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Activation Energy Impact on Chemically Reacting Eyring–Powell Nanofluid Flow Over a Stretching Cylinder

  • Research Article-Mechanical Engineering
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Abstract

The purpose of this research is to scrutinize the stagnation point flow of chemically reacting Powell–Eyring nanofluid past an inclined cylinder using the impact of activation energy with Cattaneo–Christov heat flux. Flow formulation is developed by considering the impact of nonlinear thermal radiation, binary chemical reaction, non-Fourier heat flux and the Buongiorno nanofluid model. Proper transforms yield highly nonlinear differential systems, which are solved using shooting procedure with the fourth-order R–K (Runge–Kutta) method. Comparative reviews between the formerly published literature and the current data are made for specific cases, which are inspected to be in a tremendous agreement. The narrative reviews show that the current research problem has not premeditated so far. Effectiveness of innumerable parameters is publicized graphically on velocity, temperature and concentration curves cases of various angles 0° horizontal cylinder, 45° inclined cylinder and 90° vertical cylinder. It is manifested that fluid velocity promotes with the larger values of velocity ratio. It is also noticed that concentration declines when destructive chemical reaction enhances, whilst the antithesis direction is noticed in the condition of the generative chemical reaction. Furthermore, the stream lines are closer to the cylindrical wall when α = 90° and the stream lines are far away to the cylindrical wall when α = 90°.

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Abbreviations

\( A \) :

Ratio of the velocities (stagnation point)

\( A_{1} \) :

First Rivlin–Ericksen tensor

\( B \) :

Total magnetic field

\( B_{0} \) :

Magnetic field

\( c \) :

Fluid parameter

\( C_{f} \) :

Skin friction coefficient

\( C \) :

Concentration of the fluid \( \left( {{\text{kmol}}\,{\text{m}}^{ - 3} } \right) \)

\( C_{0} \) :

Reference concentration

\( C_{w} \) :

Stretching cylinder concentration

\( C_{\infty } \) :

Concentration of the ambient fluid

\( c_{p} \) :

Specific heat at constant pressure

\( D_{B} \) :

Brownian motion diffusion coefficient

\( E_{\text{a}} \) :

Activation energy (J kg−1 K−1)

\( E \) :

Non-dimensional activation energy

\( F \) :

Dimensionless velocity

Gc:

Solutal Grashof number

Gr:

Grashof number

\( J \) :

Current density

\( k \) :

Thermal conductivity (W m−1 K−1)

\( k^{*} \) :

Mean absorption coefficient

\( k_{\text{r}} \) :

Reaction rate

\( l \) :

Characteristic length

\( M \) :

Magnetic parameter

\( n \) :

Unitless exponent fitted rate constant

Nt:

Thermophoresis parameter

Nb:

Brownian motion parameter

\( {\text{Nu}}_{x} \) :

Local Nusselt number

\( p \) :

Fluid pressure

\( \Pr \) :

Prandtl number

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

Local Reynolds number

\( R \) :

Radiation parameter

\( S \) :

Deviatoric part of stress tensor

Sc:

Schmidt number

\( {\text{Sh}}_{x} \) :

Local Sherwood number

\( T_{0} \) :

Reference temperature

\( T \) :

Temperature of the fluid (K)

\( T_{\infty } \) :

Temperature of the ambient fluid

\( T_{w} \) :

Cylinder temperature

\( u_{e} \) :

Free stream velocity

\( U_{0} \) :

Reference velocity

\( r \) :

Direction normal to the surface

\( x \) :

Direction along the surface

\( u,\,v \) :

Velocity components in \( x \) and \( r \) directions (ms−1)

\( \upsilon \) :

Kinematic viscosity

\( \zeta \) :

Similarity variable

\( \alpha \) :

Acute angle

\( \beta \) :

Fluid parameter

\( \beta_{\text{C}} \) :

Coefficient of concentration expansion

\( \beta_{\text{T}} \) :

Coefficient of thermal expansion

\( \mu \) :

Dynamic viscosity of the fluid

\( \delta ,\,\varepsilon \) :

Fluid parameters

\( \varPhi \) :

Dimensionless concentration

\( \rho \) :

Density of the fluid (kg m−3)

\( \gamma \) :

Curvature parameter

\( \varGamma \) :

Chemical reaction parameter

\( \varTheta \) :

Dimensionless temperature

\( \varTheta_{w} \) :

Temperature ratio parameter

\( \sigma^{*} \) :

Stefan–Boltzmann constant

\( \sigma \) :

Electrical conductivity of the fluid

\( \varLambda \) :

Non-dimensional thermal relaxation time

\( \lambda_{2} \) :

Relaxation time for heat flux

\( \tau_{w} \) :

Surface shear stress (N m−2)

\( w \) :

Conditions at the wall

\( \infty \) :

Ambient condition

′:

Differentiation with respect to \( \zeta \)

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Authors and Affiliations

  1. Department of Mathematics, S.A.S., Vellore Institute of Technology (VIT), Vellore, 632014, India

    S. R. R. Reddy & P. Bala Anki Reddy

  2. Department of Mathematics, Faculty of Science, Aswan University, Aswân, 81528, Egypt

    A. M. Rashad

Authors
  1. S. R. R. Reddy
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  2. P. Bala Anki Reddy
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  3. A. M. Rashad
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Correspondence to A. M. Rashad.

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Reddy, S.R.R., Bala Anki Reddy, P. & Rashad, A.M. Activation Energy Impact on Chemically Reacting Eyring–Powell Nanofluid Flow Over a Stretching Cylinder. Arab J Sci Eng 45, 5227–5242 (2020). https://doi.org/10.1007/s13369-020-04379-9

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