Consequences of activation energy and binary chemical reaction for 3D flow of Cross-nanofluid with radiative heat transfer

  • W. A. KhanEmail author
  • F. Sultan
  • M. Ali
  • M. Shahzad
  • M. Khan
  • M. Irfan
Technical Paper


In view of ecological concern and energy security, execution of refrigeration system should be enriched which can be done by improving the characteristics of working liquids. The nanoliquids have gained interest in industrial and engineering fields due to their outstanding thermophysical features. Researchers used nanoliquids as working liquid and detected substantial variations in thermal performance. In the present research work, our intention is to explore the impact of nonlinear thermal radiation and variable thermal conductivity on 3D flow of cross-nanofluid. Moreover, heat sink–source, chemical processes and activation energy are implemented. Zero mass flux relation with thermophoresis and Brownian motion mechanisms are scrutinized. The required system of ordinary ones is achieved by implementing appropriate transformations. The achieved system of ordinary ones is computed numerically by implementing bvp4c scheme. Graphs are plotted to explore the impact of various physical parameters on concentration, temperature and velocity fields. It is detected from obtained graphical data that thermophoresis and Brownian motion mechanisms significantly affect heat transport mechanism. Furthermore, graphical analysis reveals that concentration of cross-nanofluid enhances for augmented values of activation energy.


3D flow Activation energy Cross-fluid model Nanoparticles Nonlinear thermal radiation New mass flux boundary conditions 

List of symbols


Velocity components (ms−1)


Space coordinates (ms−1)


Power law index


Fitted rate constant

\(\left( {\rho c} \right)_{\text{f}}\)

Heat capacity of fluid


Temperature of fluid (K)


Variable thermal conductivity \(\left( {\frac{{\text{W}}}{{{\text{mK}}}}} \right)\)


Thermal diffusivity (ms−1)


Boltzmann constant


Brownian diffusion coefficient


Thermophoresis diffusion coefficient \(\left( {\frac{{{\text{m}}^{2} }}{\text{s}}} \right)\)


Nanoparticles concentration (K)


Dimensional heat source/sink parameter


Activation energy


Positive constants


Magnetic field strength \(\left( {\frac{{\text{A}}}{{\text{M}}}} \right)\)

\(C_{\infty }\)

Ambient concentration

\(T_{\infty }\)

Ambient fluid temperature (K)

\(k_{\infty }\)

Thermal conductivity far away from stretched surface


Heat conversion coefficient \(\left( {\frac{\text{W}}{{{\text{Km}}^{2} }}} \right)\)


Dimensionless velocities

\(C_{fx} ,C_{fy}\)

Skin fractions


Local Nusselt number


Magnetic parameter

\(U_{w} \left( {x,t} \right),V_{w} \left( {y,t} \right)\)

Stretching velocities (ms−1)


Activation energy

\(We_{1} ,We_{2}\)

Local Weissenberg numbers


Prandtl number


Lewis number


Nonlinear radiative heat flux


Brownian motion parameter


Thermophoresis parameter


Radiation parameter

\(\left( {\rho c} \right)_{\text{p}}\)

Effective heat capacity of a nanoparticle


Local Reynolds number


Ratio of stretching rates parameter


Chemical reaction constant

Greek symbols


Biot number


Effective heat capacity ratio


Dimensionless heat source or sink parameter


Dimensionless concentration


Stefan–Boltzmann constant \(\left( {\frac{{\text{S}}}{{\text{m}}}} \right)\)


Dimensionless variable


Temperature ratio parameter


Fluid density \(\left( {\frac{\text{kg}}{{{\text{m}}^{3} }}} \right)\)


Dimensionless temperature


Thermal conductivity parameter


Kinematics viscosity \(\left( {{\text{m}}^{2} {\text{s}}^{ - 1} } \right)\)


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • W. A. Khan
    • 1
    Email author
  • F. Sultan
    • 1
    • 2
  • M. Ali
    • 1
  • M. Shahzad
    • 1
  • M. Khan
    • 3
  • M. Irfan
    • 3
  1. 1.Department of MathematicsHazara UniversityMansehraPakistan
  2. 2.Department of Mathematical AnalysisGhent UniversityGhentBelgium
  3. 3.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan

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