## THERMAL SCIENCE

International Scientific Journal

### NUMERICAL INVESTIGATION OF MAGNETIC NANOFLUIDS FLOW OVER ROTATING DISK EMBEDDED IN A POROUS MEDIUM

**ABSTRACT**

Combined effects of thermal radiation and variable viscosity on a time-dependent boundary-layer flow of magnetic nanofluids over a rotating disk in the presence of the porous medium have been numerically investigated. To carry out the study, hydrocarbon based magnetic nanofluid containing magnetite Fe3O4 particles of 10 nm with magnetic phase concentration of 10% has been taken. For numerical solutions of the modelled system containing the governing equation of the flow, a MATLAB tool ODE45 is employed with shooting technique for the initial guess of the unknown boundary conditions. The flow phenomenon and heat transfer on the plate surface are characterised by various flow parameters such as viscosity variations, unsteady rotation parameter, Prandtl number, and radiation parameter. Also, a comparative thermal analysis has been carried out for magnetic nanofluids having three different bases viz. hydrocarbon, fluorocarbon, and water. Results reveal that heat transfer rate of hydrocarbon base magnetic nanofluids is 73.4511% faster than water base magnetic nanofluids, and 239.7458% faster than fluorocarbon base magnetic nanofluids. This enhanced heat transfer capacity of hydrocarbon base magnetic nanofluids will help in improving the performance of oil and ore extraction drilling systems used in mining industry and other geothermal applications.

**KEYWORDS**

PAPER SUBMITTED: 2017-03-23

PAPER REVISED: 1970-01-01

PAPER ACCEPTED: 2017-05-23

PUBLISHED ONLINE: 2017-06-04

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**Issue 6**, PAGES [2883 - 2895]

- T V Kármán, Über laminare und turbulente Reibung, ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, vol. 1, (1921), pp. 233-252.
- F Frusteri and E Osalusi, On MHD and slip flow over a rotating porous disk with variable properties, International Communications in Heat and Mass Transfer, vol. 34, (2007), pp. 492-501.
- P Ram and K Sharma, On the revolving ferrofluid flow due to a rotating disk, Int. J. Non. Sci, vol. 13, (2012), pp. 317-324.
- J M Owen and R H Rogers, Flow and heat transfer in rotating-disc systems, (1989),
- J Herrero, F Giralt, and J A Humphrey, Comparative analysis of coupled flow and heat transfer between corotating disks in rotating and fixed cylindrical enclosures, Heat transfer in gas turbines, (1994), pp. 111-121.
- H A Attia, Unsteady flow and heat transfer of viscous incompressible fluid with temperature-dependent viscosity due to a rotating disc in a porous medium, Journal of Physics A: Mathematical and General, vol. 39, (2006), p. 979.
- H Attia, Steady flow over a rotating disk in porous medium with heat transfer, Nonlinear Analysis: Modelling and Control, vol. 14, (2009), pp. 21-26.
- P Ram and V Kumar, Ferrofluid flow with magnetic field-dependent viscosity due to rotating disk in porous medium, International Journal of Applied Mechanics, vol. 4, (2012), p. 1250041.
- M Rashidi, S M Pour, T Hayat, and S Obaidat, Analytic approximate solutions for steady flow over a rotating disk in porous medium with heat transfer by homotopy analysis method, Computers & Fluids, vol. 54, (2012), pp. 1-9.
- R Ellahi, The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: analytical solutions, Applied Mathematical Modelling, vol. 37, (2013), pp. 1451-1467.
- E Osalusi and P Sibanda, On variable laminar convective flow properties due to a porous rotating disk in a magnetic field, Romanian Journal of Physics, vol. 51, (2006), p. 937.
- R EllAHI, M Hassan, and A Zeeshan, A study of heat transfer in power law nanofluid, Thermal Science, (2015), pp. 129-129.
- N S Akbar, D Tripathi, Z H Khan, and O A Bég, A numerical study of magnetohydrodynamic transport of nanofluids over a vertical stretching sheet with exponential temperature-dependent viscosity and buoyancy effects, Chemical Physics Letters, vol. 661, (2016), pp. 20-30.
- P Ram and V Kumar, Rotationally Symmetric Ferrofluid Flow and Heat Transfer in Porous Medium with Variable Viscosity and Viscous Dissipation, Journal of Applied Fluid Mechanics, vol. 7, (2014),
- S Mukhopadhyay, Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in porous medium, International Journal of Heat and Mass Transfer, vol. 52, (2009), pp. 3261-3265.
- M Uddin, P Rana, O A Bég, and A M Ismail, Finite element simulation of magnetohydrodynamic convective nanofluid slip flow in porous media with nonlinear radiation, Alexandria Engineering Journal, vol. 55, (2016), pp. 1305-1319.
- A A Khidir, Viscous dissipation, Ohmic heating and radiation effects on MHD flow past a rotating disk embedded in a porous medium with variable properties, Arabian Journal of Mathematics, vol. 2, (2013), pp. 263-277.
- A Ahmadi, A Zahmatkesh, M Hatami, and D Ganji, A comprehensive analysis of the flow and heat transfer for a nanofluid over an unsteady stretching flat plate, Powder Technology, vol. 258, (2014), pp. 125-133.
- M Fakour, A Vahabzadeh, D Ganji, and M Hatami, Analytical study of micropolar fluid flow and heat transfer in a channel with permeable walls, Journal of Molecular Liquids, vol. 204, (2015), pp. 198-204.
- E Osalusi, Effects of thermal radiation on MHD and slip flow over a porous rotating disk with variable properties, Romanian Journal of Physics, vol. 52, (2007), p. 217.
- M J Babu and N Sandeep, Effect of nonlinear thermal radiation on non-aligned bio-convective stagnation point flow of a magnetic-nanofluid over a stretching sheet, Alexandria Engineering Journal, vol. 55, (2016), pp. 1931-1939.
- G Shit and S Majee, Hydromagnetic Flow over an Inclined Non-Linear Stretching Sheet with Variable Viscosity in the Presence of Thermal Radiation and Chemical Reaction, Journal of Applied Fluid Mechanics, vol. 7, (2014),
- A Zeeshan, A Majeed, and R Ellahi, Effect of magnetic dipole on viscous ferro-fluid past a stretching surface with thermal radiation, Journal of Molecular Liquids, vol. 215, (2016), pp. 549-554.
- M Turkyilmazoglu, Nanofluid flow and heat transfer due to a rotating disk, Computers & Fluids, vol. 94, (2014), pp. 139-146.
- I Mustafa and T Javed, Heat Transfer In Natural Convection Flow Of Nanofluid Along A Vertical Wavy Plate With Variable Heat Flux, Thermal Science, vol. Accepted, (2017),
- U Akdag, S Akcay, and D Demiral, Heat Transfer In A Triangular Wavy Channel With Cuo/Water Nanofluids Under Pulsating Flow, Thermal Science, vol. Accepted, (2017),
- W Abbas and E A Sayed, Hall Current And Joule Heating Effects On Free Convection Flow Of A Nanofluid Over A Vertical Cone In Presence Of Thermal Radiation, Thermal Science, vol. Accepted, (2017),
- R B B A K Kumar, Numerical Study On Heat Transfer Characteristics Of Nanofluid Based Natural Circulation Loop, Thermal Science, vol. Accepted, (2017),
- N S Akbar, D Tripathi, and O A Bég, MHD convective heat transfer of nanofluids through a flexible tube with buoyancy: a study of nano-particle shape effects, Advanced Powder Technology, vol. 28, (2017), pp. 453-462.
- S M Snyder, T Cader, and B A Finlayson, Finite element model of magnetoconvection of a ferrofluid, Journal of Magnetism and Magnetic Materials, vol. 262, (2003), pp. 269-279.
- J Weilepp and H R Brand, Competition between the Bénard-Marangoni and the Rosensweig instability in magnetic fluids, Journal de Physique II, vol. 6, (1996), pp. 419-441.
- C-Y Hong, I Jang, H Horng, C Hsu, Y Yao, and H-C Yang, Ordered structures in Fe3O4 kerosene-based ferrofluids, Journal of applied physics, vol. 81, (1997), pp. 4275-4277.
- K A Maleque, Effects of combined temperature-and depth-dependent viscosity and Hall current on an unsteady MHD laminar convective flow due to a rotating disk, Chemical Engineering Communications, vol. 197, (2009), pp. 506-521.
- P Ram, A Bhandari, and K Sharma, Axi-symmetric ferrofluid flow with rotating disk in a porous medium, International Journal of Fluid Mechanics, vol. 2, (2010), pp. 151-161.
- H Schlichting and K Gersten, Boundary-layer theory, (2003): Springer Science & Business Media.
- P Ram, V K Joshi, K Sharma, M Walia, and N Yadav, Variable viscosity effects on time dependent magnetic nanofluid flow past a stretchable rotating plate, Open Physics, vol. 14, (2016), pp. 651-658.
- J Gregg and E Sparrow, Heat transfer from a rotating disk to fluids of any Prandtl number, (1959)