Research Papers: Micro/Nanoscale Heat Transfer

Unsteady Flow of Carreau Fluid in a Suspension of Dust and Graphene Nanoparticles With Cattaneo–Christov Heat Flux

[+] Author and Article Information
S. Mamatha Upadhya

Department of Mathematics,
Garden City College of Science
and Management Studies,
16th KM., Old Madras Road,
Bangalore 560049, Karnataka, India
e-mail: mamathasupadhya@gmail.com


Department of Mathematics,
University BDT College of Engineering,
Davangere 577004, Karnataka, India
e-mail: maheshubdt@gmail.com

C. S. K. Raju

Department of Mathematics,
GITAM School of Technology,
Bangalore 561203, India
e-mail: sivaphd90@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 4, 2017; final manuscript received March 26, 2018; published online May 22, 2018. Assoc. Editor: Thomas Beechem.

J. Heat Transfer 140(9), 092401 (May 22, 2018) (9 pages) Paper No: HT-17-1394; doi: 10.1115/1.4039904 History: Received July 04, 2017; Revised March 26, 2018

This is a theoretical exploration of the magnetohydrodynamic Carreau fluid in a suspension of dust and graphene nanoparticles. Graphene is a two-dimensional single-atom thick carbon nanosheet. Due to its high thermal conductivity, electron mobility, large surface area, and stability, it has remarkable material, electrical, optical, physical, and chemical properties. In this study, a simulation is performed by mixing of graphene + water and graphene + ethylene glycol into dusty non-Newtonian fluid. Dispersion of graphene nanoparticles in dusty fluids finds applications in biocompatibility, bio-imaging, biosensors, detection and cancer treatment, in monitoring stem cells differentiation, etc. Graphene + water and graphene + ethylene glycol mixtures are significant in optimizing the heat transport phenomena. Initially arising set of physical governing partial differential equations are transformed to ordinary differential equations (ODEs) with the assistance of similarity transformations. Consequential highly nonlinear ODEs are solved numerically through Runge–Kutta Fehlberg scheme. The computational results for nondimensional temperature and velocity profiles are presented through graphs. Additionally, the numerical values of friction factor and heat transfer rate are tabulated numerically for various physical parameter obtained. We also validated the present results with previous published study and found to be highly satisfactory. The formulated model in this study reveals that heat transfer rate and wall friction is higher in mixture of graphene + ethylene glycol when compared to graphene + water.

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Choi, U. S. , and Eastman, J. A. , 1995, “ Enhancing Thermal Conductivity of Fluids With Nanoparticles,” Argonne National Laboratory, Argonne, IL, Report No. ANL/MSD/CP--84938.
Xuan, Y. , and Li, Q. , 2000, “ Heat Transfer Enhancement of Nanofluids,” Int. J. Heat Fluid Flow, 21(1), pp. 58–64. [CrossRef]
Buongiorno, J. , 2006, “ Convective Transport in Nanofluids,” ASME J. Heat Transfer, 128(3), pp. 240–250. [CrossRef]
Bachok, N. , Ishak, A. , Nazar, R. , and Senu, N. , 2013, “ Stagnation-Point Flow Over a Permeable Stretching/Shrinking Sheet in a Copper-Water Nanofluid,” Boundary Value Probl., 2013(1), p. 39. [CrossRef]
Jayachandra Babu, M. , and Sandeep, N. , 2016, “ Three-Dimensional MHD Slip Flow of Nanofluids Over a Slendering Stretching Sheet With Thermophoresis and Brownian Motion Effects,” Adv. Powder Technol., 27(5), pp. 2039–2050. [CrossRef]
Raju, C. S. K. , Sekhar, K. R. , Ibrahim, S. M. , Lorenzini, G. , Viswanatha Reddy, G. , and Lorenzini, E. , 2017, “ Variable Viscosity on Unsteady Dissipative Carreau Fluid Over a Truncated Cone Filled With Titanium Alloy Nanoparticles,” Continuum Mech. Thermodyn., 29(6), p. 1417.
Khalil, I. , Julkapli, N. M. , Yehye, W. A. , Basirun, W. J. , and Bhargava, S. K. , 2016, “ Graphene-Gold Nanoparticles Hybrid-Synthesis, Functionalization, and Application in a Electrochemical and Surface-Enhanced Raman Scattering Biosensor,” Materials, 9(6), p. 406.
Amiri, A. , Shanbedi, M. , Rafieerad, A. R. , Rashidi, M. M. , Zaharinie, T. , Zubir, M. N. M. , Kazi, S. N. , and Chew, B. T. , 2016, “ Functionalization and Exfoliation of Graphite Into Mono Layer Graphene for Improved Heat Dissipation,” J. Taiwan Inst. Chem. Eng., 71, pp. 480–493.
Yu, W. , Xie, H. , and Bao, D. , 2010, “ Enhanced Thermal Conductivities of Nanofluids Containing Graphene Oxide Nanosheets,” Nanotechnology, 21(5), p. 55705. [CrossRef]
Beck, M. P. , Yuan, Y. , Warrier, P. , and Teja, A. S. , 2010, “ The Thermal Conductivity of Alumina Nanofluids in Water, Ethylene Glycol, and Ethylene Glycol + Water Mixtures,” J. Nanopart. Res., 12(4), pp. 1469–1477. [CrossRef]
Novoselov, K. S. , Geim, A. K. , Morozov, S. V. , Jiang, D. , Zhang, Y. , Dubonos, S. V. , Grigorieva, I. V. , and Firsov, A. A. , 2004, “ Electric Field Effect in Atomically Thin Carbon Films,” Science, 306(5696), pp. 666–669. [CrossRef] [PubMed]
Wang, S. , Jiang, S. P. , and Wang, X. , 2011, “ Microwave-Assisted One-Pot Synthesis of Metal/Metal Oxide Nanoparticles on Graphene and Their Electrochemical Applications,” Electrochim. Acta., 56(9), pp. 3338–3344. [CrossRef]
Pastoriza-Gallego, M. J. , Lugo, L. , Legido, J. L. , and Piñeiro, M. M. , 2011, “ Thermal Conductivity and Viscosity Measurements of Ethylene Glycol-Based Al2O3 Nanofluids,” Nanoscale Res. Lett., 6(1), p. 221.
Mehrali, M. , Sadeghinezhad, E. , Latibari, S. T. , Kazi, S. N. , Mehrali, M. , Zubir, M. N. B. M. , and Metselaar, H. S. C. , 2014, “ Investigation of Thermal Conductivity and Rheological Properties of Nanofluids Containing Graphene Nanoplatelets,” Nanoscale Res. Lett., 9(1), p. 15. [CrossRef] [PubMed]
Lu, N. , Li, Z. , and Yang, J. , 2009, “ Electronic Structure Engineering Via on-Plane Chemical Functionalization: A Comparison Study on Two-Dimensional Polysilane and Graphane,” J. Phys. Chem. C, 113(38), pp. 16741–16746. [CrossRef]
Sandeep, N. , and Sulochana, C. , 1998, “ MHD Flow and Heat Transfer of a Dusty Nanofluid Over a Stretching Surface in Porous Medium,” Jordan J. Civ. Eng., 11(1), pp. 149–164. https://search.proquest.com/openview/88d7f2507d96bcb60e641ca6ac83523c/1?pq-origsite=gscholar&cbl=2035891
Reddy, J. V. R. , Sugunamma, V. , Sandeep, N. , and Raju, C. S. K. , 2015, “ Chemically Reacting MHD Dusty Nanofluid Flow Over a Vertical Cone With Non-Uniform Heat Source/Sink,” Walailak J. Sci. Technol., 14(2), pp. 141–156. http://wjst.wu.ac.th/index.php/wjst/article/view/1906/651
Krishnamurthy, M. R. , Gireesha, B. J. , Gorla, R. S. R. , and Prasannakumara, B. C. , 2016, “ Suspended Particle Effect on Slip Flow and Melting Heat Transfer of Nanofluid Over a Stretching Sheet Embedded in a Porous Medium in the Presence of Nonlinear Thermal Radiation,” J. Nanofluids, 5(4), pp. 502–510. [CrossRef]
C., Sulochana , J., Prakash ., and Sandeep , 2016, “ Unsteady MHD Flow of a Dusty Nanofluid Past a Vertical Stretching Surface With Non-Uniform Heat Source/Sink,” Int. J. Sci. Eng., 10(1), pp. 1–9. https://www.researchgate.net/publication/307675919_Unsteady_MHD_flow_of_a_dusty_nanofluid_past_a_vertical_stretching_surface_with_non-uniform_heat_sourcesink
Raju, C. S. K. , and Sandeep, N. , 2016, “ Unsteady Three-Dimensional Flow of Casson-Carreau Fluids Past a Stretching Surface,” Alexandria Eng. J., 55(2), pp. 1115–1126. [CrossRef]
Sastry, D. R. V. S. R. K. , Venkataraman, V. , Kannan, K. , and Srinivasu, M. , 2016, “ Unsteady Viscous Dissipative Dusty Nanofluid Flow Over a Vertical Plate,” Int. J. Eng. Technol., 8(5), pp. 2008–2017. [CrossRef]
Raju, C. S. K. , Sandeep, N. , and Sugunamma, V. , 2016, “ Unsteady Magneto-Nanofluid Flow Caused by a Rotating Cone With Temperature Dependent Viscosity: A Surgical Implant Application,” J. Mol. Liq., 222, pp. 1183–1193. [CrossRef]
Raju, C. S. K. , and Sandeep, N. , 2017, “ Unsteady Casson Nanofluid Flow Over a Rotating Cone in a Rotating Frame Filled With Ferrous Nanoparticles: A Numerical Study,” J. Magn. Magn. Mater., 421, pp. 216–224. [CrossRef]
Raju, C. S. K. , Sandeep, N. , and Babu, M. J. , 2016, “ Effects of Non-Uniform Heat Source/Sink and Chemical Reaction on Unsteady MHD Nanofluid Flow Over a Permeable Stretching Surface,” Adv. Sci. Eng. Med., 8(3), pp. 165–174. [CrossRef]
Hashim, M. K. , 2017, “ On Cattaneo–Christov Heat Flux Model for Carreau Fluid Flow Over a Slendering Sheet,” Results Phys., 7, pp. 310–319. [CrossRef]
Hayat, T. , Qayyum, S. , Shehzad, S. A. , and Alsaedi, A. , 2017, “ Cattaneo–Christov Double-Diffusion Model for Flow of Jeffrey Fluid,” J. Braz. Soc. Mech. Sci. Eng., 39(12), pp. 4965–4971.
Rashad, A. M. , Mallikarjuna, B. , Chamkha, A. J. , and Hariprasad Raju, S. , 2016, “ Thermophoresis Effect on Heat and Mass Transfer From a Rotating Cone in a Porous Medium With Thermal Radiation,” Afrika Matematika, 27(7–8), pp. 1409–1424.
Shehzad, S. A. , Abbasi, F. M. , Hayat, T. , and Alsaedi, A. , 2016, “ Cattaneo-Christov Heat Flux Model for Darcy-Forchheimer Flow of an Oldroyd-B Fluid With Variable Conductivity and Non-Linear Convection,” J. Mol. Liq., 224(Pt. A), pp. 274–278. [CrossRef]
Waqas, M. , Hayat, T. , Farooq, M. , Shehzad, S. A. , and Alsaedi, A. , 2016, “ Cattaneo-Christov Heat Flux Model for Flow of Variable Thermal Conductivity Generalized Burgers Fluid,” J. Mol. Liq., 220, pp. 642–648. [CrossRef]
Abel, M. S. , and Mahesha, N. , 2008, “ Heat Transfer in MHD Viscoelastic Fluid Flow Over a Stretching Sheet With Variable Thermal Conductivity, Non-Uniform Heat Source and Radiation,” Appl. Math. Mod., 32(10), pp. 1965–1983. [CrossRef]


Grahic Jump Location
Fig. 2

Influence of ϕ on f′(ζ) and F′(ζ)

Grahic Jump Location
Fig. 3

Influence of M on f′(ζ) and F′(ζ)

Grahic Jump Location
Fig. 1

Physical model representing the flow problem

Grahic Jump Location
Fig. 4

Influence of βv on f′(ζ) and F′(ζ)

Grahic Jump Location
Fig. 5

Influence of A on f′(ζ) and F′(ζ)

Grahic Jump Location
Fig. 6

Influence of We on f′(ζ) and F′(ζ)

Grahic Jump Location
Fig. 7

Influence of ϕ on θ(ζ) and θp(ζ)

Grahic Jump Location
Fig. 8

Influence of R on θ(ζ) and θp(ζ)

Grahic Jump Location
Fig. 9

Influence of M on θ(ζ) and θp(ζ)

Grahic Jump Location
Fig. 10

Influence of Λ on θ(ζ) and θp(ζ)

Grahic Jump Location
Fig. 11

Influence of Ec on θ(ζ) and θp(ζ)

Grahic Jump Location
Fig. 12

Influence of βv on θ(ζ) and θp(ζ)

Grahic Jump Location
Fig. 13

Influence of βt on θ(ζ) and θp(ζ)

Grahic Jump Location
Fig. 14

Influence of A on θ(ζ) and θp(ζ)



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