Trapezoidal Silicon Microchannels Research Articles

Experimental and Numerical Study of Flow and Heat Transfer in Trapezoidal Microchannels

An experimental investigation has been performed on the laminar flow and heat transfer of water in trapezoidal silicon microchannels. Two three-dimensional (3D) heat transfer models have been developed to simulate the heat transfer performance under the same experimental conditions. Due to the sudden contraction, the velocity develops a little faster, which makes the pressure drop slightly lower than that of the neglected entrance and exit plenum regions. Due to the heat conduction in the lateral parts of wafer, the maximum temperature appears near the outlet of microchannel and the temperature is slightly different among the microchannels. Nearer to the lateral parts of wafer, the the temperature reaches the maximum for the sidewall later. With a given pumping power, the thermal resistance decreases as increase of the heating power at the substrate. However, the subthermal resistance proportion is nearly unchanged. With an increase of pumping power, the subthermal resistance proportion of convection increases rapidly at first, then gradually approaches an asymptote.

Fluid Flow in Trapezoidal Silicon Microchannels With 3D Random Rough Bottoms

In this paper, a bottom-up approach is used to construct random rough bottom walls for trapezoidal silicon microchannels with hydraulic diameters Dh from 47 μm to 241 μm. The top and side walls are set to be smooth. A computational fluid dynamics solver is used to solve the 3D Navier–Stokes equations for the water flow through the rough trapezoidal microchannels. No-slip and periodic boundary conditions are applied to achieve the fully developed flow characteristics. The effects of Reynolds number Re (75–600), relative roughness height H/Dh (1.66–5.39%), aspect ratio β (0.13–1), and base angle θ (30–90 deg) on the Poiseuille number Po are investigated. It is found that the roughness strongly affects the flow near the bottom wall but does not have significant effect on the center flow. The Po number in the developing flow region increases with the Re number and in the fully developed region tends to be independent of the Re number. The entrance length Le is found to be smaller than that in smooth channels because the roughness reduces hydraulic diameter Dh of the microchannel. It is also observed that with a certain H/Dh, the Po number has a larger deviation from the theoretical value with a smaller β, and with the same H/Dh and β, θ can also change the Po number, especially at small base angles.

First and second law analysis of fully developed gaseous slip flow in trapezoidal silicon microchannels considering viscous dissipation effect

Fully developed gaseous slip flow in trapezoidal silicon microchannels is studied. Friction factor, Nusselt number and entropy generation in the microchannel is obtained, effect of rarefaction, aspect ratio and viscous dissipation is explored and, the range of Brinkman number in which viscous dissipation effect is important and cannot be neglected is specified. The continuum approach with the velocity slip and temperature jump condition at the solid walls is applied to develop the mathematical model of problem in the trapezoidal microchannel. Transformation of trapezoidal geometry to a square provided ease of application of finite difference method in solution of the mathematical model. The effect of viscous dissipation is quantified by Brinkman number. The calculated Brinkman number for common engineering applications even with limiting operational and geometric conditions is found less than 0.005. It is observed that viscous effect for applications with Brinkman number less than 0.005 can be neglected. The region in which viscous dissipation effect cannot be neglected is specified as Br > 0.005. Decreasing effect of rarefaction and increasing effect of Brinkman number on irreversibility due to all sources, excluded axial conduction, is established. The dominant source of irreversibility in total irreversibility is specified as a function of Brinkman number.

Flow friction and heat transfer of ethanol–water solutions through silicon microchannels

An experimental investigation was performed on the flow friction and convective heat transfer characteristics of the ethanol–water solutions flowing through five sets of trapezoidal silicon microchannels having hydraulic diameters ranging from 141.7 µm to 268.6 µm. Four kinds of ethanol–water solutions with the ethanol volume concentrations ranging from 0 to 0.8 were tested under different flow and heating conditions. It was found that the cross-sectional geometric parameters had great effect on the flow friction and heat transfer, and the microchannels with a larger Wb/Wt (bottom width-to-top width ratio) and a smaller H/Wt (depth-to-top width ratio) usually had a larger friction constant and a higher Nusselt number. Entrance effects were significant for the flow friction and heat transfer in silicon microchannels, and decreased with the increase of dimensionless hydrodynamic length L and dimensionless thermal length L+h. When L > 1.0, the hydrodynamic entrance effect on the flow friction was ignorable. For the developed laminar flow in silicon microchannels, the Navier–Stokes equation was applicable. It was also found that the volume concentrations had different effects on the flow friction and heat transfer. Within the experimental range, the effect of volume concentrations on the flow friction was ignorable, and the friction constants of the ethanol–water solutions having different concentrations were the same as those of the pure water. However, volume concentrations had great effect on the convection heat transfer in silicon microchannels. With the increase of the volume concentrations, the Nusselt number of the ethanol–water solutions increased obviously, which was attributed to the combination effect of the increase in the Prantdtl number as well as the volatilization effect of the ethanol. Based on the experimental data, the dimensionless correlations for the flow friction and heat transfer of the ethanol–water solutions in the silicon microchannels in a function of the cross-sectional geometrical parameters, entrance effect and volume concentrations were proposed for the first time.

Condensation heat transfer and flow friction in silicon microchannels

An experimental investigation was performed on heat transfer and flow friction characteristics during steam condensation flow in silicon microchannels. Three sets of trapezoidal silicon microchannels, with hydraulic diameters of 77.5 µm, 93.0 µm and 128.5 µm respectively, were tested under different flow and cooling conditions. It was found that both the condensation heat transfer Nusselt number (Nu) and the condensation two-phase frictional multiplier (ϕ2Lo) were dependent on the steam Reynolds number (Rev), condensation number (Co) and dimensionless hydraulic diameter (Dh/L). With the increase in the steam Reynolds number, condensation number and dimensionless hydraulic diameter, the condensation Nusselt number increased. However, different variations were observed for the condensation two-phase frictional multiplier. With the increase in the steam Reynolds number and dimensionless hydraulic diameter, the condensation two-phase frictional multiplier decreased, while with the increase in the condensation number, the condensation two-phase frictional multiplier increased. Based on the experimental results, dimensionless correlations for condensation heat transfer and flow friction in silicon microchannels were proposed for the first time. These correlations can be used to determine the condensation heat transfer coefficient and pressure drop in silicon microchannels if the steam mass flow rate, cooling rate and geometric parameters are fixed. It was also found that the condensation heat transfer and flow friction have relations to the injection flow (a transition flow pattern from the annular flow to the slug/bubbly flow), and with injection flow moving toward the outlet, both the condensation heat transfer coefficient and the condensation two-phase frictional multiplier increased.

An experimental investigation on pressure drop of steam condensing in silicon microchannels

Experiments are carried out to study the two-phase pressure drop for water vapor condensation in four smooth trapezoidal silicon microchannels having hydraulic diameters of 109 μm, 142 μm, 151 μm, and 259 μm, respectively. It is found that two-phase frictional pressure drops in the microchannels are greatly influenced by the hydraulic diameter, mass flux and vapor quality. The two-phase pressure drop data in microchannels are compared with existing correlations for macro- and mini-channels based on the homogenous model and the separated flow model to determine their applicability to condensing flows in microchannels. A modified correlation for the Matinelli–Chisholm constant, taking into consideration of surface tension and diameter effects, is developed in the form of the Lockhart–Martinelli correlation for the pressure drop in steam condensation in microchannels. The resulting condensation pressure drop correlation equation is within ±15% of the experimental data.

Thermal and hydrodynamic analysis of gaseous flow in trapezoidal silicon microchannels

Thermal and hydrodynamic character of a hydrodynamically developed and thermally developing flow in trapezoidal silicon microchannels is analyzed. The continuum momentum and energy equations, with the velocity slip and temperature jump condition at the solid walls, are solved numerically in a square computational domain obtained by transformation of the trapezoidal geometry. The effects of rarefaction, aspect ratio and a parameter representing the fluid/wall interaction on thermal and hydrodynamic character of flow in trapezoidal microchannels are explored. It is found that the friction factor decreases if rarefaction and/or aspect ratio increase. It is also found that at low rarefactions the very high heat transfer rate at the entrance diminishes rapidly as the thermally developing flow approaches fully developed flow. At high rarefactions, heat transfer rate does not exhibit considerable changes along the microchannel, no matter the flow is developing or not.

Injection flow during steam condensation in silicon microchannels

An experimental investigation with the combined use of visualization and measurement techniques was performed on flow pattern transitions and wall temperature distributions in the condensation of steam in silicon microchannels. Three sets of trapezoidal silicon microchannels, having hydraulic diameters of 53.0 µm, 77.5 µm and 128.5 µm, respectively, were tested under different flow and cooling conditions. It was found that during the transitions from the annular flow to the slug/bubbly flow, a peculiar flow pattern injection flow appeared in silicon microchannels. The location at which the injection flow occurred was dependent on the Reynolds number, condensation number and hydraulic diameter. With increase in the Reynolds number, or decrease in the condensation number and hydraulic diameter, the injection flow moved towards the channel outlet. Based on the experimental results, a dimensionless correlation for the location of injection flow in functions of the Reynolds number, condensation number and hydraulic diameter was proposed for the first time. This correlation can be used to determine the annular flow zone and the slug/bubbly flow zone, and further to determine the dominating condensation flow pattern in silicon microchannels. Wall temperature distributions were also explored in this paper. It was found that near the injection flow, wall temperatures have a rapid decrease in the flow direction, while upstream and downstream far away from the injection flow, wall temperatures decreased mildly. Thus, the location of injection flow can also be determined based on the wall temperature distributions. The results presented in this paper help us to better understand the condensation flow and heat transfer in silicon microchannels.

Condensation flow patterns in silicon microchannels

A simultaneous visualization and measurement experiment was carried out to investigate condensation flow patterns of steam flowing through an array of trapezoidal silicon microchannels, having a hydraulic diameter of 82.8 μm and a length of 30 mm. The degassed and deionized water steam flowing in the microchannels was cooled by flowing water of 8 °C from the bottom. The silicon microchannels were covered with a thin transparent pyrex glass from the top which enabled the visualization of flow patterns. Experiments were performed at different inlet pressures ranging from 4.15 × 10 5 Pa to 1.25 × 10 5 Pa (with corresponding mass fluxes decreasing from 47.5 g/cm 2 s to 19.3 g/cm 2 s) while the outlet pressure was maintained at a value of 10 5 Pa. Different condensation flow patterns such as fully droplet flow, droplet/annular/injection/slug-bubbly flow, annular/injection/slug-bubbly flow, and fully slug-bubbly flow were observed in the microchannels. At a given inlet pressure and mass flux, the flow pattern depended on both the location and time. Of particular interest is that the vapor injection flow, consisting of a series of bubble growth and detachment activities, appeared and disappeared periodically. During the disappearance period of injection flow, the slug-bubbly flow at downstream changed to the single-phase liquid flow due to the reversed flow of outlet condensate, while the annular flow at upstream changed to the vapor flow due to the effect of incoming vapor. Therefore, two-phase flow and single-phase flow appeared alternatively in the microchannels, causing large fluctuations of wall temperatures as well as other measurements. It was also found that the occurrence of vapor injection flow moved from the outlet toward the inlet as the mass flux was decreased. The vapor injection flow and its induced condensation instabilities in microchannels are reported here for the first time.

Friction factors in smooth trapezoidal silicon microchannels with different aspect ratios

An experiment has been conducted to measure the friction factor of laminar flow of deionized water in smooth silicon microchannels of trapezoidal cross-section with hydraulic diameters in the range of 25.9–291.0 μm. It is shown that the friction constant of these microchannels is greatly influenced by the cross-sectional aspect ratio, W b/ W t. Based on the 334 data points, a correlation equation for the friction constant of a fully developed laminar flow of water in these microchannels is obtained in terms of the cross-sectional aspect ratio. The experimental data is found to be in good agreement with an existing analytical solution for an incompressible, fully developed, laminar flow under no-slip boundary condition. It is confirmed that the Navier–Stokes equations are still valid for the laminar flow of deionized water in smooth silicon microchannels having hydraulic diameter as small as 25.9 μm. For smooth channels with larger hydraulic diameters of 103.4–291.0 μm, transition from laminar to turbulent flow is found at Re=1500–2000.

An experimental study of convective heat transfer in silicon microchannels with different surface conditions

An experimental investigation has been performed on the laminar convective heat transfer and pressure drop of water in 13 different trapezoidal silicon microchannels. It is found that the values of Nusselt number and apparent friction constant depend greatly on different geometric parameters. The laminar Nusselt number and apparent friction constant increase with the increase of surface roughness and surface hydrophilic property. These increases become more obvious at larger Reynolds numbers. The experimental results also show that the Nusselt number increases almost linearly with the Reynolds number at low Reynolds numbers ( Re<100), but increases slowly at a Reynolds number greater than 100. Based on 168 experimental data points, dimensionless correlations for the Nusselt number and the apparent friction constant are obtained for the flow of water in trapezoidal microchannels having different geometric parameters, surface roughnesses and surface hydrophilic properties. Finally, an evaluation of heat flux per pumping power and per temperature difference is given for the microchannels used in this experiment.

Gas flow characteristics in straight silicon microchannels

Experiments have been conducted to investigate nitrogen gas flow characteristics through four trapezoidal silicon microchannels with different hydraulic diameters. The volume flow rate and pressure ratio are measured in the experiments. It is found that the friction coefficient is no longer a constant, which is different from the conventional theory. The characteristics are first explained by the theoretical analysis. A simplified rectangular model (rectangular straight channel model) is then proposed. The experimental results are compared with the theoretical predictions based on the simplified rectangular model and the two-dimensional flow between the parallel-plate model which was usually used. The difference between the experimental data and the theoretical predictions is found in the high-pressure ratio cases. The influence of the gas compressibility effect based on the Boltzmann gas kinetic analysis method is studied to interpret the discrepancy. We discuss two important factors affecting the application extent of different prediction models.

Heat transfer for water flow in trapezoidal silicon microchannels

Experiments were conducted to investigate heat transfer characteristics of water flowing through trapezoidal silicon microchannels with a hydraulic diameter ranging from 62 to 169 μm. A numerical analysis was also carried out by solving a conjugate heat transfer problem involving simultaneous determination of the temperature field in both the solid and the fluid regions. The experimental results were compared with the numerical predictions and a significant difference was found. The comparison results indicated that the experimentally determined Nusselt number is much lower than that given by the numerical analysis. The measured lower Nusselt numbers may be due to the effects of surface roughness of the microchannel walls. Based on a roughness-viscosity model established in our previous work, a modified relation which accounts for the roughness-viscosity effects was proposed to interpret the experimental results.

Pressure-driven water flows in trapezoidal silicon microchannels

Experiments were conducted to investigate flow characteristics of water through trapezoidal silicon microchannels with a hydraulic diameter ranging from 51 to 169 μm. In the experiments, the flow rate and pressure drop across the microchannels were measured at steady states. The experimental results were compared with the predictions from the conventional laminar flow theory. A significant difference between the experimental data and the theoretical predictions was found. Experimental results indicate that pressure gradient and flow friction in microchannels are higher than those given by the conventional laminar flow theory. The measured higher pressure gradient and flow friction maybe be due to the effect of surface roughness of the microchannels. A roughness–viscosity model is proposed to interpret the experimental data.