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Arrhenius activation energy aspects in mixed convection Carreau nanofluid with nonlinear thermal radiation

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Abstract

This exertion is part of a liable approach for the advancement of nanotechnology and nanoscience to scrutinize the thermal and rheological aspects of the nanofluids. The conformist heat transport fluids are broadly reported to be one of the notable reasons of the reduced enactment of heat transport tools, boosting the energy charges. For this concern to be stable, nanofluids have been familiarized as probable proxies to the conformist fluids because of their intensify aptitude of heat transport coefficient. Here, the up-front goal is to investigate the aspect of nonlinear radiated and chemical reaction with aspects of Arrhenius activation energy in Carreau nanofluid. Additionally, mixed convection, MHD, and new mass flux theory is explored. The framed system is envisioned numerically via bvp4c. Temperature field intensifies against enhanced values of radiation and thermophoresis parameters, respectively. Concentration has conflicted performance for escalating activation energy and Brownian motion parameters, respectively.

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Abbreviations

\(u,v,w\) :

Velocity components

\(x,y,z\) :

Space coordinates

\(t\) :

Time

\(\nu\) :

Kinematic viscosity

\(\Gamma\) :

Material rate constant

\(n\) :

Power law index

\(\sigma\) :

Electrical conductivity

\(B_{0}\) :

Magnetic strength

\(\rho_{f}\) :

Fluid density

\(g\) :

Gravity

\((\rho c)_{f}\) :

Heat capacity of fluid

\(\xi_{T}\) :

Thermal expansion coefficient

\(T_{\infty }\) :

Nanofluid ambient temperature

\(C_{\infty }\) :

Nanofluid ambient concentration

\(D_{B}\) :

Brownian diffusion coefficient

\(D_{T}\) :

Thermophoresis diffusion coefficient

\(q_{r}\) :

Radiative heat flux

\(k^{ * }\) :

Mean absorption coefficient

\(\sigma^{ * }\) :

Stefan-Boltzmann constant

\(k_{r}\) :

Reaction rate

\(m( - 1 < m < 1)\) :

Fitted rate constant

\(E_{A}\) :

Activation energy

\(\kappa\) :

Boltzmann constant

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

Stretching velocities

\(\xi_{C}\) :

Solutal expansion coefficient

\(T\) :

Nanofluid temperature

\(T_{w}\) :

Wall temperature

\(C\) :

Nanoparticles concentration

\(\alpha\) :

Thermal diffusivity

\(\tau\) :

Effective heat capacity ratio

\(k\) :

Thermal conductivity

\(a,b,\beta\) :

Positive constants

MHD:

Magnetohydrodynamics

ODEs:

Ordinary differential equations

PDEs:

Partial differential equations

HAM:

Homotopy analysis method

\(\eta\) :

Dimensionless variable

\(We\) :

Local Weissenberg number

\(M\) :

Magnetic parameter

\(S\) :

Unsteadiness parameter

\(\lambda^{*}\) :

Thermal buoyancy parameter

\(N^{*}\) :

Buoyancy ratio parameter

\(R_{d}\) :

Thermal radiation parameter

\(\theta_{w}\) :

Temperature ratio parameter

\(N_{b}\) :

Brownian motion parameter

\(N_{t}\) :

Thermophoresis parameter

\(\Pr\) :

Prandtl number

\(Le\) :

Lewis number

\(E_{A}\) :

Activation energy parameter

\(\Lambda_{1}\) :

Reaction rate parameter

\(\Lambda_{2}\) :

Temperature difference parameter

\(\tau_{xz} ,\tau_{yz}\) :

Surface shear stresses

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

Skin friction coefficients

\(Nu_{x}\) :

Local Nusselt number

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

Local Reynolds number

\(f\) :

Dimensionless velocities

\(\theta\) :

Dimensionless temperature

\(\phi\) :

Dimensionless concentration

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Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan

    M. Irfan & M. Rashid

  2. Department of Mathematical Sciences Federal, Urdu University of Arts, Sciences and Technology, Islamabad, 44000, Pakistan

    M. Irfan

  3. Department of Mathematics, University of Jhang, Gojra Road, Jhang, 35200, Pakistan

    M. S. Anwar

  4. NUTECH School of Applied Sciences and Humanities, National University of Technology, Islamabad, 44000, Pakistan

    M. Waqas

  5. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    W. A. Khan

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  1. M. Irfan
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  2. M. S. Anwar
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Correspondence to M. Irfan.

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Irfan, M., Anwar, M.S., Rashid, M. et al. Arrhenius activation energy aspects in mixed convection Carreau nanofluid with nonlinear thermal radiation. Appl Nanosci 10, 4403–4413 (2020). https://doi.org/10.1007/s13204-020-01498-5

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