Fully Developed Flow of Third-Grade Fluid in the Plane Duct with Convection on the Walls

Ebrahimi, S. M.; Abbasi, Morteza; Khaki, M.

doi:10.1007/s40997-016-0031-7

Cited by 9 publications

(6 citation statements)

References 17 publications

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“…The mathematical formulations of collocation method (CM) and least squared method (LSM) were provided in Sahebi et al (2015) and Ebrahimi et al (2016) instead of other methods (Gethin, 1989;Roberts, 1985). It should be noted many trial functions can be introduced, which can satisfy the boundary conditions.…”

Section: Application Of Least Square Methods and Collocation Methodsmentioning

confidence: 99%

Third-grade non-Newtonian fluid flow and heat transfer in two coaxial pipes with a variable radius ratio with magnetic field

Javanmard

Taheri

Askari

et al. 2020

HFF

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Purpose The purpose of this paper is to investigate the hydromagnetic third-grade non-Newtonian fluid flow and heat transfer between two coaxial pipes with a variable radius ratio. Design/methodology/approach To solve the approximate nonlinear and linear problems with variable coefficients, a trial function was applied. Methods include collocation, least square and Galerkin that can be applied for obtaining these coefficients. Findings It is revealed that an increase of the non-Newtonian parameter, Hartmann number, and radius ratio leads to an augmentation of the absolute value of the dimensionless velocity, temperature, velocity gradient, and temperature gradient of about 10-60%. Further, the augmentation of Bi1 reduces the absolute value of the dimensionless temperature profile and dimensionless temperature gradient about three to four times; hence, the dimensionless heat transfer rate reduces. However, the growth of Bi2 has a contrary impact. Besides, the increase of Pr and Ec leads to an increase in the dimensionless temperature profile and dimensionless temperature gradient; therefore, the dimensionless heat transfer rate increases. Originality/value The convection heat transfer on the walls of the pipes is considered, and the nonlinear coupled momentum and energy equations are solved using the least squared method and collocation methods, respectively.

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Section: Application Of Least Square Methods and Collocation Methodsmentioning

confidence: 99%

Third-grade non-Newtonian fluid flow and heat transfer in two coaxial pipes with a variable radius ratio with magnetic field

Javanmard

Taheri

Askari

et al. 2020

HFF

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“…In the other method, the Collocation Method (C.M.) [17][18][19], described in the following section, is used to obtain the dimensionless velocity distribution relation. The velocity distribution is plotted using the obtain relation.…”

Section: The Problem Solutionmentioning

confidence: 99%

Effect of Non-uniform Magnetic Field on Non-newtonian Fluid Separation in a Diffuser

Moghimi

Abbasi

Jamei

et al. 2020

IJE

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The purpose of the present study is to investigate the boundary layer separation point in a magnetohydrodynamics diffuser. As an innovation, the Re value on the separation point is determined for the non-Newtonian fluid flow under the influence of the non-uniform magnetic field due to an electrical solenoid, in an empirical case. The governing equations including continuity and momentum are solved by applying the semi-analytical collocation method (C.M.). The analysis revealed that for specific values of De from 0.4 to 1.6, α from 20 o to 2.5 o and Ha from zero to 8, the Re value on the separation point is increased from 52.94 to 1862.78; thus, the boundary layer separation postponed. Furthermore, the impact of the magnetic field intensity on the separation point is analyzed from the physical point of view. It is observed the wall shear stress increases by increasing magnetic field intensity that leads to delaying the boundary layer separation.

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“…The analytical solution of a fully developed flow of third-grade fluid in the plane duct with convection on the walls was studied by Ebrahimi et al 15 They neglected the advection term and solved the governing equation using the collocation method. They reported when the non-Newtonian parameter increases, the velocity and temperature profiles become flattened, and the convection heat transfer reduces.…”

Section: Introductionmentioning

confidence: 99%

Impact of Angular Magnetic Field and Convective Boundary Condition on Heat Transfer of Newtonian Fluid Flow in a Channel

Saeidi

Bagheri

Ghamati

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this study, the heat transfer of a laminar, steady, fully developed, and Newtonian fluid flow in a channel is investigated. The main goal of the present study is solving the hydromagnetic Newtonian fluid flow and heat transfer inside a channel with the angular magnetic field and convective boundary conditions on the walls. As a novelty, the effect of thermal diffusion and advection term the walls and Joule heating in the energy equation has been considered. The governing equations include the continuity, momentum, and energy are presented, and considering the assumptions are simplified. Afterward, employing the dimensionless parameters, the governing equations are transformed into dimensionless forms. The exact solution is provided for the momentum equation. For solving the full energy equation, the analytical collocation method (CM) is conducted. The results are validated using the 4th order Runge-Kutta method. The results demonstrated that the dimensionless velocity, the bulk temperature inside the channel, and the channel wall's heat transfer rate decline when the Hartmann number and the magnetic field angle increase. Since the Prandtl and Eckert numbers reduce, the dimensionless temperature becomes more uniform, and the heat transfer rate on the channel wall decreases. Since the Biot number augments, the dimensionless temperature inside the channel reduces, but the channel wall's heat transfer rate first increases and then reduces.

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Fully Developed Flow of Third-Grade Fluid in the Plane Duct with Convection on the Walls

Cited by 9 publications

References 17 publications

Third-grade non-Newtonian fluid flow and heat transfer in two coaxial pipes with a variable radius ratio with magnetic field

Third-grade non-Newtonian fluid flow and heat transfer in two coaxial pipes with a variable radius ratio with magnetic field

Effect of Non-uniform Magnetic Field on Non-newtonian Fluid Separation in a Diffuser

Impact of Angular Magnetic Field and Convective Boundary Condition on Heat Transfer of Newtonian Fluid Flow in a Channel

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