Abstract
The steady-state electro-kinetic-driven flow and heat transfer in circular micro-channels are studied under hydrodynamic fully developed and thermally developing conditions. Based on the linearized Poisson–Boltzmann equation, an exact solution of the electrical potential distribution is obtained. The analytic solutions of the velocity and temperature profiles are then obtained, and the effects of some hydrodynamic and thermal parameters on flow and heat transfer are investigated. The interesting plug-like velocity profile produced by external electrical field is not usually observed in the pressure-driven flows. In this case, the very large velocity gradient near the wall of the micro-channel may result in the enhanced temperature close to the wall (depending on the relative importance of viscous dissipation compared with the other terms); the temperature values of other portions of the flow field are increased slightly. Decreasing both Reynolds and Prandtl numbers leads to increasing the bulk fluid temperature. Nusselt number decreases in the thermally developing region.
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Abbreviations
- c p :
-
Specific heat (J/kg K)
- e :
-
Electron charge (C)
- E z :
-
Dimensionless electrical field strength
- Ek :
-
Eckert number
- F z :
-
Dimensionless electrical force per unit volume
- h z :
-
Local convection heat transfer coefficient (W/m2 K)
- I ν (x):
-
Modified Bessel function of the first kind and order ν
- k B :
-
Boltzmann constant (J/K)
- k f :
-
Fluid thermal conductivity (W/m K)
- L :
-
Length of channel (m)
- M :
-
Ratio of electrical to frictional forces
- n 0 :
-
Bulk ion concentration (m−3)
- Nu :
-
Nusselt number
- Pe :
-
Peclet number
- Pr:
-
Prandtl number
- q′′:
-
Dimensionless heat flux
- r :
-
Dimensionless radial coordinate
- R :
-
Radius of the micro-channel (m)
- Re :
-
Reynolds number
- s :
-
Ratio of half channel diameter to Debye length
- T :
-
Dimensionless temperature
- T m (z):
-
Local mean fluid temperature (K)
- T s :
-
Constant wall temperature (K)
- U :
-
Reference velocity (m/s)
- V z :
-
Dimensionless axial velocity
- z :
-
Dimensionless axial coordinate
- \({{\mathbb{Z}}}\) :
-
Valence of ionic species
- \({\varepsilon }\) :
-
Electric permittivity of solution (F/m)
- κ :
-
Debye–Huckel parameter (m−1)
- λ :
-
Eigenvalue
- μ :
-
Dynamic viscosity (kg/m s)
- ρ :
-
Fluid density (kg/m3)
- ρ e :
-
Net volume charge density (C m−3)
- ψ :
-
Dimensionless electrical potential
- ζ :
-
Dimensionless zeta potential at the wall
- m :
-
Mean value
- *:
-
Dimensional quantities
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Moghadam, A.J. Thermally Developing Flow Induced by Electro-Osmosis in a Circular Micro-Channel. Arab J Sci Eng 39, 1261–1270 (2014). https://doi.org/10.1007/s13369-013-0717-8
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DOI: https://doi.org/10.1007/s13369-013-0717-8