Lie Group Analysis of Nanofluid Slip Flow with Stefan Blowing Effect via Modified Buongiorno’s Model: Entropy Generation Analysis

  • Puneet Rana
  • Nisha Shukla
  • O. Anwar Bég
  • Anuj BhardwajEmail author
Original Research


This article presents a detailed theoretical and computational analysis of alumina and titania-water nanofluid flow from a horizontal stretching sheet. At the boundary of the sheet (wall), velocity slip, thermal slip and Stefan blowing effects are considered. The Pak-Cho viscosity and thermal conductivity model is employed together with the non-homogeneous Buongiorno nanofluid model. The equations for mass, momentum, energy and nanoparticle species conservation are transformed via Lie-group transformations into a dimensionless system. The partial differential boundary value problem is therefore rendered into nonlinear ordinary differential form. With appropriate boundary conditions, the emerging normalized equations are solved with the semi-numerical homotopy analysis method (HAM). To consider entropy generation affects a second law thermodynamic analysis is also carried out. The impact of some physical parameters on the skin friction, Nusselt number, velocity, temperature and entropy generation number (EGM) are represented graphically. This analysis shows that diffusion parameter is a key factor to retards the friction and rate of heat transfer at the surface. Further, temperature of fluid decreases for the higher value of thermal slip parameter. In addition, EGM enhances with nanoparticles ambient concentration and Reynolds number. A numerical validation of HAM results is also included. The computations are relevant to thermodynamic optimization of nano-material processing operations.


Nanofluid HAM Entropy generation analysis Stefan blowing effect Slip flow 

List of symbols


Nanoparticles concentration (–)


Brownian diffusion (m2/s)


Thermophoresis diffusion (m2/s)


Ratio of thermophoresis and Brownian motion parameter


Eckert number (–)


Dimensionless stream function (–)


Enthalpy (J)


Thermal conductivity [W/(mK)]


Nusselt number (–)


Velocity slip parameter (m)


Thermal slip parameter (m)


Prandtl number (–)


Embedding parameter (–)


Gas constant [J/(molK)]


Reynolds number (–)

\( \phi \)

Dimensionless concentration (–)


Volumetric rate of entropy generation [J/(Km3 s)]


Characteristic entropy [J/(Km3 s)]


Schmidt number (–)


Temperature (K)


Velocity (m/s) along x-axis


Velocity (m/s) along y-axis

Greek Symbol

\( \rho \)

Density (kg/m3)

\( \mu \)

Dynamic viscosity (Ns/m2)

\( \phi \)

Concentration (–)

\( \psi \)

Stream function (m2/s)

\( \upsilon \)

Kinematic viscosity (m2/s)

\( \delta \)

Thermal slip parameter (–)

\( \rho c \)

Heat capacity [J/(Km3)]

\( \theta \)

Dimensionless temperature (–)

\( \chi \)

Diffusive constant (–)

\( \lambda_{1} \)

Dimensionless velocity slip parameter

\( \lambda_{2} \)

Dimensionless thermal slip parameter

\( \eta \)

Similarity variable (–)


\( \infty \)

Ambient condition

\( w \)

Condition on surface









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Copyright information

© Foundation for Scientific Research and Technological Innovation 2019

Authors and Affiliations

  1. 1.Department of MathematicsJaypee Institute of Information TechnologyNoidaIndia
  2. 2.Fluid Mechanics and Propulsion, Aeronautical and Mechanical Engineering, School of Computing, Science and EngineeringUniversity of SalfordSalfordUK

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