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Carbon nanotubes (CNTs)-based flow between two spinning discs with porous medium, Cattaneo–Christov (non-Fourier) model and convective thermal condition

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Abstract

Inspired by various applications (ocean’s renewable power technologies, spinning disc reactor, engineering systems, etc.) of fluid flow between rotating disc, we have investigated magnetohydrodynamic flow of multi-wall and single-wall carbon nanotubes (MWCNTs and SWCNTs)-based fluid between two rotating, coaxial and parallel stretching discs with porous medium and convective thermal condition. The non-vanishing relaxation time in the dissipative process is assumed. The energy equation is developed by using Cattaneo–Christov heat flux model. ND-Solve command of MATHEMATICA software is used for the numerical solution of the governing equations. The physical behaviour of axial, radial and tangential velocity along with temperature of nanofluid is discussed in detail. When porous permeability parameter is small, then tangential velocity of MWCNTs-based fluid is higher than that of the SWCNTs-based fluid. Moreover, when porous permeability parameter is small, the Reynolds number retards the tangential velocity but when porous permeability parameter is large, Reynolds number boots the tangential velocity up.

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Abbreviations

\(a_1,a_2\) :

Stretching rates of lower and upper disc, respectively

\({B_1}, {B_2}\) :

Ratio of stretching rate to angular velocity

\({C_1},{C_2}\) :

Skin friction coefficients at lower and upper disc, respectively

\(h_1, h_2\) :

Convective heat transfer coefficients at lower and upper disc, respectively

\({k_0}\) :

Permeability of porous medium

\({k_{\mathrm{nf}}}\) :

Thermal conductivity of nanofluid

\({\mathrm{Nu}_1}, {\mathrm{Nu}_2}\) :

Nusselt numbers at lower and upper discs

Pr:

Prandtl number

Re:

Reynolds number

T :

Fluid temperature

\(T_0, T_1\) :

Temperature at lower and upper discs, respectively

\({\gamma _1}, {\gamma _2}\) :

Thermal Biot numbers at lower and upper disc

\({\upsilon _{\mathrm{nf}}}\) :

Kinematic coefficient of viscosity

\({(\rho {c_\mathrm{p}})_{\mathrm{nf}}}\) :

Heat capacity of nanofluid

\({\omega _1, \omega _2}\) :

Angular velocity of lower and upper disc, respectively

\(\lambda\) :

Thermal relaxation parameter

\({\beta }\) :

Porous permeability parameter

\(\phi\) :

Nanoparticle solid volume fraction

\(\Omega\) :

The rotation parameter

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Acknowledgements

One of the authors Mr. Bhuvaneshvar Kumar is highly thankful to Ms. Prachi Chauhan for inspiring him to carry out this research work.

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Authors and Affiliations

  1. Department of Mathematics and Computing, Indian Institute of Technology (ISM), Dhanbad, Jharkhand, 826004, India

    B. Kumar, G. S. Seth & M. K. Singh

  2. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    A. J. Chamkha

  3. Institute of Theoretical and Applied Research (ITAR), Duy Tan University, Hanoi, 100000, Vietnam

    A. J. Chamkha

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Kumar, B., Seth, G.S., Singh, M.K. et al. Carbon nanotubes (CNTs)-based flow between two spinning discs with porous medium, Cattaneo–Christov (non-Fourier) model and convective thermal condition. J Therm Anal Calorim 146, 241–252 (2021). https://doi.org/10.1007/s10973-020-09952-w

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