Unsteady stagnation point flow of Oldroyd-B nanofluid with heat generation/absorption and nonlinear thermal radiation

  • Tasawar Hayat
  • Sajid Qayyum
  • Muhammad Waqas
  • Ahmed Alsaedi
Technical Paper


This article addresses unsteady stagnation point flow of Oldroyd-B nanofluid past an impermeable stretching sheet. Characteristics of heat transfer are described within the frame of heat generation/absorption and nonlinear radiative process. Intention in present analysis is to develop a model for nanomaterial containing Brownian motion and thermophoresis phenomena. The resulting nonlinear differential systems have been solved for the convergent homotopic solutions. Behavior of sundry variable for the velocity, temperature and concentration are addressed. Numerical values examined the local Nusselt number. It is revealed that velocity field enhances for dimensionless retardation time while reverse situation is observed regarding dimensionless relaxation time. Temperature and heat transfer rate are enhanced via larger nonlinear thermal radiation and temperature parameters. Moreover, behavior of Brownian motion and thermophoresis on the concentration field is quite reverse.


Oldroyd-B nanofluid Nonlinear thermal radiation Stagnation point flow Convective flow Heat generation/absorption 

List of symbols

\( u,v \)

Velocity components (\( ms^{ - 1} \))

\( \eta \)

Dimensionless space variable

\( x,y \)

Space coordinates (\( m \))

\( f \)

Dimensionless velocity

\( T \)

Fluid temperature (K)

\( \theta \)

Dimensionless temperature

\( T_{f} \)

Convective fluid temperature (K)

\( \phi \)

Dimensionless concentration

\( T_{\infty } \)

Ambient temperature (K)

\( \psi \)

Stream function

\( C \)

Fluid concentration

\( S \)

Unsteadiness parameter

\( C_{\infty } \)

Ambient concentration

\( \alpha \)

Dimensionless relaxation time constant

\( u_{w} \)

Stretching velocity (\( ms^{ - 1} \))

\( \beta \)

Dimensionless retardation time constant

\( u_{e} \)

Ambient velocity (\( ms^{ - 1} \))


Ratio of velocities

\( \alpha_{1} \)

Fluid relaxation time

\( R \)

Radiation parameter

\( \alpha_{2} \)

Fluid retardation

\( \Pr \)

Prandtl number

\( \nu \)

Kinematic viscosity (\( m^{2} s^{ - 1} \))

\( \theta_{w} \)

Temperature parameter

\( \mu_{f} \)

Dynamics viscosity (Pa.s)

\( N_{b} \)

Brownian motion parameter

\( \rho_{f} \)

Fluid density (\( kgm^{ - 3} \))

\( N_{t} \)

Thermophoresis parameter

\( \rho_{p} \)

Particle density (\( kgm^{ - 3} \))

\( \delta \)

Heat generation/absorption parameter

\( c_{p} \)

Specific heat (\( kgm^{2} s^{ - 1} K^{ - 1} \))

\( Sc \)

Schmidt number

\( Q^{*} \)

Heat generation/absorption coefficient (\( Jm^{ - 3} K^{ - 1} s^{ - 1} \))

\( B_{n} \)

Biot number

\( q_{r} \)

Radiative heat flux

\( Nu_{x} \)

Local Nusselt number

\( \tau \)

Capacity ratio

\( \text{Re}_{x} \)

Local Reynolds number

\( k_{f} \)

Thermal conductivity (\( kgms^{ - 3} K^{ - 1} \))

\( \sigma^{*} \)

Stefan–Boltzmann constant

\( h_{t} \)

Convective heat transfer coefficient

\( k^{*} \)

Coefficient of mean absorption

\( D_{B} \)

Brownian diffusion coefficient (\( m^{2} s^{ - 1} \))

\( a,b,c \)

Positive constants

\( D_{T} \)

Thermophoresis diffusion coefficient (\( m^{2} s^{ - 1} \))

\( q_{w} \)

Surface heat flux


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • Tasawar Hayat
    • 1
    • 2
  • Sajid Qayyum
    • 1
  • Muhammad Waqas
    • 1
  • Ahmed Alsaedi
    • 2
  1. 1.Department of MathematicsQuaid-I-Azam University 45320IslamabadPakistan
  2. 2.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

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