Numerical Investigation of Thermally Developing and Fully Developed Electro-Osmotic Flow in Channels with Rounded Corners

Abstract

Electro-osmotic flow, that is, the motion of a polar fluid in microducts induced by an external electric field, is one micro-effect which allows fluid circulation without the use of mechanical pumping. This is of interest in the thermal management of electronic devices, as microchannels with cross sections of almost arbitrary shape can easily be integrated on the chips. It is therefore important to assess how the geometry of the channel influences the heat transfer performance. In this paper, the thermal entry region and the fully developed electro-osmotic flow in a microchannel of rectangular cross section with smoothed corners is investigated for uniform wall temperature. For the fully developed region, correlations for the Poiseuille and Nusselt numbers considering the aspect ratio and nondimensional smoothing radius are given, which can be used for practical design purposes. For thermally developing flow, it is highlighted how smoothing the corners increases the value of the local Nusselt number, with increases up to 18% over sharp corners, but that it also shortens the thermal entry length. It is also found that Joule heating in the fluid may cause a reversal of the heat flux, and that the thermal entry length has a linear dependence on the Reynolds number and the hydraulic diameter and on the logarithm of the nondimensional Joule heating.

Optimised Electro-Osmotic Flow in Rectangular Microchannels with Smoothed Corners

“…The corresponding governing equations with suitable boundary conditions are written in the following directly in non-dimensional form; for a detailed description of how the equations are obtained using the Gouy-Chapman model, [2], see e.g. [25,27].…”

“…As discussed in [27], use of a preparation length, [30], to account for Joule heating within the fluid is not necessary in this case.…”

“…The numerical solution of Eqs. ( 1), ( 3) and (4) was obtained using the open source software GNU Octave and a number of additional libraries, as detailed in [27]. The electric potential and velocity fields are solved sequentially over the two-dimensional domain corresponding to the cross-section; this would not appear possible for the energy equation, Eq.…”

Performance Evaluation Criteria for Triangular Microchannels with Smoothed Corners

“…The equations are then solved numerically with an approach detailed in [19]. Knowledge of u* and ϑ * allows computation of the Nu and Po; details can be found in [13,16,19]; these quantities are then employed to compute the objective functions needed by the PEC chosen for the optimization. In general, the use of PEC allows the achievement of one of the goals listed below:…”

“…No viscous dissipation is considered, and Performance evaluation criteria (PEC) are used in order to determine heat transfer enhancement under defined constraints [7,10], and are sometimes coupled to second-law analyses [11]. This work complements other investigations by the same authors which dealt with other micro-geometries or boundary conditions [12][13][14], considered viscous dissipation [15,16] or electro-osmotic effects [17][18][19].…”