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Analytical Investigation on CNT Based Maxwell Nano-fluid with Cattaneo–Christov Heat Flux Due to Thermal Radiation

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Abstract

At first, we derive a series form solution of the coupled highly nonlinear equations, which includes various conditions. Then, via the method of directly defined inverse mapping with the series form solution firstly reported in this paper, we can obtain theoretical and approximate analytical analysis about the transfer of heat as well as the magnetohydrodynamic flow of Maxwell nanofluid by the influence of convective heating with effects of thermal radiation. In the energy equation, heat flux model is adopted to develop the equations for viscoelastic relaxation over boundary layer flow. For this investigation, we considered base liquid as engine oil and other forms of carbon nanotubes such as single walled nanotubes and multi-walled nanotubes. Suitable similarity transformations are applied for transformation of given boundary layer flow equations. Results are compared numerically by Keller–Box method. It is found that for both singled and multi-walled carbon nanotube based nanofluids the thermal relaxation time and temperature function are inversely proportional. More interestingly it is noted that for the two types of nanofluids, fluid relaxation parameter exactly coordinates with heat transfer rate as well as skin friction investigated. Also shown that the base functions of solutions are highly convergence.

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Abbreviations

u′, v′:

Velocity components (m s−1)

x, y :

Coordinates

\( \hat{q} \) :

Heat flux

T w :

Wall temperature (K)

\( T_{\infty } \) :

Ambient temperature (K)

g :

Gravitational force (m s−2)

C p :

Specific heat (J kg−1 K−1)

\( \bar{V} \) :

Velocity vector

q r :

Radiative heat flux

k e :

Mean absorption coefficient

T :

Fluid temperature

f :

Nondimensional stream function

Gr x :

Grashof number

M :

Magnetic parameter

Nr :

Radiation parameter

Pr :

Prandtl number

C fx :

Skin friction coefficient

Nu x :

Nusselt number

Re x :

Reynolds number

λ 1 :

Fluid relaxation time

\( \hat{\rho } \) :

Density (kg m−3)

μ′:

Dynamic viscosity (N m s−1)

β :

Thermal expansion coefficient (K−1)

σ :

Electrical conductivity

λ 2 :

Thermal relaxation time

\( \bar{\alpha } \) :

Thermal diffusivity (m2 s−1)

σ s :

Stefan–Bolzmann constant

ϕ :

Volume fraction of nanoparticles

\( \bar{\psi } \) :

Stream function

η :

Similarity variable

θ :

Nondimensional temperature

ξ :

Velocity slip factor

ζ :

Thermal slip factor

nf :

Nanofluid

f :

Base fluid

w :

Condition at wall

∞:

Condition at infinity

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Acknowledgements

We thank editor and anonymous reviewers for their comments on an earlier version of the manuscript and that greatly improved in the revised manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Acharya Nagarjuna University, Ongole, AP, 523001, India

    K. Gangadhar & K. Keziya

  2. Department of Mathematics, School of Humanities and Sciences, SASTRA (Deemed to be University), Thanjavur, TN, India

    T. Kannan

  3. Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur, South Ambazhari Road, Nagpur, Maharahashtra, 440010, India

    Shankar Rao Munjam

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  1. K. Gangadhar
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Gangadhar, K., Keziya, K., Kannan, T. et al. Analytical Investigation on CNT Based Maxwell Nano-fluid with Cattaneo–Christov Heat Flux Due to Thermal Radiation. Int. J. Appl. Comput. Math 6, 124 (2020). https://doi.org/10.1007/s40819-020-00876-5

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