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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

  • P. Durgaprasad
  • S. V. K. Varma
  • Mohammad Mainul Hoque
  • C. S. K. Raju
Original Article

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.

Keywords

Grapheme nanoparticles Non-uniform heat source or sink Casson fluid Thermophoresis Brownian motion MHD Porous layers 

List of symbols

u, v, w

Velocity components in x, y and z directions

Cp

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

Dm

Molecular diffusivity of the species concentration

Cs

Concentration susceptibility

C

Concentration of the fluid

Tm

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

f1

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

j1

Dimensionless velocity slip parameter

j2

Dimensionless temperature jump parameter

j3

Dimensionless concentration jump parameter

Cf

Wall skin friction coefficient

Nux

Local Nusselt number

Shx

Local Sherwood number

Rex

Local Reynolds number

Greek Symbols

ϕ

Dimensionless concentration

η

Similarity variable

σ

Electrical conductivity of the fluid

γ

Ratio of specific heats

θ

Dimensionless temperature

ρnf

Density of the nanofluid

knf

Thermal conductivity of the nanofluid

μnf

Dynamic viscosity of nanofluid

υf

Kinematic viscosity

δ

Wall thickness parameter

ξ1, ξ2

Mean free path (constant)

ξ3, ξ4

Mean free path (constant)

Γ

Positive characteristic time

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

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Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.Department of MathematicsSri Venkateswara UniversityTirupatiIndia
  2. 2.Disipline of Chemical EngineeringUniversity of NewcastleCallaghanAustralia
  3. 3.Department of MathematicsGITAM School of TechnologyBangaloreIndia

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