# American Institute of Mathematical Sciences

## Channel flow of fractionalized H2O-based CNTs nanofluids with Newtonian heating

 1 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam 2 Department of Mathematics, City University of Science and Information Technology, Peshawar, 25000, Pakistan 3 Department of Applied Mathematics, Princess Nourah bint Abdulrahman University Riyadh, Saudi Arabia

* Corresponding author: Ilyas Khan, ilyaskhan@tdt.edu.vn

Received  March 2018 Revised  May 2018 Published  March 2019

The present article deals to study heat transfer analysis due to convection occurs in a fractionalized H2O-based CNTs nanofluids flowing through a vertical channel. The problem is modeled in terms of fractional partial differential equations using a modern trend of the fractional derivative of Atangana and Baleanu. The governing equation (momentum and energy equations) are subjected to physical initial and boundary conditions. The fractional Laplace transformation is used to obtain solutions in the transform domain. To obtain semi-analytical solutions for velocity and temperature distributions, the Zakian's algorithm is utilized for the Laplace inversions. For validation, the obtained solutions are compared in tabular form using Tzou's and Stehfest's numerical methods for Laplace inversion. The influence of fractional parameter is studied and presented in graphs and discussed.

Citation: Ilyas Khan, Muhammad Saqib, Aisha M. Alqahtani. Channel flow of fractionalized H2O-based CNTs nanofluids with Newtonian heating. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020043
##### References:

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##### References:
Flow configuration and coordinate system
Variation of the velocity profile for water-based MWCNT nanofluid due to $\alpha$when $\phi = 0.03\, \mathit{\rm{and}}\, Gr = 5$
Variation of the temperature profile for water-based MWCNT nanofluid due to $\alpha$when $\phi = 0.03.$
Variation of the velocity profile for water based MWCNT nanofluid due to $\phi$when $\phi = 0.5\, \mathit{\rm{and}}\, Gr = 5$
Variation of the temperature profile for water-based MWCNT nanofluid due to $\phi$when $\phi = 0.5\, \mathit{\rm{and}}\, Gr = 5$
Comparison of velocity profiles for water-based MWCNT and SWCNT nanofluids when $\alpha = 0.5,\, \phi = 0.3\, \mathit{\rm{and}}\, Gr = 5$
Comparison of temperature profiles for water-based MWCNT and SWCNT nanofluids when $\alpha = 0.5,\, \phi = 0.3\, \mathit{\rm{and}}\, Gr = 5$
Comparison of velocity profile using different algorithms
Comparison of temperature distribution using different algorithms
Thermophysical properties of water and CNTs nanoparticles
 Material Base fluid Nanoparticles Water MWCNT SWCNT ${\rho \left( {{\rm{kg}}/{{\rm{m}}^3}} \right)}$ 997 1600 2600 ${C_p}\left( {{\rm{J}}/{\rm{kg}}\;{\rm{K}}} \right)$ 4179 796 425 ${K\left( {{\rm{W}}/{\rm{mK}}} \right)}$ 0.613 6600 Pr 6.2 - -
 Material Base fluid Nanoparticles Water MWCNT SWCNT ${\rho \left( {{\rm{kg}}/{{\rm{m}}^3}} \right)}$ 997 1600 2600 ${C_p}\left( {{\rm{J}}/{\rm{kg}}\;{\rm{K}}} \right)$ 4179 796 425 ${K\left( {{\rm{W}}/{\rm{mK}}} \right)}$ 0.613 6600 Pr 6.2 - -
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