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

Ilyas Khan; Muhammad Saqib; Aisha M. Alqahtani

doi:10.3934/dcdss.2020043

Article Contents

2020, Volume 13, Issue 3: 769-779. Doi: 10.3934/dcdss.2020043

This issue Previous Article Extension of triple Laplace transform for solving fractional differential equations Next Article Analysis of the Fitzhugh Nagumo model with a new numerical scheme

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

Received: February 28, 2018

Revised: April 30, 2018

Published: December 2019

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Abstract

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.

Keywords:

Mathematics Subject Classification: 35R09, 35R11.

Citation:

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Figure 1. Flow configuration and coordinate system

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Figure 2. Variation of the velocity profile for water-based MWCNT nanofluid due to $ \alpha $when $ \phi = 0.03\, \mathit{\rm{and}}\, Gr = 5 $

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Figure 3. Variation of the temperature profile for water-based MWCNT nanofluid due to $ \alpha $when $ \phi = 0.03. $

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Figure 4. Variation of the velocity profile for water based MWCNT nanofluid due to $ \phi $when $ \phi = 0.5\, \mathit{\rm{and}}\, Gr = 5 $

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Figure 5. Variation of the temperature profile for water-based MWCNT nanofluid due to $ \phi $when $ \phi = 0.5\, \mathit{\rm{and}}\, Gr = 5 $

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Figure 6. Comparison of velocity profiles for water-based MWCNT and SWCNT nanofluids when $ \alpha = 0.5,\, \phi = 0.3\, \mathit{\rm{and}}\, Gr = 5 $

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Figure 7. Comparison of temperature profiles for water-based MWCNT and SWCNT nanofluids when $ \alpha = 0.5,\, \phi = 0.3\, \mathit{\rm{and}}\, Gr = 5 $

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Figure 8. Comparison of velocity profile using different algorithms

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Figure 9. Comparison of temperature distribution using different algorithms

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Table 1. 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	-	-

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