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Combined effects of Brownian motion and thermophoresis parameters on three-dimensional (3D) Casson nanofluid flow across the porous layers slendering sheet in a suspension of graphene nanoparticles

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Abstract

The present study emphases on the three-dimensional (3D) Casson nanofluid flow across a slendering sheet in porous layers by considering the thermophoresis and Brownian motion effect. The proposed mathematical model has a tendency to characterise the effect of the non-uniform heat source/sink. In the present simulation, the graphene–water-based nanoparticles have been used at two different temperatures namely 10 and 50 °C. The nonlinear ordinary differential equations are solved using the Runge–Kutta Feldberg integration method. The characteristics of velocity, temperature and concentration boundary layers in the presence of graphene–water nanoparticles are presented for different physical parameters such as heat source/sink parameter, thermophoresis parameter, Brownian motion parameter, Casson fluid parameter, porosity parameter, volume fraction and velocity power index parameter. Moreover, the friction factor coefficients, Nusselt number and Sherwood number are also estimated and discussed for aforesaid physical parameters. It is found that there is a significant increase in the thermal and concentration boundary layer thickness when the strength of the thermophoresis parameter is increased. In contrast, thermal boundary layer increases with the rise in the Brownian motion parameter, while the reverse trend holds true for concentration field. In addition, the rate of heat and mass transfer rate are higher in case of graphene–water nanoparticle at 50 °C compared to 10 °C temperature.

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Abbreviations

u, v, w :

Velocity components in x, y and z directions

C p :

Specific heat capacity at constant pressure

f, g :

Dimensionless velocities

A :

Coefficient related to stretching sheet

m :

Velocity power index parameter

B(x):

Magnetic field parameter

T :

Temperature of the fluid

k :

Thermal conductivity

D m :

Molecular diffusivity of the species concentration

C s :

Concentration susceptibility

C :

Concentration of the fluid

T m :

Mean fluid temperature

T ∞ :

Temperature of the fluid in the free stream

C ∞ :

Concentration of the fluid in the free stream

\(j_{1}^{*}\) :

Dimensional velocity slip parameter

\(j_{2}^{*}\) :

Dimensional temperature jump parameter

\(j_{3}^{*}\) :

Dimensional concentration jump parameter

f 1 :

Maxwell’s reflection coefficient

a :

Thermal accommodation coefficient

b :

Physical parameter related to stretching sheet

d :

Concentration accommodation coefficient

m :

Velocity power index parameter

Pr :

Prandtl number

q′′′:

Non-uniform heat source/sink parameter

B(x):

Dimensional magnetic field parameter

M :

Magnetic interaction parameter

K :

Porosity parameter

Nt:

Thermophoresis parameter

Le :

Lewis number

Nb:

Brownian motion parameter

j 1 :

Dimensionless velocity slip parameter

j 2 :

Dimensionless temperature jump parameter

j 3 :

Dimensionless concentration jump parameter

C f :

Wall skin friction coefficient

Nu x :

Local Nusselt number

Sh x :

Local Sherwood number

Re x :

Local Reynolds number

ϕ :

Dimensionless concentration

η :

Similarity variable

σ :

Electrical conductivity of the fluid

γ :

Ratio of specific heats

θ :

Dimensionless temperature

ρ nf :

Density of the nanofluid

k nf :

Thermal conductivity of the nanofluid

μ nf :

Dynamic viscosity of nanofluid

υ f :

Kinematic viscosity

δ :

Wall thickness parameter

ξ 1, ξ 2 :

Mean free path (constant)

ξ 3, ξ 4 :

Mean free path (constant)

Γ:

Positive characteristic time

References

  1. Lee SW, Lee SS, Yang EH (2009) A study on field emission characteristics of planar graphene layers obtained from a highly oriented pyrolyzed graphite bloc. Nanoscale Res Lett 4:1218–1221

    Article  Google Scholar 

  2. Malesevic A, Kemps R, Vanhulsel A, Chowdhury PM, Alexander V, Chris VH (2008) Field emission from vertically aligned few-layer graphene. J Appl Phys 104:084301

    Article  Google Scholar 

  3. Mao LF (2011) A theoretical analysis of field emission from graphene nanoribbons. Carbon 49(8):2709–2714

    Article  Google Scholar 

  4. Haque AKMM, Kwon S, Kim J, Noh J, Huh S, Chung H, Jeong H (2015) An experimental study on thermal characteristics of nanofluid with graphene and multi-wall carbon nanotubes. J Cent South Univ 22:3202–3210

    Article  Google Scholar 

  5. Baby TT, Prabhu SR (2012) Experimental study on the field emission properties of metal oxide nanoparticle–decorated graphene. J Appl Phys 111:034311

    Article  Google Scholar 

  6. Bhargava R, Goyal M (2014) MHD non-Newtonian nanofluid flow over a permeable stretching sheet with heat generation and velocity slip. Int J Math Comput Nat Phys Eng 8(6):910–916

    Google Scholar 

  7. Cortell R (2014) MHD (magneto-hydrodynamic) flow and radiative nonlinear heat transfer of a viscoelastic fluid over a stretching sheet with heat generation/absorption. Energy 74:896–905

    Article  Google Scholar 

  8. Raju CSK, Sandeep N, Sugunamma V, Babu MJ, Reddy JVR (2016) Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface. Eng Sci Technol Int J 19(1):45–52

    Article  Google Scholar 

  9. Hayat T, Imtiaz M, Alsaedi A, Kutbi MA (2015) MHD three dimensional flow of nanofluid with velocity slip and nonlinear thermal radiation. J Magn Magn Mater 396:31–37

    Article  Google Scholar 

  10. Animasaun IL, Raju CSK, Sandeep N (2016) Unequal diffusivities case of homogeneous–heterogeneous reactions within viscoelastic fluid flow in the presence of induced magnetic-field and nonlinear thermal radiation. Alex Eng J 55(2):1595–1606

    Article  Google Scholar 

  11. Nelson E (1967) Dynamical theories of Brownian motion, vol 3. Princeton University Press, Princeton

    MATH  Google Scholar 

  12. Nadeem S, Haq RU, Akbar NS (2014) MHD three-dimensional boundary layer flow of Casson nanofluid past a linearly stretching sheet with convective boundary condition. IEEE Trans Nanotechnol 13(1):109–115

    Article  Google Scholar 

  13. Raju CSK, Hoque MM, Anika NN, Mamatha SU, Sharma P (2017) Natural convective heat transfer analysis of MHD unsteady Carreau nanofluid over a cone packed with alloy nanoparticles. Powder Technol 317:408–416

    Article  Google Scholar 

  14. Raju CSK, Hoque MM, Sivasankar T (2016) Radiative flow of Casson fluid over a moving wedge filled with gyrotactic microorganisms. Adv Powder Technol 28(2):575–583

    Article  Google Scholar 

  15. Raju CSK, Sandeep N (2016) Unsteady three-dimensional flow of Casson–Carreau fluids past a stretching surface. Alex Eng J 55(2):1115–1126

    Article  Google Scholar 

  16. Beg OA, Hoque MM, Wahiduzzaman M, Alam MM, Ferdows M (2014) Spectral numerical simulation of mageneto-physiological laminar Dean flow. J Mech Med Biol 14(4):1450047

    Article  Google Scholar 

  17. Hoque MM, Alam MM (2013) Effects of Dean number and curvature on fluid flow through a curved pipe with magnetic field. Procedia Eng 56:243–253

    Article  Google Scholar 

  18. Hoque MM, Alam MM, Ferdows M, Beg OA (2013) Numerical simulation of Dean number and curvature effects on magneto-bio-fluid flow through a curved conduit. Proc Inst Mech Eng H J Eng Med 227(11):1155–1170

    Article  Google Scholar 

  19. Hoque MM, Anika NN, Alam MM (2013) Numerical analysis of magnetohydrodynamics flow in a curved duct. Int J Sci Eng Res 4(7):607–617

    Google Scholar 

  20. Hoque MM, Alam MM (2015) A numerical study of MHD laminar flow in a rotating curved pipe with circular cross section. Open J Fluid Dyn 5:121–127

    Article  Google Scholar 

  21. Hoque MM, Anika NN, Alam MM (2013) Magnetic effects on direct numerical solution of fluid flow through a curved pipe with circular cross section. Eur J Sci Res 103(3):343–361

    Google Scholar 

  22. Reddy GJ, Kethireddy B, Kumar M, Hoque MM (2018) A molecular dynamics study on transient non-Newtonian MHD Casson fluid flow dispersion over a radiative vertical cylinder with entropy heat generation. J Mol Liq 252:245–262

    Article  Google Scholar 

  23. Sulochana C, Ashwinkumar GP, Sandeep N (2016) Similarity solution of 3D Casson nanofluid flow over a stretching sheet with convective boundary conditions. J Niger Math Soc 35:128–141

    Article  MathSciNet  MATH  Google Scholar 

  24. Babu MJ, Sandeep N (2016) 3D MHD slip flow of a nanofluid over a slendering stretching sheet with thermophoresis and Brownian motion effects. J Mol Liq 222:1003–1009

    Article  Google Scholar 

  25. Sandeep N, Koriko OK, Animasaun IL (2016) Modified kinematic viscosity model for 3D Casson fluid flow within boundary layer formed on a surface at absolute zero. J Mol Liq 221:1197–1206

    Article  Google Scholar 

  26. Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles. Paper presented at the international mechanical engineering congress and exposition, San Francisco, USA

  27. Buongiorno J (2005) Convective transport in nanofluids. J Heat Transf 128(3):240–250

    Article  Google Scholar 

  28. Gireesha BJ, Mahanthesh B, Rashidi MM (2015) MHD boundary layer heat and mass transfer of a chemically reacting Casson fluid over a permeable stretching surface with non-uniform heat source/sink. Int J Ind Math 7:247–260

    Google Scholar 

  29. Sheikholeslami M, Ganji DD (2015) Nanofluid flow and heat transfer between parallel plates considering Brownian motion using DTM. Comput Methods Appl Mech Eng 283:651–663

    Article  MathSciNet  MATH  Google Scholar 

  30. Malvandi A, Heysiattalab S, Ganji DD (2016) Thermophoresis and Brownian motion effects on heat transfer enhancement at film boiling of nanofluids over a vertical cylinder. J Mol Liq 216:503–509

    Article  Google Scholar 

  31. Fani B, Kalteh M, Abbassi A (2015) Investigating the effect of Brownian motion and viscous dissipation on the nanofluid heat transfer in a trapezoidal micro channel heat sink. Adv Powder Technol 26:83–90

    Article  Google Scholar 

  32. Angayarkanni SA, Philip J (2015) Review on thermal properties of nanofluids: recent developments. Adv Colloid Interface Sci 225:146–176

    Article  Google Scholar 

  33. Khan WA, Aziz A (2011) Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux. Int J Therm Sci 50(7):1207–1214

    Article  Google Scholar 

  34. Kim J, Kang YT, Choi CK (2004) Analysis of convective instability and heat transfer characteristics of nanofluids. Phys Fluids 16:2395–2401

    Article  MATH  Google Scholar 

  35. Sheikholeslami M (2017) Numerical simulation of magnetic nanofluid natural convection in porous media. Phys Lett A 381(5):494–503

    Article  Google Scholar 

  36. Sheikholeslami M (2017) Influence of Lorentz forces on nanofluid flow in a porous cylinder considering Darcy model. J Mol Liq 225:903–912

    Article  Google Scholar 

  37. Sheikholeslami M (2017) Magnetic field influence on nanofluid thermal radiation in a cavity with tilted elliptic inner cylinder. J Mol Liq 229:137–147

    Article  Google Scholar 

  38. Sheikholeslami M (2017) Magnetohydrodynamic nanofluid forced convection in a porous lid driven cubic cavity using Lattice Boltzmann method. J Mol Liq 231:555–565

    Article  Google Scholar 

  39. Sheikholeslami M (2017) Influence of magnetic field on nanofluid free convection in an open porous cavity by means of Lattice Boltzmann method. J Mol Liq 234:364–374

    Article  Google Scholar 

  40. Sheikholeslami M, Rokni HB (2017) Nanofluid two phase model analysis in existence of induced magnetic field. Int J Heat Mass Transf 107:288–299

    Article  Google Scholar 

  41. Sheikholeslamia M, Bhattib MM (2017) Active method for nanofluid heat transfer enhancement by means of EHD. Int J Heat Mass Transf 109:115–122

    Article  Google Scholar 

  42. Sheikholeslamia M, Hayat T, Alsaedic A (2017) Numerical study for external magnetic source influence on water based nanofluid convective heat transfer. Int J Heat Mass Transf 106:745–755

    Article  Google Scholar 

  43. Sheikholeslamia M, Shehzadb SA (2017) Magnetohydrodynamic nanofluid convection in a porous enclosure considering heat flux boundary condition. Int J Heat Mass Transf 106:1261–1269

    Article  Google Scholar 

  44. Sheikholeslamia M, Shehzadb SA (2017) Thermal radiation of ferrofluid in existence of Lorentz forces considering variable viscosity. Int J Heat Mass Transf 109:82–92

    Article  Google Scholar 

  45. Khader M, Megahed AM (2003) Numerical solution for boundary layer flow due to a nonlinearly stretching sheet with variable thickness and slip velocity. Eur Phys J Plus 128:100–108

    Article  Google Scholar 

  46. Devi SPA, Prakash M (2016) Slip flow effects over hydromagnetic forced convective flow over a slendering stretching sheet. J Appl Fluid Mech 9(2):683–692

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Sri Venkateswara University, Tirupati, India

    P. Durgaprasad & S. V. K. Varma

  2. Disipline of Chemical Engineering, University of Newcastle, Callaghan, 2308, Australia

    Mohammad Mainul Hoque

  3. Department of Mathematics, GITAM School of Technology, Bangalore, 561203, India

    C. S. K. Raju

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  1. P. Durgaprasad
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  2. S. V. K. Varma
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  3. Mohammad Mainul Hoque
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  4. C. S. K. Raju
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Correspondence to Mohammad Mainul Hoque.

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Durgaprasad, P., Varma, S.V.K., Hoque, M.M. et al. Combined effects of Brownian motion and thermophoresis parameters on three-dimensional (3D) Casson nanofluid flow across the porous layers slendering sheet in a suspension of graphene nanoparticles. Neural Comput & Applic 31, 6275–6286 (2019). https://doi.org/10.1007/s00521-018-3451-z

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