Development of MHD flow in the entrance region of a channel

Wu, S. T.; Fu, Tao; Wear, M.B.

doi:10.1051/rphysap:0197100603040900

Cited by 4 publications

(3 citation statements)

References 2 publications

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“…The momentum equation outcomes are validated by the results of Wu et al 26 and Lima and Reˆgo. 27 The fully developed velocity profile is defined as…”

Section: Numerical Verificationmentioning

confidence: 67%

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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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“…The momentum equation outcomes are validated by the results of Wu et al 26 and Lima and Reˆgo. 27 The fully developed velocity profile is defined as…”

Section: Numerical Verificationmentioning

confidence: 67%

“…For solving equation ( 19) using CM, initially, the obtained dimensionless velocity distribution, equation (26), is inserted in equation (19). Afterward, a trial function that satisfied the boundary conditions is assumed as follow…”

Section: Solution Of Energy Equationmentioning

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:

View full text Add to dashboard Cite

show abstract

“…The primary studies about the effect of magnetic field on the magnetohydrodynamic development length were done by [29][30][31][32][33][34][35][36][37]. Maciulaitis and Loeffler [34] presented a relation for magnetohydrodynamic development length.…”

Section: Introductionmentioning

confidence: 99%

The influence of magnetic field on the fluid flow in the entrance region of channels: analytical/numerical solution

Taheri

2019

SN Appl. Sci.

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The present paper investigates the steady laminar development flow of a Newtonian incompressible electrically conducting fluid in a plane channel subjected to a uniform transverse external magnetic field. In order to solve the problem, the analytical integral momentum method and numerical finite volume method (FVM) are conducted. In integral momentum solution, the Pohlhausen's fourth-degree velocity profile is assumed. Applying the boundary conditions leads to the appearance of a new dimensionless parameter named auxiliary parameter (AP). It is shown that the value of AP depends on the magnitude of magnetic intensity and the pressure gradient. For each specified value of AP, distinct velocity distribution and as a result, a correlation for computing the magnetic development length is obtained. Besides, the FVM is applied to solve the same problem and the correlation for estimating the magnetic development length is obtained. It can be concluded that for a particular engineering application of magnetohydrodynamics channel flows, the associated value of AP can be determined by the numerical investigation. The results of numerical solution are compared with the analytical results and it can be concluded that the results for AP = − 6 are in agreement with the numerical results. Further, the effect of Hartmann and Reynolds number on the magnetic development length and Lorentz force are illustrated. It was shown that as the Hartmann number increases, the value of development length and Lorentz force are reduced. KeywordsChannel · Integral momentum method · Magnetic development length · Magnetohydrodynamics · Numerical method List of symbols a Half width of channel (m) AP Auxiliary parameter B 0 External magnetic field (T) Ha Hartmann number P Pressure (Pa) Re Reynolds number u x-Component of the velocity (m/s) U Inlet velocity (m/s) u c Potential core velocity (m/s) v y-Component of the velocity (m/s) x Coordinate in the direction of flow (m) x em /D Dimensionless MHD development length y Coordinate in the direction normal to flow (m) ρ Density (kg/m 3 ) σ Electrical conductivity (Ω m) −1 δ Boundary layer thickness (m) υ Kinematic viscosity (m/s 2 ) η Arbitrary variable

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Linearized analysis of magnetohydrodynamic entrance flow in a vertical channel with combined thermal convection

Hendrix

1977

Appl. Sci. Res.

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Development of MHD flow in the entrance region of a channel

Cited by 4 publications

References 2 publications

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

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

The influence of magnetic field on the fluid flow in the entrance region of channels: analytical/numerical solution

Linearized analysis of magnetohydrodynamic entrance flow in a vertical channel with combined thermal convection

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