Document Type : Research Paper

Authors

1 BS&H, Sree Vidyanikethan Engineering College, Tirupati-517102, India

2 Department of Mathematics, VIT University, Vellore-632014, India

3 GITAM University, Bangalore, Karnataka, India

Abstract

In this study, the Brownian motion and thermophoresis effects on the MHD ferrofluid flow over a cone with thermal radiation were discussed. Kerosene with the magnetic nanoparticles (Fe3O4) was considered. A set of transformed governing nonlinear coupled ordinary differential equations were solved numerically using Runge-Kutta based shooting technique. A simulation was performed by mixing ferrous particles with base fluids. Also, dual solutions for Casson Ferrofluid flow over a cone with rotation and without rotation effects were presented. An agreement of the present solutions with those published in literature was found. The effect of dimensionless parameters on velocity, temperature and concentration profiles along with the friction factor coefficients, Nusselt number, and the Sherwood numbers were discussed with the help of graphs and tables. It was found that the volume fraction of Ferro nanoparticles, magnetic field parameter, and Brownian motion parameters are controlling the friction factor coefficients, Nusselt number and Sherwood numbers for both the rotation and without rotation effects cases. 

Graphical Abstract

Mixed convection on radiative unsteady Casson ferrofluid flow due to cone with Brownian motion and thermophoresis: A numerical study

Keywords

Main Subjects

[1]     P. Cheng, “Similarity solutions for mixed convection from horizontal impermeable surfaces in saturated porous media”, International Journal Heat Mass Transfer, Vol. 20, No. 9, pp. 893-898, (1977).
[2]     P. Cheng, “Natural convection in a porous medium: external flows, NATO Advanced study in natural convection:Fundamentals and Applications, Izmir, Turkey, pp. 16-27,(1985).
[3]     D. A. Nield, A. Bejan, “Convection in porous media”, second edition, Springer-Verlag, New York, (1999).
[4]     I. Pop, D. B. Ingham, “Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media”, Pergamon, Oxford, (2001).
[5]     C.S.K. Raju, and N.Sandeep, “Unsteady Casson nanofluid flow over a rotating cone in a rotating frame filled with ferrous nanoparticles: A Numerical study”, Journal of Magnetism and Magnetic Materials, Vol. 421, pp. 216-224, (2017).
[6]     C. S. K. Raju, N. Sandeep, C. Sulochana, V. Sugunamma, “Effects of aligned magnetic field and radiation on the flow of ferrofluids over a flat plate with non-uniform heat source/sink”, International Journal of  Science and Engineering, Vol. 8, No. 2, pp. 151-158, (2015).
[7]     B. Rushikumar, R. Sivaraj, “Heat and mass transfer in MHD viscoelastic fluid flow over a vertical cone and flat plate with variable viscosity”, International Journal of Heat and Mass Transfer, Vol. 56, Nos. 1-2, pp. 370-379, (2013).
[8]     A. J. Chamkha, S. Abbasbandy, A. M. Rashad, K. Vajravelu, “Radiation effects on mixed convection about a cone embedded in a porous medium filled with a nanofluid”, Meccanica, Vol. 48, pp. 275-285, (2013).
[9]     N. Sandeep, C. Sulochana, C. S. K. Raju, M. Jayachandrababu, V. Sugunamma, “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, No. 1, pp. 312-327, (2015).
[10]   S. Jothimani, S. P. Anjali Devi, “Oblique magnetic field effects over stability in superposed viscous Ferro fluids”, Journal of Magnetism and Magnetic materials, Vol. 222, No. 99, pp. 1-7, (2000).
[11]   B. Siddappa, M. S. Abel, “Non-Newtonian Flow past a Stretching Plate”, Journal of Applied Mathematics and Physics, Vol. 36, pp. 890-892, (1985).
[12]   C. S. K. Raju, N. Sandeep, V. Sugunamma, M. Jayachandrababu, J. V. Ramana Reddy, “Heat and mass transfer in magneto hydrodynamic Casson fluid over an exponentially permeable stretching surface”, Engineering Science and Technology, an International Journal, Vol. 19,No.1, pp.45-52,(2016).
[13]   B. J. Gireesha, B. Mahanthesh and M.M Rashidi, “MHD boundary layer heat and mass transfer of a chemically reacting Casson fluid over a permeable stretching surface with non-uniform heat source/sink”, International Journal of Industrial Mathematics, Vol. 7, No. 3, pp. 247-260, (2015).
[14]   C. S. K. Raju, M. Jayachandrababu, N. Sandeep, “Chemically reacting radiative MHD Jeffery nanofluid flow over a cone in porous medium”, International Journal of Engineering Research  In Africa, Vol. 19, pp. 75-90, (2016).
[15]   S. Nadeem, Rashid Mehmood and Noreen Sher Akbar, “Optimized analytical solution for oblique flow of a Casson-Nano fluid with convective boundary     conditions”,    International Journal of Thermal Sciences, Vo. 78, pp. 90-100, (2014).
[16]   W. A. Khan, Z. H. Khan, R. U. Haq, “Flow and heat transfer of Ferro fluids over a flat plate with uniform heat flux”, The European Physical journal plus, Vol. 130, No. 86, (2015).
 [17] M. Sheikholeslami M. G. Bandpy, “Free convection of Ferro fluid in a cavity heated from below in the presence  of  an external magnetic field”, Powder Technology, Vol. 256, pp. 490-498, (2014).
[18]   A. Mahdy, A. J. Chamkha, Y. Baba, “Double-diffusive convection with variable viscosity from a vertical truncated cone in porous media in the presence of magneticfield and radiation effects”,  Computers   and   Mathematics with Applications, Vol. 59, No. 12,  pp. 3867-3878, (2010).
[19]   D. Anilkumar, S. Roy, “Unsteady mixed convection flow on a rotating cone in a rotating fluid”, Applied Mathematics and Computation, Vol. 155, pp. 545-561, (2004).
[20]   S. Saleem, N. Nadeem, “Analytical treatment of unsteady mixed convection MHD flow on a rotating cone in a rotating frame”, Journal of the  Taiwan Institute of Chemical Engineers, Vol. 44, pp. 596-604, (2013).
[21]   Chakravarthula S K Raju, Naramgari Sandeep, “Dual solutions for unsteady heat and mass transfer in Bio-convection flow towards a rotating cone/plate in a rotating fluid”, International Journal of Engineering Research. In Africa, Vol. 20, pp. 161-176, (2015).
[22]      M. Kumari, I. Pop, G. Nath, “Mixed convection along a vertical cone”, International Communications in Heat and Mass Transfer, Vol. 16, pp. 247-255, (1989).
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