Electrohydrodynamically Augmented Internal Forced Convection

  • Michal TalmorEmail author
  • Jamal Seyed-Yagoobi
Reference work entry


Many thermal devices, such as heat exchangers and heat pipes, utilize forced convection of internal flows as their main mechanism for heat transport. This chapter addresses the fundamentals associated with internal flows by providing the mathematical model for the simplest case of forced convection – a laminar flow in a circular tube. As an example for the application of this fundamental theory, the modern topic of electrohydrodynamically driven dielectric liquids and liquid films for heat transfer in internal flows in macro- and microscales is presented.


Fluid Parameters

\( \overline{v} \)

Fluid velocity vector \( \left[\frac{m}{s}\right] \)

vx , mean

Mean fluid velocity \( \left[\frac{m}{s}\right] \)


Pressure [Pa]


Temperature [K]


Mean temperature [K]

\( \dot{m} \)

Mass flux \( \left[\frac{\mathrm{kg}}{s}\right] \)


Shear stress \( \left[\frac{N}{m^2}\right] \)


Friction coefficient


Reynolds number


Heat flux density \( \left[\frac{W}{m^2}\right] \)


Nusselt number

Electrical Parameters

\( \overline{E} \)

Electric field vector \( \left[\frac{V}{m}\right] \)


Electric field magnitude \( \left[\frac{V}{m}\right] \)


Electric potential [V]

\( \overline{J} \)

Current density vector \( \left[\frac{C}{m^3s}\right] \)

\( {\overline{f}}_g \)

Force density of gravity \( \left[\frac{N}{m^3}\right] \)

\( {\overline{f}}_{EHD} \)

EHD body force density \( \left[\frac{N}{m^2}\right] \)


Net charge density, \( {n}_e-{p}_e\ \left[\frac{C}{m^3}\right] \)

ne, pe

-/+ Charge densities \( \left[\frac{C}{m^3}\right] \)

n, p

Ionic species densities [m−3]


Onsager parameter


Onsager function


Bessel function, first kind, order one


Heterocharge layer thickness [m]


Zeta potential [V]


Angular frequency [s−1]


Wave number [m−1]



Heat transfer coefficient \( \left[\frac{W}{m^2K}\right] \)


Fluid mass density \( \left[\frac{\mathrm{kg}}{m^3}\right] \)


Fluid dynamic viscosity [Pa·s]


Specific heat \( \left[\frac{J}{K}\right] \)


Thermal conductivity \( \left[\frac{W}{\mathrm{mK}}\right] \)


Thermal diffusivity \( \left[\frac{m^2}{s}\right] \)


Electric permittivity \( \left[\frac{\mathrm{kg}}{m^3}\right] \)


Electric conductivity \( \left[\frac{S}{m}\right] \)


Ionic mobility \( \left[\frac{m^2}{\mathrm{Vs}}\right] \)


Charge relaxation time [s]


Equilibrium ionic density [m−3]


Equilibrium charge density \( \left[\frac{C}{m^3}\right] \)


Dissociation constant [m−3s−1]


Recombination constant [s−1]


Gravitational acceleration \( \left[\frac{m}{s^2}\right] \)

Domain Parameters


Time [s]

r, θ, x

Cylindrical coordinates


Channel cross sectional area [m2]


Hydraulic Channel Diameter [m]


Hydraulic channel radius [m]

\( \widehat{n} \)

Normal direction unit vector


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Initial condition or surface

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In the given direction

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Positive or negative


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Multi-Scale Heat Transfer Laboratory, Department of Mechanical EngineeringWorcester Polytechnic InstituteWorcesterUSA

Section editors and affiliations

  • Sumanta Acharya
    • 1
  1. 1.Herff College of Engineering,Department of Mechanical EngineeringThe University of MemphisMemphisUSA

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