015), 681 – 695.

S.S. Uma Devi and S.P. Anjali Devi, Numerical investigation of three-dimensional hybrid Cu–Al2O3/water nanofluid flow over a stretching sheet with effecting Lorentz force subject to Newtonian heating, Canadian Journal of Physics 94(5) (2016), 490 – 496.

K. Vajravelu and D. Rollins, Heat transfer in a viscoelastic fluid over a stretching sheet, Journal of Mathematical Analysis and Applications 158(1) (1991), 241 – 255.




DOI: http://dx.doi.org/10.26713%2Fjims.v10i1-2.630

eISSN 0975-5748; pISSN 0974-875X