Viscous heating of a laminar flow in the thermal entrance region of a rectangular channel with rounded corners and uniform wall temperature

Electro-osmotic flows are a means of circulating polar fluids through microchannels without resorting to mechanical pumping. The lack of moving parts, of noise and the ease of integration in silicon chips make them an interesting option for microchip cooling and miniaturized total analysis systems. This paper describes an optimization in terms of first- and second-law analysis of the cross-section of a microchannel subject to electro-osmotic flow. Starting from rectangular cross-sections of different aspect ratios, its corners are progressively smoothed and the resulting Poiseuille and Nusselt numbers computed. Performance evaluation criteria are then used to assess the change in, among others, heat transfer rate, temperature difference between wall and bulk fluid, and equivalent pumping power. The entropy number is also computed and the results commented. It is found that the latter criterion highlights a configuration of minimum entropy generation, whereas the trends of the heat transfer and temperature difference are opposite to that of the equivalent pumping power.

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

Section: Temperature Fieldmentioning

confidence: 99%

Optimised Electro-Osmotic Flow in Rectangular Microchannels with Smoothed Corners

Lorenzini

Suzzi

2023

J. Phys.: Conf. Ser.

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“…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:…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

Performance Evaluation Criteria for Triangular Microchannels with Smoothed Corners

Suzzi

Lorenzini

2022

J. Phys.: Conf. Ser.

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The manufacturing capabilities available today for microchannels make it possible to produce in a comparatively easy, quick and cheap way several cross-sections, possibly allowing modifications of the macro-geometry. Another way is smoothing the corners of polygona cross-sections: this eliminates low-gradient areas and increases transport phenomena, i.e. frictional losses and heat transfer. Several ways of assessing the relative performance of the new shape in comparison to the original have been suggested over the years, among which are Performance Evaluation Criteria (PEC), as proposed by Bergles and Webb. PEC are based on a first-law analysis and aim at extremising the thermal power, heat exchange area, inlet temperature difference or pumping power under varying constraints. In this work equilateral triangular microchannels with uniform wall temperature are considered, through which a liquid flows in fully-developed, steady laminar regime. The cross-sectional area has its corners progressively rounded, and the velocity and temperature profiles are determined, in order to compute the Poiseuille, Nusselt and Stanton numbers, which are then employed in computing the objective functions for some PEC.

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“…The investigation was then extended to pressure-driven flows in microchannels with and without viscous dissipation, [19,20], and to electro-osmotic flows in the fully developed and constant heat flux and perimeter temperature case [21], employing the results to carry out a first-law analysis based on performance evaluation criteria (PEC), [22], and on entropy production minimisation. Though it is often neglected in the analysis of transport phenomena in laminar flows within microchannels, the study of the thermal entry region of a hydrodynamically fully developed, flow, known as the Graetz problem, is a feature which may become dominant, as demonstrated for the case of non-negligible viscous dissipation, [23], and of electro-osmotic flows with uniform temperature over the channel walls, [24]. This work investigates the change in constrained heat transfer performance, expressed as the change in heat flux or temperature difference from a reference configuration (i.e.…”

Section: Introductionmentioning

confidence: 99%

Performance assessment of electro-osmotic flow of rectangular microchannels with smoothed corners

Suzzi,

Lorenzini

2023

J. Phys.: Conf. Ser.

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Microchannel heat sinks are a viable alternative to traditional thermal management systems when high fluxes over small surfaces are involved. To avoid high pressure drops especially when liquids are concerned, electro-osmotic flow, a phenomenon which is relevant at the microscales only, can be employed profitably. Joule heating, which occurs every time an electrical current is circulated through a conductor with finite electrical resistance, may hamper the application of electro-osmotic flows significantly; its effects must therefore be investigated, as should the influence of the entry length on the overall transport phenomena which occur in the microchannel, especially so since channels with uniform temperature at the walls tend to be somewhat short, to mitigate heat generation due to Joule heating. In this paper the transport phenomena occurring within a microchannel of rectangular cross-section with uniform wall temperature through which an electro-osmotic flow occurs is studied, while considering the flow fully developed hydrodynamically but thermally developing (Graetz problem). The corners are then smoothed progressively and the effect of this change in the shape of the cross-section over the non-dimensional dissipated power or temperature difference between wall and fluid is investigated using the performance evaluation criteria introduced by Webb. Correlations are suggested for the Poiseuille and Nusselt numbers for all configurations as are criteria to obtain the maximum allowable channel length, i.e. the length of the channel over which the walls start to cool the fluid, owing to Joule heating, in terms of the hydraulic diameter.

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Viscous heating of a laminar flow in the thermal entrance region of a rectangular channel with rounded corners and uniform wall temperature

Cited by 22 publications

References 24 publications

Optimised Electro-Osmotic Flow in Rectangular Microchannels with Smoothed Corners

Optimised Electro-Osmotic Flow in Rectangular Microchannels with Smoothed Corners

Performance Evaluation Criteria for Triangular Microchannels with Smoothed Corners

Performance assessment of electro-osmotic flow of rectangular microchannels with smoothed corners

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