**ABSTRACT**

In this paper, we study the effects of Thermophoresis and nonlinear convection on mixed convective flow of viscous incompressible rotating fluid due to rapidly rotating cone in a porous medium, whose surface temperature and concentration are higher than the temperature and concentration of its surrounding fluid. The governing equations for the conservation of mass, momentum, energy and concentration are transformed, using similarity transformations and the solutions are obtained by employing shooting method that uses Runge-Kutta method and Newton Raphson method. A comparison of the present results with previously published work for special cases shows a good agreement. The effects of temperature and concentration, ratio of angular velocities, relative temperature difference parameter, thermophoretic coefficients on velocity, temperature and concentration profiles as well as tangential and circumferential skin friction coefficients, Nusselt number and Sherwood number results are discussed in detail. The results indicate that the temperature is more influential compared to concentration. Also, the wall thermophoretic deposition velocity changes according to different values of pertinent parameter. Applications of the study arise in aerosol technology, space technology, astrophysics and geophysics, which related to temperature-concentration-dependent density.

**KEYWORDS**

PAPER SUBMITTED: 2015-06-19

PAPER REVISED: 2015-12-27

PAPER ACCEPTED: 2016-01-21

PUBLISHED ONLINE: 2016-01-30

- Nield, D.A., Bejan, A., Convection in Porous Media, 3rd edn. Springer., New York, USA, 2006
- Ingham, D.B., Pop, I., Transport phenomenon in porous media, vol.III, Elsevier, Oxford., 2005.
- Rashidi, M.M., Anwar Bég, O., Rahimzadeh, N., A Generalized Differential Transform Method for Combined Free and Forced Convection Flow about Inclined Surfaces in Porous Media, Chemical Engineering Communications 199(2012), 2, pp. 257-282.
- Rashidi, M.M., Kavyani, N., Abelman, S., Uddin, M.J., Freidoonimehr, N., Double Diffusive MHD Mixed Convective Slip Flow along a Radiating Moving Vertical Flat Plate with Convective Boundary Condition, PLOS ONE 9 (2014), 10, Article number e109404.
- Rashidi, M.M., Momoniat, E., Mohammad, F., Basiri Parsa, A., Lie Group Solution for Free Convective Flow of a Nanofluid Past a Chemically Reacting Horizontal Plate in Porous Media, Mathematical Problems in Engineering Volume 2014 (2014), Article number 239082.
- Hering, R.G., Grosh, R.J., Laminar combined convection from a rotating cone, ASME Journal of Heat Transfer, 85(1963), pp. 29-34.
- Himasekahr, K., Sarma, P.K., Janardhan, K., Laminar mixed convection from vertical rotating cone, International Communication in heat and mass transfer, 16(1989), pp. 99-106.
- Saravanan, S., Centrifugal acceleration induced convection in a magnetic fluid saturated anisotropic rotating porous medium, Transport in porous media, 77(2009), pp. 79-86.
- Gouse Mohiddin, S., Prasad, V.R., Varma, S.V.K., Anwar Beg, O., Numerical study of unsteady free convective heat and mass transfer in a walters-B viscoelastic flow along a vertical cone, International Journal of Applied Mathematics and Mechanics, 6(2010), 15, pp. 88-114.
- Rashidi, M.M., Laraqi, N., Basiri Parsa, A., Analytical Modeling of Heat Convection in Magnetized Micropolar Fluid by Using Modified Differential Transform Method, Heat Transfer-Asian Research 40(2011), 3, pp. 187-204.
- Rashidi, M.M., Erfani, E., Analytical Method for Solving Steady MHD Convective and Slip Flow due to a Rotating Disk with Viscous Dissipation and Ohmic Heating, Engineering Computations 29(2012), 6, 562-579.
- Chamkha, A.J., Ahmed, S.E., Unsteady MHD heat and mass transfer by mixed convection flow in the forward stagnation region of a rotating sphere at different wall conditions, Chemical Engineering Communications, 199(2012), pp. 122-141.
- Chamkha, A.J., Rashad, A.M., Unsteady heat and mass transfer by MHD mixed convection flow from a rotating cone with chemical reaction and soret and Dufour effects, The Canadian Journal of Chemical Engineering, 9999(2013), pp. 1-10.
- Hariprasad Raju, S., Mallikarjuna, B., Varma, S.V.K., Thermophoretic effect on double diffusive convective flow of a chemically reacting fluid over a rotating cone in a porous medium, International Journal of Scientific and Engineering Research, 6(2015), 1, pp. 198-204.
- Salah, F., Aziz, Z.A., Ching, D.L.C., New exact solutions for MHD transient rotating flow of a second-grade fluid in a porous medium, Journal of Applied Mathematics, 2011(2011), Article ID 823034, 8pages.
- Bhadauria, B.S., Siddheshwar, P.G., Suthar, Om.P., Nonlinear thermal instability in a rotating viscous fluid layer under temperature/gravity modulation, ASME Journal of Heat Transfer, 134(2012), pp. 102502-1-9.
- Rashad, A.M., Effects of radiation and variable viscosity on unsteady MHD flow of a rotating fluid from stretching surface in porous medium, Journal of the Egyptian Mathematical Society, 22(2014), pp. 134-142.
- Bhuvanavijaya, R., Mallikarjuna, B., Effect of variable thermal conductivity on convective heat and mass transfer over a vertical plate in a rotating system with variable porosity regime, Journal of Naval Architecture and Marine Engineering, 11(2014), pp. 83-92.
- Talbot, L., Cheng, R.K., Schefer, R.W., Wills, D.R., Thermophoresis of particles in a heated boundary layer, Journal of Fluid Mechanics, 101(1980), pp. 737-758.
- Srinivasacharya. D, Mallikarjuna, B, and Bhuvanavijaya. R, Soret and Dufour effects on mixed convection along a vertical wavy surface in a porous medium with variable properties, Ain Shams Engineering Journal, 6(2015), pp. 553-564.
- Nadeem, S., Saleem, S., Analytical study of rotating non-Newtonian nanofluid on a rotating cone, Journal of Thermophysics and Heat Transfer, 28(2014), 2, pp. 295-302.
- A. Basiri Parsa, M.M. Rashidi, O. Anwar Bég, S.M. Sadri, Semi-Computational Simulation of Magneto-Hemodynamic Flow in a Semi-Porous Channel Using Optimal Homotopy and Differential Transform Methods, Computers in Biology and Medicine 43 (9) (2013) 1142-1153.
- O. Anwar Bég, M.M. Rashidi, T.A. Bég, M. Asadi, Homotopy analysis of transient magneto-bio-fluid dynamics of micropolar squeeze film in a porous medium: A model for magneto-bio-rheological lubrication, Journal of Mechanics in Medicine and Biology 12 (03) (2012).