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Analytical solution of mixed electromagnetic/pressure driven gaseous flows in microchannels

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Abstract

The influences of wall-slip/jump conditions on the fluid flow and heat transfer for hydrodynamically and thermally fully developed electrically conducting gaseous flow subject to an electromagnetic field inside a parallel plate microchannel with constant heat flux at walls are studied under the assumptions of a low-magnetic Reynolds number. The governing equations are non-dimensionalized and then analytical solutions are derived for the friction and the heat transfer coefficients. The fluid flow and the heat transfer characteristics obtained in the analytical solutions are discussed in detail for different parameters such as the Knudsen, Hartmann, and Brinkman numbers. The velocity profiles verify that even with a constant Knudsen number, applying a stronger electromagnetic field gives rise to an increase in the slip velocity. The results also reveal that on increasing the Hartmann number, the heat transfer rate as well as the friction factor is enhanced, whereas it tends to suppress the movement of the fluid. Further, it is found that the Nusselt and the Poiseuille numbers are less sensitive to the electromagnetic field effects with increase in rarefaction.

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Abbreviations

A :

Constant parameter, \( \frac{RePr}{{T_{\text{s}} - T_{\text{i}} }}\frac{{{\text{d}}T_{\text{w}} }}{{{\text{d}}x}} \)

B :

Magnetic field strength

Br :

Brinkman number

c p :

Specific heat at constant pressure

D :

Hydraulic diameter

E :

Electric field strength

f :

Friction factor

H :

Height of channel

Ha :

Hartmann number

k :

Thermal conductivity of fluid

K :

−E/(U m B)

Kn :

Knudsen number

L :

Characteristic length

Nu :

Nusselt number

p :

Pressure

Po :

Poiseuille number, f Re

Pr :

Prandtl number

Re :

Reynolds number

Re m :

Magnetic Reynolds number, σμ m U m L

S :

Cross-section area

T :

Temperature

U, V :

Dimensional velocity component in the x, y directions

u, v :

Dimensionless velocity component in the x, y directions

U i :

Inlet velocity

U m :

Mean velocity

X, Y:

Dimensional position in coordinate system

x, y :

Dimensionless position in coordinate system

γ :

Specific heat ratio of fluid

λ :

Mean free path

μ :

Dynamic viscosity of fluid

μ m :

Magnetic permeability

ρ :

Density of fluid

θ :

Dimensionless temperature

σ :

Electric conductivity

σ v :

Tangential momentum accommodation coefficient

σ T :

Thermal accommodation coefficient

γ :

Specific heat ratio of fluid

a:

Pure electromagnetic field

i:

Fluid properties at the inlet

m:

Mean

s:

Fluid properties at the wall

w:

Wall

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Mostafa Shojaeian

  2. Department of Electrical Engineering, Arak Branch, Islamic Azad University, Arak, Iran

    Morteza Shojaeian

Authors
  1. Mostafa Shojaeian
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  2. Morteza Shojaeian
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Correspondence to Mostafa Shojaeian.

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Shojaeian, M., Shojaeian, M. Analytical solution of mixed electromagnetic/pressure driven gaseous flows in microchannels. Microfluid Nanofluid 12, 553–564 (2012). https://doi.org/10.1007/s10404-011-0897-z

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  • DOI: https://doi.org/10.1007/s10404-011-0897-z

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