Analytical solution by Laplace-ritz variational method for non-Newtonian nanofluid inside a circular tube

Tahiri, Antar; Mansouri, Kacem

doi:10.1016/j.ijmecsci.2017.12.006

Cited by 6 publications

(4 citation statements)

References 35 publications

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“…To find the numerical solution of Eq (38) along with the initial and boundary conditions (39) for n 6 ¼ 1, MATLAB bvp4c numerical solver is used. In order to use the bvp4c solver one has to convert Eq (37) into a system of first order ordinary differential equations, that is…”

Section: Plos Onementioning

confidence: 99%

“…The exact solution of the Stokes' flow of a non-Newtonian nanofluid in a porous medium by considering the Navier's slip condition is studied in [38]. Tahiri and Mansouri [39] form analytical solutions for the flow of non-Newtonian nanofluid inside a circular tube by applying the Laplace-Ritz variational method. The authors discussed the effect of different emerging parameters on the velocity and temperature of nanofluid.…”

Section: Introductionmentioning

confidence: 99%

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Group theoretical analysis for unsteady magnetohydrodynamics flow and radiative heat transfer of power-law nanofluid subject to Navier’s slip conditions

Javaid

Aziz

2021

PLoS ONE

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The present work covers the flow and heat transfer model for the Power-law nanofluid in the presence of a porous medium over a penetrable plate. The flow is caused by the impulsive movement of the plate embedded in Darcy’s porous medium. The flow and heat transfer models are examined with the effect of linear thermal radiation in the flow regime. The Rosseland approximation is utilized for the optically thick nanofluid. The governing partial differential equations are solved using Lie symmetry analysis to find the reductions and invariants for the closed-form solutions. These invariants are then utilized to obtain the exact solutions for the shear-thinning, Newtonian, and shear-thickening nanofluids. In the end, all solutions are plotted for the Cu-water nanofluid to observe the effect of different emerging flow and heat transfer parameters.

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Section: Plos Onementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Group theoretical analysis for unsteady magnetohydrodynamics flow and radiative heat transfer of power-law nanofluid subject to Navier’s slip conditions

Javaid

Aziz

2021

PLoS ONE

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“…e author uses the Lie symmetry and generalized group approach to find the solutions. Tahiri and Mansouri [37] presented the analytical solutions using the Laplace-Ritz variational method for the flow of non-Newtonian nanofluid inside a circular tube. Aziz and Javaid [38] and Aziz et al [39] applied the Lie symmetry method on the flow and heat transfer of MHD third grade nanofluid in the presence of thermal radiation and with uniform internal heat source/sink, respectively.…”

Section: Introductionmentioning

confidence: 99%

Group Invariant Solutions for Flow and Heat Transfer of Power-Law Nanofluid in a Porous Medium

Javaid

Aziz

2021

Mathematical Problems in Engineering

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The present work covers the flow and heat transfer model for the power-law nanofluid in the presence of a porous medium over the penetrable plate. The flow is caused by the impulsive movement of the plate embedded in Darcy’s type porous medium. The flow and heat transfer model has been examined with the effect of linear thermal radiation and the internal heat source or sink in the flow regime. The Rosseland approximation is utilized for the optically thick nanofluid. To form the closed-form solutions for the governing partial differential equations of conservation of mass, momentum, and energy, the Lie symmetry analysis is used to get the reductions of governing equations and to find the group invariants. These invariants are then utilized to obtain the exact solution for all three cases, i.e., shear thinning fluid, Newtonian fluid, and shear thickening fluid. In the end, all solutions are plotted for the cu -water nanofluid and discussed briefly for the different emerging flow and heat transfer parameters.

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“…However, in some cases, the shear thickening behavior is observed when the nanoparticles increase. Tahiri and Mansouri [21,22] have studied analytically the convective heat transfer using non-Newtonian nanofluid within circular duct, taking into consideration the effect of viscous dissipation. It's demonstrated that the non-Newtonian nanofluids show a better efficiency in term of heat transfer compared to the Newtonian nanofluids.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Non-Newtonian Nanofluid Flows Within Circular Duct under Convective Boundary Condition

Tahiri¹,

Mansouri²,

Kouider³

et al. 2021

MMEP

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At the outset, this work aims to carried out an analytical investigation of forced convection by establishing a laminar flow into circular duct under convective boundary conditions of the third type for non-Newtonian nanofluid, the fluid containing TiO2 uniformly dispersed in aqueous solution with 0.5wt% of CMC solutions (Carboxymethyl Cellulose) is used as working fluid. The viscous dissipation effects are taken into account, the employed methodology is based on a combination of the Ritz variational approach with the Laplace transformation technique, so the power-law fluids flow model is used to describe the non-Newtonian fluid behavior. The effect of dimensionless parameters such as Biot (Bi), Brinkman (Br), Peclet (Pe) numbers, power-law index (n), and nanoparticles concentration (φ) on the temperature distribution contours and on the examined local Nusselt number. Our results have been compared with those found in the literature in particular the cases of base fluids (φ=0) with and without viscous dissipation effects.

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Analytical solution by Laplace-ritz variational method for non-Newtonian nanofluid inside a circular tube

Cited by 6 publications

References 35 publications

Group theoretical analysis for unsteady magnetohydrodynamics flow and radiative heat transfer of power-law nanofluid subject to Navier’s slip conditions

Group theoretical analysis for unsteady magnetohydrodynamics flow and radiative heat transfer of power-law nanofluid subject to Navier’s slip conditions

Group Invariant Solutions for Flow and Heat Transfer of Power-Law Nanofluid in a Porous Medium

Analytical Solution of Non-Newtonian Nanofluid Flows Within Circular Duct under Convective Boundary Condition

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