Pressure-Driven Flow of Cross Fluid Along a Stationary Plate Subject to Binary Chemical Reaction and Arrhenius Activation Energy

  • M. MustafaEmail author
  • Aiman Sultan
  • Mahmood Rahi
Research Article - Mechanical Engineering


The present paper deals with the flow of Cross rheological fluid along a stationary rigid plate caused by stream-wise pressure gradient. Flow field is affected by uniform magnetic field acting normal to the plate axis. Interaction of flow field with chemically reacting solute is modeled through the advection–diffusion equation in which temperature dependency of the reaction rate on activation energy is considered. Energy equation containing source term and variable thermal conductivity is treated. Locally similar solutions are obtained and interpreted for a certain range of embedded parameters. Shear-thinning aspect of Cross fluid is apparent from the computational results. A monotonic decay in vertical velocity is noticed for increasing values of flow behavior index (n) which, in turn, leads to pronounced heat conduction. An important finding is that activation energy of chemical reaction remarkably alters the solute concentration near the plate.


Generalized Newtonian fluid Chemical reaction Activation energy Falkner–Skan flow 

List of Symbols

\(\left( x,y \right) \)

Cartesian coordinate system


Velocity components along x- and y-directions, respectively


Consistency index


Dimensionless stream function


Magnetic flux density


Positive constant


Magnetic interaction parameter


Specific heat


Variable thermal conductivity


Flow behavior index


Activation energy


Fitted rate constant


Heat source/sink


Dimensionless activation energy


Prandtl number


Local Reynolds number


Local Weissenberg number


Schmidt number


Fluid temperature


Solute concentration


Skin friction coefficient


Local Nusselt number


Local Sherwood number

\(\tau _{w}\)

Shear stress at the plate


Wall heat flux


Wall mass flux


Velocity of the outer flow

Greek Symbols

\(\dot{\gamma }\)

Shear rate

\(\eta \)

Similarity variable

\(\theta \)

Dimensionless temperature

\(\phi \)

Dimensionless concentration

\(\eta _{0}\)

Viscosity at zero shear rate

\(\eta _{\infty }\)

Infinite shear rate viscosity

\(\delta \)

Temperature difference parameter

\(\sigma _{1}\)

Fluid electrical conductivity

\(\epsilon \)

Dimensionless constant

\(\rho \)

Fluid density

\(\kappa \)

Boltzmann constant

\(\sigma \)

Dimensionless reaction parameter


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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.School of Natural Sciences (SNS)National University of Sciences and Technology (NUST)IslamabadPakistan
  2. 2.Higher Colleges of Technology (HCT)Abu DhabiUnited Arab Emirates

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