Incompressible Laminar Developing Flow in Microchannels

Galvis, Elmer; Yarusevych, Serhiy; Culham, J. R.

doi:10.1115/1.4005736

Cited by 31 publications

(22 citation statements)

References 20 publications

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“…Therefore, well estimate of the channel's MHD development length has a significant role to design pertinent systems and solve practical problems in many industrial and scientific fields [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Although researches about the hydrodynamic development length and suggesting the more accurate relation for development length have been studied until now [24][25][26][27][28], but the attention about the magnetohydrodynamic development length and presenting the correlation for predicting it is not noticeable.…”

Section: Introductionmentioning

confidence: 99%

“…According to the above discussion, although a number of mathematical expressions for estimating the development length in channel flows without MHD effects have been existed in the literature [25,27,28,[41][42][43], but very little work has been done to present the closed-form correlation for predicting the MHD development length in MHD channel flows.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

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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“…Galivis and Yarusevych et al [24] numerically studied the entrance region length of microchannels with hydraulic diameters between 100 and 500 µm. The Reynolds numbers ranged from 0.5 to 200 and aspect ratios from 1 to 5.…”

Section: Introductionmentioning

confidence: 99%

“…Although some studies on the entrance length in microscale channels have been done, as Table 2 presents, the previous studies were mainly qualitative, and the applicable results are still limited-especially for laminar flow at low Reynolds numbers. Even though some of them proposed correlations of entrance length [23,24], the inlet conditions were given as a uniform velocity in these studies, which does not simulate real inlet velocities. Therefore, further study is necessary to explore the factors influencing the entrance length in microscale channels.…”

Section: Introductionmentioning

confidence: 99%

Flow Characteristics of the Entrance Region with Roughness Effect within Rectangular Microchannels

Huang

et al. 2019

Micromachines

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We conducted systematic numerical investigations of the flow characteristics within the entrance region of rectangular microchannels. The effects of the geometrical aspect ratio and roughness on entrance lengths were analyzed. The incompressible laminar Navier–Stokes equations were solved using finite volume method (FVM). In the simulation, hydraulic diameters ( D h ) ranging from 50 to 200 µm were studied, and aspect ratios of 1, 1.25, 1.5, 1.75, and 2 were considered as well. The working fluid was set as water, and the Reynolds number ranged from 0.5 to 100. The results showed a good agreement with the conducted experiment. Correlations are proposed to predict the entrance lengths of microchannels with respect to different aspect ratios. Compared with other correlations, these new correlations are more reliable because a more practical inlet condition was considered in our investigations. Instead of considering the influence of the width and height of the microchannels, in our investigation we proved that the critical role is played by the aspect ratio, representing the combination of the aforementioned parameters. Furthermore, the existence of rough elements obviously shortens the entrance region, and this effect became more pronounced with increasing relative roughness and Reynolds number. A similar effect could be seen by shortening the roughness spacing. An asymmetric distribution of rough elements decreased the entrance length compared with a symmetric distribution, which can be extrapolated to other irregularly distributed forms.

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“…These works provide an insight on the importance of entrance region studies for small-scale flow. An experimental work on thermo-hydrodynamic and thermal developing in an array rectangular mini channel with flow Reynolds number variance has been explored in (6,7). They discovered a very high heat transferred in the entrance channel region which is essential for heat flux removal applications.…”

Section: Introductionmentioning

confidence: 99%

Investigation on entrance length for electroosmotic flow in circular and noncircular cross section nanochannel

Yaakub

Yunas

Majlis

2017

AIP Conference Proceedings

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Incompressible Laminar Developing Flow in Microchannels

Cited by 31 publications

References 20 publications

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

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

Flow Characteristics of the Entrance Region with Roughness Effect within Rectangular Microchannels

Investigation on entrance length for electroosmotic flow in circular and noncircular cross section nanochannel

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