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Published in: Arabian Journal for Science and Engineering 2/2020

11-12-2019 | Research Article - -Mechanical Engineering

Nonlinear Mixed Convection Flow of Nanofluid Past a Moving Vertical Slender Cylinder

Authors: P. M. Patil, Madhavarao Kulkarni, P. S. Hiremath

Published in: Arabian Journal for Science and Engineering | Issue 2/2020

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Abstract

In this article, the nonlinear mixed convection flow of nanofluid past a slender cylinder, which is vertically moving with constant velocity, with viscous dissipation effects is examined. The governing equations of the flow are in the form of dimensional nonlinear partial differential equations (NPDEs), which are brought to non-dimensional form, along with the boundary conditions, by employing non-similar transformations. The resultant non-dimensional NPDEs are solved by adopting quasilinearization technique and implicit finite difference method. The numerical study focuses analysis of various non-dimensional parameters, such as Brownian diffusion Nb, nonlinear mixed convection \(\gamma\), Richardson number Ri, Lewis number Le, Eckert number or viscous dissipation Ec, thermophoresis Nt, nanoparticle buoyancy ratio Nr, velocity ratio \(\varepsilon\), on profiles as well as gradients in detail. The numerical results unveil that the increasing values of Ec increase temperature of the fluid. Further, wall gradients for energy transfer and also nanoparticle mass transfer are studied in the presence as well as in the absence of nonlinear mixed convection effects. At \(\xi = 1\) as Nt increases from 0.05 to 0.15, the friction between the wall and the fluid increases by about 15.23% and 22.41% for Nb = 0.15 and Nb = 0.3, respectively.

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Literature
1.
go back to reference Vajravelu, K.; Sastri, K.S.: Fully developed laminar free convection flow between two parallel vertical walls. Int. J. Heat Mass Transf. 20, 655–660 (1977) Vajravelu, K.; Sastri, K.S.: Fully developed laminar free convection flow between two parallel vertical walls. Int. J. Heat Mass Transf. 20, 655–660 (1977)
2.
go back to reference Bhargava, R.; Agarwal, R.S.: Fully developed free convection flow in a circular pipe. Ind. J. Pure Appl. Math. 10, 357–365 (1979)MATH Bhargava, R.; Agarwal, R.S.: Fully developed free convection flow in a circular pipe. Ind. J. Pure Appl. Math. 10, 357–365 (1979)MATH
4.
go back to reference Bandaru, M.; Rashidi, M.M.; Raju, H.: Influence of non-linear convection and thermophoresis on heat and mass transfer from a rotating cone to fluid flow in porous medium. Therm. Sci. 21, 2781–2793 (2017) Bandaru, M.; Rashidi, M.M.; Raju, H.: Influence of non-linear convection and thermophoresis on heat and mass transfer from a rotating cone to fluid flow in porous medium. Therm. Sci. 21, 2781–2793 (2017)
6.
go back to reference Ziabicki, A.: Fundamentals of Fibre Formation. Wiley, New York (1976) Ziabicki, A.: Fundamentals of Fibre Formation. Wiley, New York (1976)
7.
go back to reference Chamkha, A.J.; Khaled, A.-R.A.: Similarity solutions for hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media. Int. J. Numer. Methods Heat Fluid Flow 10, 94–115 (1999)MATH Chamkha, A.J.; Khaled, A.-R.A.: Similarity solutions for hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media. Int. J. Numer. Methods Heat Fluid Flow 10, 94–115 (1999)MATH
8.
go back to reference Chamkha, A.J.: Coupled heat and mass transfer by natural convection about a truncated cone in the presence of magnetic field and radiation effects. Numer. Heat Trans. A 39, 511–530 (2001) Chamkha, A.J.: Coupled heat and mass transfer by natural convection about a truncated cone in the presence of magnetic field and radiation effects. Numer. Heat Trans. A 39, 511–530 (2001)
9.
go back to reference Takhar, H.S.; Chamkha, A.J.; Nath, G.: Unsteady mixed convection flow from a rotating vertical cone with a magnetic field. Heat Mass Transf. 39, 297–304 (2003) Takhar, H.S.; Chamkha, A.J.; Nath, G.: Unsteady mixed convection flow from a rotating vertical cone with a magnetic field. Heat Mass Transf. 39, 297–304 (2003)
10.
go back to reference Damseh, R.A.; Al-Odata, M.Q.; Chamkha, A.J.; Shannak, B.A.: Combined effect of heat generation or absorption and first-order chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface. Int. J. Therm. Sci. 48, 1658–1663 (2009) Damseh, R.A.; Al-Odata, M.Q.; Chamkha, A.J.; Shannak, B.A.: Combined effect of heat generation or absorption and first-order chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface. Int. J. Therm. Sci. 48, 1658–1663 (2009)
11.
go back to reference Khedr, M.E.M.; Chamkha, A.J.; Bayomi, M.: MHD flow of a micropolar fluid past a stretched permeable surface with heat generation or absorption. Nonlinear Anal. Model. 14, 27–40 (2009)MATH Khedr, M.E.M.; Chamkha, A.J.; Bayomi, M.: MHD flow of a micropolar fluid past a stretched permeable surface with heat generation or absorption. Nonlinear Anal. Model. 14, 27–40 (2009)MATH
12.
go back to reference Magyari, E.; Chamkha, A.J.: Combined effect of heat generation or absorption and first-order chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface: the full analytical solution. Int. J. Therm. Sci. 49, 1821–1829 (2010) Magyari, E.; Chamkha, A.J.: Combined effect of heat generation or absorption and first-order chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface: the full analytical solution. Int. J. Therm. Sci. 49, 1821–1829 (2010)
13.
go back to reference Chen, T.S.; Mucoglu, A.: Buoyancy effects on forced convection along a vertical cylinder with uniform surface heat flux. ASME J. Heat Transf. 98, 523–525 (1976) Chen, T.S.; Mucoglu, A.: Buoyancy effects on forced convection along a vertical cylinder with uniform surface heat flux. ASME J. Heat Transf. 98, 523–525 (1976)
14.
go back to reference Chen, T.S.; Yuh, C.F.: Combined heat and mass transfer in natural convection along a vertical cylinder. Int. J. Heat Mass Transf. 23, 451–461 (1980)MATH Chen, T.S.; Yuh, C.F.: Combined heat and mass transfer in natural convection along a vertical cylinder. Int. J. Heat Mass Transf. 23, 451–461 (1980)MATH
15.
go back to reference Bui, M.N.; Cebeci, T.: Combined free and forced convection on vertical slender cylinders. ASME J. Heat Transf. 107, 476–478 (1985) Bui, M.N.; Cebeci, T.: Combined free and forced convection on vertical slender cylinders. ASME J. Heat Transf. 107, 476–478 (1985)
16.
go back to reference Wang, T.Y.; Kleinstruver, C.: General analysis of steady mixed convection heat transfer on vertical slender cylinders. ASME J. Heat Transf. 111, 393–398 (1989) Wang, T.Y.; Kleinstruver, C.: General analysis of steady mixed convection heat transfer on vertical slender cylinders. ASME J. Heat Transf. 111, 393–398 (1989)
17.
go back to reference Daskalakis, J.E.: Mixed free and forced convection in the incompressible boundary layer along a rotating vertical cylinder with fluid injection. Int. J. Energy Res. 17, 689–695 (1993) Daskalakis, J.E.: Mixed free and forced convection in the incompressible boundary layer along a rotating vertical cylinder with fluid injection. Int. J. Energy Res. 17, 689–695 (1993)
18.
go back to reference Richelle, E.; Tasse, R.; Riethmuller, M.L.: Momentum and thermal boundary layer along a slender cylinder in axial flow. Int. J. Heat Fluid Flow 16, 99–105 (1995) Richelle, E.; Tasse, R.; Riethmuller, M.L.: Momentum and thermal boundary layer along a slender cylinder in axial flow. Int. J. Heat Fluid Flow 16, 99–105 (1995)
19.
go back to reference Takhar, H.S.; Chamkha, A.J.; Nath, G.: Combined heat and mass transfer along a vertical moving cylinder with a free stream. Heat Mass Transf. 36, 237–246 (2000) Takhar, H.S.; Chamkha, A.J.; Nath, G.: Combined heat and mass transfer along a vertical moving cylinder with a free stream. Heat Mass Transf. 36, 237–246 (2000)
20.
go back to reference Roy, S.; Anilkumar, D.: Unsteady mixed convection from a moving vertical slender cylinder. ASME J. Heat Transf. 128, 368–373 (2006) Roy, S.; Anilkumar, D.: Unsteady mixed convection from a moving vertical slender cylinder. ASME J. Heat Transf. 128, 368–373 (2006)
21.
go back to reference Patil, P.M.; Roy, S.; Chamkha, A.J.; Kulkarni, P.S.: Unsteady mixed convection flow from a moving vertical slender cylinder in the presence of viscous dissipation. Int. J. Micro-Nano Therm. Fluid Transp. Phenom. 2, 281–305 (2011) Patil, P.M.; Roy, S.; Chamkha, A.J.; Kulkarni, P.S.: Unsteady mixed convection flow from a moving vertical slender cylinder in the presence of viscous dissipation. Int. J. Micro-Nano Therm. Fluid Transp. Phenom. 2, 281–305 (2011)
22.
go back to reference Patil, P.M.; Roy, S.; Pop, I.: Unsteady effects on mixed convection boundary layer flow from a permeable slender cylinder due to nonlinearly power law stretching. Comput. Fluids 56, 17–23 (2012)MathSciNetMATH Patil, P.M.; Roy, S.; Pop, I.: Unsteady effects on mixed convection boundary layer flow from a permeable slender cylinder due to nonlinearly power law stretching. Comput. Fluids 56, 17–23 (2012)MathSciNetMATH
23.
go back to reference Patil, P.M.; Roy, S.; Pop, I.: Chemical reaction effects on unsteady mixed convection boundary layer flow past a permeable slender vertical cylinder due to a nonlinearly stretching velocity. Chem. Eng. Commun. 200, 398–417 (2013) Patil, P.M.; Roy, S.; Pop, I.: Chemical reaction effects on unsteady mixed convection boundary layer flow past a permeable slender vertical cylinder due to a nonlinearly stretching velocity. Chem. Eng. Commun. 200, 398–417 (2013)
24.
go back to reference Patil, P.M.; Pop, I.: Unsteady mixed convection flow from a slender vertical cylinder due to impulsive change in wall velocity and temperature. Therm. Sci. 17, 1023–1034 (2013) Patil, P.M.; Pop, I.: Unsteady mixed convection flow from a slender vertical cylinder due to impulsive change in wall velocity and temperature. Therm. Sci. 17, 1023–1034 (2013)
25.
go back to reference Aydin, O.; Kaya, A.: MHD mixed convection of a viscous dissipating fluid about a vertical slender cylinder. Desal. Water. Treat. 51, 3576–3583 (2013) Aydin, O.; Kaya, A.: MHD mixed convection of a viscous dissipating fluid about a vertical slender cylinder. Desal. Water. Treat. 51, 3576–3583 (2013)
26.
go back to reference Rashad, A.M.; Chamkha, A.J.; Mallikarjuna, B.; Abdou, M.M.M.: Mixed bioconvection flow of a nanofluid containing gyrotactic microorganisms past a vertical slender cylinder. Front. Heat Mass Transf. 10, 21 (2018) Rashad, A.M.; Chamkha, A.J.; Mallikarjuna, B.; Abdou, M.M.M.: Mixed bioconvection flow of a nanofluid containing gyrotactic microorganisms past a vertical slender cylinder. Front. Heat Mass Transf. 10, 21 (2018)
27.
go back to reference Choi, S.U.S.; Eastman, J.A.: Enhancing thermal conductivity of fluids with nanoparticles. In: Proceedings of the International Mechanical Engineering Congress and Exhibition ASME, San Francisco, California, USA, FED/231MD, pp. 99–105 (1995) Choi, S.U.S.; Eastman, J.A.: Enhancing thermal conductivity of fluids with nanoparticles. In: Proceedings of the International Mechanical Engineering Congress and Exhibition ASME, San Francisco, California, USA, FED/231MD, pp. 99–105 (1995)
28.
go back to reference Sudarsana Reddy, P.; Chamkha, A.J.: Soret and Dufour effects on MHD convective flow of Al2O3–water and TiO2–water nanofluids past a stretching sheet in porous media with heat generation/absorption. Adv. Powder Technol. 27, 1207–1218 (2016) Sudarsana Reddy, P.; Chamkha, A.J.: Soret and Dufour effects on MHD convective flow of Al2O3–water and TiO2–water nanofluids past a stretching sheet in porous media with heat generation/absorption. Adv. Powder Technol. 27, 1207–1218 (2016)
29.
go back to reference Gorla, R.S.R.; Chamkha, A.: Natural convective boundary layer flow over a nonisothermal vertical plate embedded in a porous medium saturated with a nanofluid. Nanoscale Microscale Therm. 15, 81–94 (2011) Gorla, R.S.R.; Chamkha, A.: Natural convective boundary layer flow over a nonisothermal vertical plate embedded in a porous medium saturated with a nanofluid. Nanoscale Microscale Therm. 15, 81–94 (2011)
30.
go back to reference RamReddy, Ch; Murthy, P.V.S.N.; Chamkha, A.J.; Rashad, A.M.: Soret effect on mixed convection flow in a nanofluid under convective boundary condition. Int. J. Heat Mass Transf. 64, 384–392 (2013) RamReddy, Ch; Murthy, P.V.S.N.; Chamkha, A.J.; Rashad, A.M.: Soret effect on mixed convection flow in a nanofluid under convective boundary condition. Int. J. Heat Mass Transf. 64, 384–392 (2013)
31.
go back to reference Zaraki, A.; Ghalambaz, M.; Chamkha, A.J.; Ghalambaz, M.; Rossi, D.D.: Theoretical analysis of natural convection boundary layer heat and mass transfer of nanofluids: effects of size, shape and type of nanoparticles, type of base fluid and working temperature. Adv. Powder Technol. 26, 935–946 (2015) Zaraki, A.; Ghalambaz, M.; Chamkha, A.J.; Ghalambaz, M.; Rossi, D.D.: Theoretical analysis of natural convection boundary layer heat and mass transfer of nanofluids: effects of size, shape and type of nanoparticles, type of base fluid and working temperature. Adv. Powder Technol. 26, 935–946 (2015)
32.
go back to reference Chamkha, A.J.; Abbasbandy, S.; Rashad, A.M.; Vajravelu, K.: Radiation effects on mixed convection about a cone embedded in a porous medium filled with a nanofluid. Meccanica 48, 275–285 (2013)MathSciNetMATH Chamkha, A.J.; Abbasbandy, S.; Rashad, A.M.; Vajravelu, K.: Radiation effects on mixed convection about a cone embedded in a porous medium filled with a nanofluid. Meccanica 48, 275–285 (2013)MathSciNetMATH
33.
go back to reference Ghalambaz, M.; Behseresht, A.; Behseresht, J.; Chamkha, A.: Effects of nanoparticles diameter and concentration on natural convection of the Al2O3–water nanofluids considering variable thermal conductivity around a vertical cone in porous media. Adv. Powder Technol. 26, 224–235 (2015) Ghalambaz, M.; Behseresht, A.; Behseresht, J.; Chamkha, A.: Effects of nanoparticles diameter and concentration on natural convection of the Al2O3–water nanofluids considering variable thermal conductivity around a vertical cone in porous media. Adv. Powder Technol. 26, 224–235 (2015)
34.
go back to reference Reddy, P.S.; Sreedevi, P.; Chamkha, A.J.: MHD boundary layer flow, heat and mass transfer analysis over a rotating disk through porous medium saturated by Cu-water and Ag-water nanofluid with chemical reaction. Powder Technol. 307, 46–55 (2017) Reddy, P.S.; Sreedevi, P.; Chamkha, A.J.: MHD boundary layer flow, heat and mass transfer analysis over a rotating disk through porous medium saturated by Cu-water and Ag-water nanofluid with chemical reaction. Powder Technol. 307, 46–55 (2017)
35.
go back to reference Lin, Y.; Jiang, Y.: Effects of Brownian motion and thermophoresis on nanofluids in a rotating circular groove: a numerical simulation. Int. J. Heat Mass Transf. 123, 569–582 (2018) Lin, Y.; Jiang, Y.: Effects of Brownian motion and thermophoresis on nanofluids in a rotating circular groove: a numerical simulation. Int. J. Heat Mass Transf. 123, 569–582 (2018)
36.
go back to reference Hayat, T.; Khan, M.I.; Waqas, M.; Alsaedi, A.: Newtonian heating effect in nanofluid flow by a permeable cylinder. Results Phys. 7, 256–262 (2017) Hayat, T.; Khan, M.I.; Waqas, M.; Alsaedi, A.: Newtonian heating effect in nanofluid flow by a permeable cylinder. Results Phys. 7, 256–262 (2017)
37.
go back to reference Raju, C.S.K.; Saleem, S.; Mamatha, S.U.; Hussain, I.: Heat and mass transport phenomena of radiated slender body of three revolutions with saturated porous: buongiorno’s model. Int. J. Therm. Sci. 132, 309–315 (2018) Raju, C.S.K.; Saleem, S.; Mamatha, S.U.; Hussain, I.: Heat and mass transport phenomena of radiated slender body of three revolutions with saturated porous: buongiorno’s model. Int. J. Therm. Sci. 132, 309–315 (2018)
38.
go back to reference Hayat, T.; Rashid, M.; Alsaedi, A.; Asghar, S.: Nonlinear convective flow of Maxwell nanofluid past a stretching cylinder with thermal radiation and chemical reaction. J. Braz. Soc. Mech. Sci. Eng. 41, 86 (2019) Hayat, T.; Rashid, M.; Alsaedi, A.; Asghar, S.: Nonlinear convective flow of Maxwell nanofluid past a stretching cylinder with thermal radiation and chemical reaction. J. Braz. Soc. Mech. Sci. Eng. 41, 86 (2019)
39.
go back to reference Saleem, S.; Firdous, H.; Nadeem, S.; Khan, A.U.: Convective heat and mass transfer in magneto Walter’s B nanofluid flow induced by a rotating cone. Arab. J. Sci. Eng. 44, 1515–1523 (2019) Saleem, S.; Firdous, H.; Nadeem, S.; Khan, A.U.: Convective heat and mass transfer in magneto Walter’s B nanofluid flow induced by a rotating cone. Arab. J. Sci. Eng. 44, 1515–1523 (2019)
40.
go back to reference Fahad, G.; Amri, A.: Analytical solution for fully developed flows of nanofluids in mixed-convection zone within vertical channels. Arab. J. Sci. Eng. 44, 739–752 (2019) Fahad, G.; Amri, A.: Analytical solution for fully developed flows of nanofluids in mixed-convection zone within vertical channels. Arab. J. Sci. Eng. 44, 739–752 (2019)
41.
go back to reference Patil, P.M.; Pop, I.: Effects of surface mass transfer on unsteady mixed convection flow over a vertical cone with chemical reaction. Heat Mass Transf. 47, 1453–1464 (2011) Patil, P.M.; Pop, I.: Effects of surface mass transfer on unsteady mixed convection flow over a vertical cone with chemical reaction. Heat Mass Transf. 47, 1453–1464 (2011)
42.
go back to reference Patil, P.M.; Latha, D.N.; Roy, S.; Momoniat, E.: Non-similar solutions of mixed convection flow from an exponentially stretching surface. Ain Shams Eng. J. 8, 697–705 (2017) Patil, P.M.; Latha, D.N.; Roy, S.; Momoniat, E.: Non-similar solutions of mixed convection flow from an exponentially stretching surface. Ain Shams Eng. J. 8, 697–705 (2017)
43.
go back to reference Patil, P.M.; Shashikant, A.; Hiremath, P.S.: Influence of liquid hydrogen and nitrogen on MHD triple diffusive mixed convection nanoliquid flow in presence of surface roughness. Int. J. Hydrogen Energy 43, 201101–201107 (2018) Patil, P.M.; Shashikant, A.; Hiremath, P.S.: Influence of liquid hydrogen and nitrogen on MHD triple diffusive mixed convection nanoliquid flow in presence of surface roughness. Int. J. Hydrogen Energy 43, 201101–201107 (2018)
44.
go back to reference Patil, P.M.; Shashikant, A.; Roy, S.; Momoniat, E.: Unsteady mixed convection over an exponentially decreasing external flow velocity. Int. J. Heat Mass Transf. 111, 643–650 (2017) Patil, P.M.; Shashikant, A.; Roy, S.; Momoniat, E.: Unsteady mixed convection over an exponentially decreasing external flow velocity. Int. J. Heat Mass Transf. 111, 643–650 (2017)
45.
go back to reference Patil, P.M.; Ramane, H.S.; Roy, S.; Hindasageri, V.; Momoniat, E.: Influence of mixed convection in an exponentially decreasing external flow velocity. Int. J. Heat Mass Transf. 104, 392–399 (2017) Patil, P.M.; Ramane, H.S.; Roy, S.; Hindasageri, V.; Momoniat, E.: Influence of mixed convection in an exponentially decreasing external flow velocity. Int. J. Heat Mass Transf. 104, 392–399 (2017)
46.
go back to reference Patil, P.M.; Roy, M.; Roy, S.; Momoniat, E.: Triple diffusive mixed convection along a vertically moving surface. Int. J. Heat Mass Transf. 117, 287–295 (2018) Patil, P.M.; Roy, M.; Roy, S.; Momoniat, E.: Triple diffusive mixed convection along a vertically moving surface. Int. J. Heat Mass Transf. 117, 287–295 (2018)
47.
go back to reference Schlichting, H.; Gersten, K.: Boundary Layer Theory. Springer, New York (2000)MATH Schlichting, H.; Gersten, K.: Boundary Layer Theory. Springer, New York (2000)MATH
48.
go back to reference Buongiorno, J.: Convective transport in nanofluids. J. Heat Transf. 128, 140–250 (2006) Buongiorno, J.: Convective transport in nanofluids. J. Heat Transf. 128, 140–250 (2006)
49.
go back to reference Varga, R.S.: Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs (2000)MATH Varga, R.S.: Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs (2000)MATH
Metadata
Title
Nonlinear Mixed Convection Flow of Nanofluid Past a Moving Vertical Slender Cylinder
Authors
P. M. Patil
Madhavarao Kulkarni
P. S. Hiremath
Publication date
11-12-2019
Publisher
Springer Berlin Heidelberg
Published in
Arabian Journal for Science and Engineering / Issue 2/2020
Print ISSN: 2193-567X
Electronic ISSN: 2191-4281
DOI
https://doi.org/10.1007/s13369-019-04286-8

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