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Enhancement of heat transfer in a convergent/divergent channel by using carbon nanotubes in the presence of a Darcy–Forchheimer medium

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Abstract

This article explores the influence of thermal radiation on the flow and heat transfer of single-walled carbon nanotubes over both a convergent and divergent channel. Flow is induced due to a Darcy–Forchheimer medium. Further, the heat transfer mechanism is analyzed in the presence of a thermal radiation process. Guided by some appropriate similarity transformations, the fundamental PDEs are converted into a self-similar system of coupled non-linear ODEs. The findings are obtained with the help of the Runge–Kutta-45-based shooting method. The roles of the Reynolds number, porosity parameter, inertia coefficient parameter, Prandtl number and radiation parameter are presented graphically. Results are displayed and show that the rate of heat transfer is higher in a divergent channel as compared to a convergent channel.

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Abbreviations

\(c\) :

Indicating shrinking/stretching parameter

\(Kp\) :

Porosity parameter

\(Fr\) :

Inertia coefficient

\(Re\) :

Reynolds number

\(Pr\) :

Prandtl number

\(R\) :

Radiation parameter

\(C_{f}\) :

Skin friction co efficient

\(Nu\) :

Nusselt number

\(\alpha\) :

Opening angle parameter

\(k_{f}\) :

Thermal conductivity of base fluid

\(k_{nf}\) :

Thermal conductivity of nanofluid

\(U\) :

Velocity of the channel

\(T_{w}\) :

Temperature at the channel wall

\(U_{w}\) :

Velocity at the channel wall

\(F\) :

Non-uniform inertia coefficient of porous medium

\(P\) :

Fluid pressure

\(k\) :

Permeability of porous medium

\(c_{b}\) :

Drag coefficient

\(T\) :

Fluid temperature and

\(q_{rad}\) :

The radiative heat flux

\(\sigma^{*}\) :

Stefan–Boltzmann constant

\(k^{*}_{nf}\) :

Mean absorption coefficient

\(\rho_{nf}\) :

Density of nanofluid

\(\mu_{nf}\) :

Dynamic viscosity of nanofluid

\(\left( {\rho c_{p} } \right)_{nf}\) :

Heat capacity of nanofluid

\(\rho_{f}\) :

Density of base fluid

\(\mu_{f}\) :

Dynamic viscosity of base fluid

\(\left( {\rho c_{p} } \right)_{f}\) :

Heat capacity of base fluid

\(\phi\) :

Solid volume fraction of nanofluid

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at Majmaah University for funding this work under Project Number RGP-2019-16.

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Authors and Affiliations

  1. SJM Institute of Technology, Chitredurga, Karnataka, 577502, India

    K. Ganesh Kumar

  2. Faculty of Medicine and Health Science, Ghent University, 9000, Gent, Belgium

    Mohammad Rahimi-Gorji

  3. Department of Mathematics, Acharya Nagarjuna University Campus, Ongole, AP, 523 001, India

    M. Gnaneswara Reddy

  4. Mechanical Engineering Department, Prince Mohammad Endowment for Nanoscience and Technology, Prince Mohammad Bin Fahd University, Al-Khobar, 31952, Saudi Arabia

    Ali. J. Chamkha

  5. Department of Mechanical and Industrial Engineering, College of Engineering, Majmaah University, Majmaah, 11952, Kingdom of Saudi Arabia

    Ibrahim M. Alarifi

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  1. K. Ganesh Kumar
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  4. Ali. J. Chamkha
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Correspondence to Ibrahim M. Alarifi.

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Kumar, K.G., Rahimi-Gorji, M., Reddy, M.G. et al. Enhancement of heat transfer in a convergent/divergent channel by using carbon nanotubes in the presence of a Darcy–Forchheimer medium. Microsyst Technol 26, 323–332 (2020). https://doi.org/10.1007/s00542-019-04489-x

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