Neural Computing and Applications

, Volume 31, Issue 10, pp 6275–6286 | Cite as

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 HoqueEmail author
  • C. S. K. Raju
Original Article


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.


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


Specific heat capacity at constant pressure

f, g

Dimensionless velocities


Coefficient related to stretching sheet


Velocity power index parameter


Magnetic field parameter


Temperature of the fluid


Thermal conductivity


Molecular diffusivity of the species concentration


Concentration susceptibility


Concentration of the fluid


Mean fluid temperature


Temperature of the fluid in the free stream


Concentration of the fluid in the free stream


Dimensional velocity slip parameter


Dimensional temperature jump parameter


Dimensional concentration jump parameter


Maxwell’s reflection coefficient


Thermal accommodation coefficient


Physical parameter related to stretching sheet


Concentration accommodation coefficient


Velocity power index parameter


Prandtl number


Non-uniform heat source/sink parameter


Dimensional magnetic field parameter


Magnetic interaction parameter


Porosity parameter


Thermophoresis parameter


Lewis number


Brownian motion parameter


Dimensionless velocity slip parameter


Dimensionless temperature jump parameter


Dimensionless concentration jump parameter


Wall skin friction coefficient


Local Nusselt number


Local Sherwood number


Local Reynolds number

Greek Symbols


Dimensionless concentration


Similarity variable


Electrical conductivity of the fluid


Ratio of specific heats


Dimensionless temperature


Density of the nanofluid


Thermal conductivity of the nanofluid


Dynamic viscosity of nanofluid


Kinematic viscosity


Wall thickness parameter

ξ1, ξ2

Mean free path (constant)

ξ3, ξ4

Mean free path (constant)


Positive characteristic time


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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