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

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Abstract

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.

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Abbreviations

\(u,v,w\) :

Velocity components (ms−1)

\(x,y,z\) :

Space coordinates (ms−1)

\(n\) :

Power law index

\(m\) :

Fitted rate constant

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

Heat capacity of fluid

\(T\) :

Temperature of fluid (K)

\(k(T)\) :

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

\(\alpha_{1}\) :

Thermal diffusivity (ms−1)

\(k^{*}\) :

Boltzmann constant

\(D_{\text{B}}\) :

Brownian diffusion coefficient

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

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

\(C\) :

Nanoparticles concentration (K)

\(Q_{0}\) :

Dimensional heat source/sink parameter

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

Activation energy

\(a,b\) :

Positive constants

\(B_{0}\) :

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

\(h_{\text{f}}\) :

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

\(f,g\) :

Dimensionless velocities

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

Skin fractions

\(Nu_{x}\) :

Local Nusselt number

\(M\) :

Magnetic parameter

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

Stretching velocities (ms−1)

\(E\) :

Activation energy

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

Local Weissenberg numbers

\(Pr\) :

Prandtl number

\(Le\) :

Lewis number

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

Nonlinear radiative heat flux

\(N_{\text{b}}\) :

Brownian motion parameter

\(N_{\text{t}}\) :

Thermophoresis parameter

\(R_{\text{d}}\) :

Radiation parameter

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

Effective heat capacity of a nanoparticle

\(Re_{x}\) :

Local Reynolds number

\(\alpha\) :

Ratio of stretching rates parameter

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

Chemical reaction constant

\(\gamma\) :

Biot number

\(\tau\) :

Effective heat capacity ratio

\(\lambda\) :

Dimensionless heat source or sink parameter

\(\phi\) :

Dimensionless concentration

\(\sigma\) :

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

\(\eta\) :

Dimensionless variable

\(\theta_{\text{f}}\) :

Temperature ratio parameter

\(\rho_{\text{f}}\) :

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

\(\theta\) :

Dimensionless temperature

\(\varepsilon\) :

Thermal conductivity parameter

\(\nu\) :

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

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Authors and Affiliations

  1. Department of Mathematics, Hazara University, Mansehra, Pakistan

    W. A. Khan, F. Sultan, M. Ali & M. Shahzad

  2. Department of Mathematical Analysis, Ghent University, Ghent, Belgium

    F. Sultan

  3. Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

    M. Khan & M. Irfan

Authors
  1. W. A. Khan
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  2. F. Sultan
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  3. M. Ali
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Correspondence to W. A. Khan.

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Technical Editor: Cezar Negrao, PhD.

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Khan, W.A., Sultan, F., Ali, M. et al. Consequences of activation energy and binary chemical reaction for 3D flow of Cross-nanofluid with radiative heat transfer. J Braz. Soc. Mech. Sci. Eng. 41, 4 (2019). https://doi.org/10.1007/s40430-018-1482-0

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