Document Type: Research Paper

Authors

1 Vellore Institute of Technology

2 Department of Mathematics, Vellore Institute of Technology, Vellore-632014, Tamil Nadu, India

Abstract

This study deals with the three-dimensional flow of a chemically reacting magnetohydrodynamic Sisko fluid over a bidirectional stretching surface filled with the ferrous nanoparticles in the presence of non-uniform heat source/sink, nonlinear thermal radiation, and suction/injection. After applying the self-suitable similarity transforms, the nonlinear ordinary differential equations are solved numerically using Runge-Kutta and Newton’s methods. Results present the effects of various non-dimensional governing parameters on velocity, temperature and concentration profiles. Also, computed and discussed the friction factor coefficients along with the local Nusselt and Sherwood numbers. Similarity solutions for suction and injection cases are presented. A good agreement in the present results with the existed literature under some special limited cases is found. It is found that heat and mass transfer performance of Sisko ferrofluid is significantly high in injection case when compared with the suction case. Increasing values of the stretching parameter enhance the heat and mass transfer rate. 

Graphical Abstract

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Main Subjects

[1]          B. C. Sakiadis, “Boundary layer behavior on continuous solid surfaces”, American Institute of Chemical Engineering Journal, Vol. 7, pp. 26-28 (1961).

[2]          B. J. Gireesha, J. Manjunatha and  C. S. Bagawedi, “Unsteady hydro magnetics boundary layer flow and heat transfer of dusty fluid over a stretching sheet”,  Afrika Matematika,  Vol. 23, pp. 229-241, (2012).

[3]          B. I. Olajuwon and J. L. Oahimire, “Effect of thermal radiation and chemical reaction on heat and mass transfer in an MHD micro polar fluid with heat generation”, Afrika Matematika, Vol. 25, pp. 911-931, (2014).

[4]          D. S. Chauhan and R. Agarwal, “MHD coupled-flow and heat transfer across a porous layer due to an oscillating plate with radiation”, Afrika Matematika, Vol. 24, pp. 391-405, (2013).

[5]          O. D. Makinde, P. O. Olanrewaju and W. M. Charles, “Unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture, Afrika Matematika, Vol. 22, pp. 65-78, (2011).

[6]          K. Das, “Effects of thermophoresis and thermal radiation on MHD mixed convective heat and mass transfer flow” Afrika Matematika, Vol. 24, pp. 511-524, (2013).

[7]          D. Srinivasacharya and M. Upendar, “Soret and Dufour effects on MHD free convection in a micro polar fluid”, Afrika Matematika, Vol. 25, pp. 693-705, (2014).

[8]          O. D. Makinde and A. Aziz, “Boundary layer flow of a nanofluid past a stretching sheet with convective boundary condition”, International Journal of Thermal Sciences, Vol. 50, pp. 1326-1332, (2011).

[9]          P. O. Olanrewaju, A. A. Adigun,O. D.  Fenwa,  A. Oke and A. Funmi, “Unsteady free convective flow of sisko fluid with radiative heat transfer past a flat plate moving through a binary mixture”, Thermal Energy and power engineering, Vol. 2,  pp. 109-117, (2013).

[10]      M. Khan, A. Shazad, “On boundary layer flow of a sisko fluid over a stretching sheet”, Quaestiones Mathematicae, Vol. 36, pp. 137-151, (2013).

[11]      N. Sandeep, V. Sugunamma and P. Mohan Krishna, “Effects of radiation on an unsteady natural convective flow of a EG-Nimonic 80a nanofluid past an infinite vertical plate”, Advances in Physics Theories and Applications, Vol. 23, pp. 36-43, (2013).

[12]      A. Munir, A. Shazad and M. Khan, “Convective flow of sisko fluid over a birectional stretching surface”, Plos One, Vol. 10, ID: 0130342, (2015).

[13]      M. Khan and A. Shahzad, “On axisymmetric flow of sisko fluid over a radially stretching sheet”, International Journal of Non-linear Mechanics, Vol. 47, pp. 999-1007, (2012).

[14]      M. Khan, S. Munawar and S. Abbasbandy, “Steady flow and heat transfer of a sisko fluid in annular pipe”, International Journal of Heat and Mass Transfer, Vol. 53, pp. 1290-1297, (2010).

[15]      C. S.K. Raju, N. Sandeep, C. Sulochana and  V. Sugunamma, “Effects of aligned magneticfield and radiation on the flow of ferrofluids over a flat plate with non-unifom heat source/sink”, International Journal of Science and Engineering, Vol. 8, pp. 151-158, (2015).

[16]      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”, International Journal of Heat and Mass transfer, Vol. 62, pp. 526-533, (2013).

[17]      T. Hayat, B. A. Muhammad,  H. A. Hamed and S. A. Muhammad, “Three-dimensional mixed convection flow of viscoelastic fluid with thermal radiation and convective conditions” Plos One, Vol. 9, ID: 0090038,(2014).

[18]      P. Mohan Krishna, N. Sandeep, and V. Sugunamma, “Effects of Radiation and chemical reaction on MHD convective flow over a permeable stretching surface with suction and heat generation”, Walailak Journal of Science and Technology, Vol. 12, pp.831-847, (2015).

[19]      W. N. Zhou, and Y. Y. Yan,  “Numerical investigation of the effects of a magnetic field on nanofluid flow and heat transfer by the lattice Boltzmann method”, Numerical Heat transfer part A: Applications: An International Journal of  Computation and Methodology, Vol. 68, No. 1, pp. 1-16, (2015).

[20]      N. Sandeep,  C. Sulochana, C. S. K. Raju, and M. Jayachandrababu, “ Unsteady boundary layer flow of thermophoretic MHD nanofluid past a stretching sheet with space and time dependent internal heat source/sink, Applications and Applied Mathematics, Vol. 10, pp. 312-327, (2015).

[21]      T. Hayat, M. Imtiaz, A. Alsaedi and R. Mansoor, “MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions”, Chinese Physics B, Vol. 23, ID: 054701, (2014).

[22]      B. Shankar, and Y. Yirga, “Unsteady heat and mass transfer in MHD flow of nanofluids over stretching sheet with a non-uniform heat source/sink”, International Journal of Mathematical, Computational, Statistical, Natural and Physical Engineering, Vol. 7, No. 12, pp. 1248-1255, (2013).

[23]      N. Sandeep and C. Sulochana, “Dual solutions for unsteady mixed flow of MHD micro polar fluid over a stretching/shrinking sheet with non-uniform heat source/sink”, Engineering Science and Technology, an International Journal, Vol. 18, No. 4, pp. 738-745,  (2015).

[24]      S. Das, H. K. Mandal, R. N. Jana and  O.D. Makinde, “Magneto-nanofluid flow past an impulsively started porous flat plate in a rotating frame”, Journal of Nanofluids, Vol. 4, pp. 167-175, (2015).

[25]      I. L. Animasaun, “Effects of thermophoresis, variable viscosity and thermal conductivity on free convective heat and mass transfer of non-darcian MHD dissipative Casson fluid flow with suction and nth order of chemical reaction”, Journal of the Nigerian Mathematical Society, Vol. 34, pp. 11-31 (2015).

[26]      W. N. Mutuku-Njane, and O.D. Makinde, “MHD nanofluid flow over a permeable vertical plate with convective heating”, Journal of Computational and Theoretical NanoScience, Vol. 11, pp. 667-675, (2014).

[27]      C. Y. Wang, “The three dimensional flow due to a stretching flat surface”, Physics of Fluids, Vol. 27, pp. 1915-1917, (1984).

[28]      I. C. Liu and H. I. Anderson, “Heat transfer over a bidirectional stretching sheet with variable thermal conditions”, International   Journal   of    Heat    Mass

Transfer, Vol. 51, pp. 4018-4024, (2008).

[29]      W. A. Khan, and I. Pop, “Boundary layer flow of a nanofluid past a stretching sheet”, International Journal of  Heat and Mass Transfer, Vol. 53, pp. 2477-2483, (2010).

[30]      R. S. R. Gorla and I. Sidawi, “Free convection on a vertical stretching surface with suction and blowing”, Applied Scientific Research, Vol. 52, pp. 247-257, (1994).

[31]      B. Mallikarjuna, A. M. Rashad,  A. J. Chamka and S. HariprasadRaju,  “Chemical reaction effects on MHD convective heat and mass transfer  flow past a rotating vertical cone embedded in a variable porosity regime”, Afrika Matematica,Vol. 27, pp. 645-665, (2015).

[32]      M. JayachandraBabu and N. Sandeep, “Effect of variable heat source/sink on chemically reacting 3D slip flow caused by a slendering stretching sheet”, International Journal of Engineering Research in Africa, Vol. 25,  pp. 58-69, (2 016).

[33]      R. Vijayaragavan,N. Sandeep and  S. Karthikeyan, “Cross diffusion effects on chemically reacting radiativeMicropolar fluid flow past a stretching/shrinking sheet”, Global Journal of Pure and Applied Mathematics, Vol. 12, No. 3, pp. 370-376, (2016).

[34]      J. V. Ramana Reddy, V. Sugunamma, and N. Sandeep, “MHD ferrofluid flow due to bidirectional exponentially stretching surface”, Global Journal of Pure and Applied Mathematics, Vol. 12, No. 3, pp. 107-113,  (2016).

[35]      P. M. Krishna, N. Sandeep, J. V, R. Reddy and V. Sugunamma, “Dual solutions for unsteady flow of Powell-Eyring fluid past an inclined stretching sheet”, Journal of Naval  Architecture and Marine Engineering, Vol. 13, pp. 89-99,  (2016).

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