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Framing the Activation Energy and Binary Chemical Reaction on CNT’s with Cattaneo–Christov Heat Diffusion on Maxwell Nanofluid in the Presence of Nonlinear Thermal Radiation

  • Research Article - Mechanical Engineering
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Abstract

A theoretical model is drafted to inspect the hydromagnetic flow of carbon nanotubes (CNT’s) suspended in a Maxwell nanofluid by means of activation energy with binary chemical reaction over a stretching sheet. Modified Arrhenius function is measured instead of the energy activation. Heat transport phenomena are explored in energy expression through a nonlinear thermal radiation and viscous dissipation, which is incorporated with a novel theory specifically Cattaneo–Christov model of heat diffusion—a sophisticated form of Fourier’s heat flux formula. The flow analysis is reported in attendance of convective slip and suction. Two different kinds of CNT’s (i.e. single and multiple walls) are consistently dispersed in the base fluid (engine oil) to illustrate the fine points of the flow. The governing system of mathematical expressions for the locally similar flow is tackled numerically by Runge–Kutta-based MATLAB bvp4c package. The procured solutions are drawn for different values of pertinent parameters of interest. The temperature of the fluid escalates with the nonlinear thermal radiation. Activation energy boosts up the concentration, and a negative trend is observed for rate of chemical reaction.

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Abbreviations

g :

Acceleration due to gravity

\(T_{\infty }\) :

Ambient fluid temperature

C-CHFM:

Cattaneo–Christov heat flux model

\(h_{f}\) :

Convective heat transfer coefficient

Ec :

Eckert number

M :

Magnetic parameter

E :

Non-dimensional activation energy

Pr :

Prandtl number

q r :

Radiative heat flux

Sc :

Schmidt number

S :

Suction/injection parameter

T:

Temperature

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

Thermal conductivities of CNT’s

\(k_{f}\) :

Thermal conductivities of the host fluid

\(k_{nf}\) :

Thermal conductivities of the nanofluid

Rd :

Thermal radiation

B:

Uniform magnetic field strength,

\(U_{w}\) :

Velocity at wall

\(u\) :

Velocity components along the x-axis

\(v\) :

Velocity components along y-axis

A :

Velocity slip factor

\(v_{w}\) :

Wall mass flux

\(T_{w}\) :

Wall temperature

σ :

Non-dimensional chemical reaction rate constant

θ w :

Temperature ratio parameter

\(\mu_{f}\) :

Viscosity of base fluid

\(\mu_{nf}\) :

Viscosity of nanofluids

\(\chi\) :

Nanoparticles fraction

\(\rho_{f}\) :

Density of the base fluid

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

Thermal conductivities of CNT’s

\((\rho C_{p} )_{f}\) :

Heat capacity of a fluid

\((\rho C_{p} )_{nf}\) :

Heat capacitance of the nanofluid

\((\rho C_{p} )_{\text{CNT}}\) :

Heat capacity of CNT’s

\(\rho_{nf}\) :

Density of the nanofluid

σ** :

Electric conductivity

\(\alpha_{nf}\) :

Thermal diffusivity of nanofluids

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Authors and Affiliations

  1. Department of Applied Mathematics, Yogi Vemana University, Kadapa, 516005, India

    K. Subbarayudu & S. Suneetha

  2. Department of Mathematics, School of Advanced Sciences, VIT, Vellore, 632014, India

    P. Bala Anki Reddy

  3. Department of Mathematics, Faculty of Science, Aswan University, Aswan, 81528, Egypt

    A. M. Rashad

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  1. K. Subbarayudu
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  2. S. Suneetha
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  3. P. Bala Anki Reddy
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  4. A. M. Rashad
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Correspondence to A. M. Rashad.

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Subbarayudu, K., Suneetha, S., Bala Anki Reddy, P. et al. Framing the Activation Energy and Binary Chemical Reaction on CNT’s with Cattaneo–Christov Heat Diffusion on Maxwell Nanofluid in the Presence of Nonlinear Thermal Radiation. Arab J Sci Eng 44, 10313–10325 (2019). https://doi.org/10.1007/s13369-019-04173-2

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