Poiseuille Number Research Articles

Analytical solutions of slip flow and H1 heat transfer in elliptical microchannels

The slip flow and heat transfer problems inside a micro- or nano-channel are active research topics. Understanding the velocity and temperature distributions in these channels is essential in both theory and applications. In this paper, the analytical solutions of the fully developed slip flow and heat transfer under the H1 boundary condition in elliptical microchannels are obtained with the velocity slip and temperature jump. The separation of variables method is employed to solve the momentum and energy equations, and the coefficient of the velocity profile is calculated using the binomial series twice. Based on the result of the velocity profile, the analytical solution of the temperature profile is also derived. A new model is deduced to predict the Poiseuille number in elliptical microchannels. The close-form solution of the Nusselt number is first obtained and can serve as a benchmark for other approaches.

High throughput millifluidics mixer with double triangle baffle for improvement of mixing performance and reduction of flow resistance designed by grey relational analysis

To improve the mixing performance and reduce flow resistance, in this study, a novel mixer with double triangle baffles was designed and optimized by the combination of CFD simulation and grey relation analysis method. Mixing index and Poiseuille number were selected as two key indexes to evaluate the mixing performance and flow resistance of the mixer. The orthogonal experiment was conducted with selecting the aspect ratio of baffles (α), the thickness of baffles (h), the spacing between adjacent baffles (c) and the number of baffles (d) as design variables. Among all design variables, d has the greatest influence on the mixer performances. The results show that the optimized mixer has a maximum increase of 14.25% in mixing index and a maximum decrease in Poiseuille number of 60.02%. Finally, the optimal configuration was scaled-up to centimeter level, which makes the mixer have high mixing performance, low flow resistance and high throughput at the same time. All the findings provide useful references for high throughput mixer design and optimization.

Influence mechanisms of flow channel geometry on water transfer and pressure loss in planar membrane humidifiers for PEM fuel cells

The humidification of the cathode inlet air is of great significance to maintain the internal water dynamic balance and improve the performance for fuel cells. In this paper, a numerical simulation of the effect of flow channel geometry on the water transport capacity and pressure loss is carried out in a planar membrane humidifier. The intrinsic influence mechanism is explained by theoretical analysis of the simulation results. Five cross-sectional shapes of flow channels including equilateral triangle, isosceles triangle, square, rectangle and semi-circle are designed, and three geometric factors of centroid height, perimeter and hydraulic diameter are extracted to characterize the different shapes. The results show that there is a strong correlation between the water transport performance and the centroid height of the flow channel cross-section, and the correlation coefficient is 0.999, which is much higher than 0.547 for perimeter and 0.533 for hydraulic diameter. The study also found that the Darcy–Weisbach formula is more accurate than the Hagen–Poiseuille equation in predicting pressure loss because it introduces the Poiseuille number, which depends on the cross-sectional geometry, to modify the Darcy friction factor. Among the five proposed flow channel pressure loss, the Darcy–Weisbach formula has a maximum prediction deviation of 2.5%, while that of Hagen–Poiseuille equation is 11.8%. The research conclusions can provide theoretical guidance for the design of planar membrane humidifiers.

Estimate of the Effect of Rarefaction on the Poiseuille Number in a Long Annular Channel under Partial Accomodation of Gas Molecules

Estimate of the Effect of Rarefaction on the Poiseuille Number in a Long Annular Channel under Partial Accomodation of Gas Molecules

Impact of secondary flow on the single-phase flow in spiral microchannels: An experimental study

Spiral microchannels have a wide range of applications, such as microscale cooling, fluid mixing and particle sorting, in micro-fluidic devices. The flow characteristics of spiral microchannels play an important role in the design and operation of these devices. An experimental study of the laminar flow characteristics in spiral microchannels is conducted for different Reynolds numbers from 51 to 985. Microchannels have rectangular cross sections and follow Archimedean spiral pathways with different spiral and cross-section parameters. The results show that the pressure drop of the spiral microchannel increases with increasing spiral diameter and aspect ratio, but decreases with spiral pitch and hydrodynamic diameter. In addition, the effect of the spiral and cross-section parameters on pressure drop is evident at the high Reynolds number. Under the influence of additional friction caused by the secondary flow, the friction factor of the spiral microchannel is higher than that of the straight channel, and its value increases with the increase in curvature of the microchannel. The correlation of the Poiseuille number in the spiral microchannel is established on the basis of the experimental results, and 95.3% of the experimental data fall within the error band of ±18%.

H1 and H2 Forced Convection in Semi-Elliptic Ducts

Abstract The fully developed forced convection with H1 and/or H2 conditions in a semi-elliptic duct is studied. Such ducts model conduits attached to a flat surface and etched microfluidic channels. Due to differences in materials, the duct wall may be highly conductive (H1) or poorly conductive (H2) or a mixture of both. This paper presents analytic small aspect ratio asymptotic solutions and tables of Poiseuille and Nusselt numbers for various aspect ratios and boundary conditions.

Analytical and numerical investigation of Poiseuille flow through semi-elliptic annulus

A fully developed laminar flow through semi-elliptic annulus formed between two confocal elliptical ducts, driven by a constant pressure-gradient, has been analyzed. The elliptic cylindrical coordinate system has been used to determine the exact solutions for “wide” and “narrow” semi-elliptic annuli with cross sections being symmetric about the minor and major axes of the confocal elliptic boundaries, respectively. For both configurations, exact analytical expressions have been obtained for velocity distribution, volume flow rate, shear stress, and Poiseuille number. The results are expressed in terms of two non-dimensional physical parameters: the ratio of the length of the semi-minor axis to the semi-major axis of the outer boundary, ro, 0 ≤ro<1, and the ratio of the length of semi-major axes of inner and outer elliptic boundaries, rma, c ≤rma<1, with c being the non-dimensional focal distance of the elliptic boundaries. Based on the analytical expressions, the graphical and tabulated results of the flow fields are presented for representative values of ro and rma to illustrate the characteristic features of the flow. Numerical evaluation of the analytical expressions shows that the flow field and the corresponding distributions of velocity and shear stresses are characteristically different for wide and narrow semi-elliptic annuli. In addition to the analytical results, a bivariate Chebyshev pseudospectral method is formulated in the elliptic-cylindrical coordinate system for obtaining the numerical solution of the problem. The numerical results show that the proposed method yields “exponential convergence” or “infinite order of accuracy,” as expected from a spectral method; exact agreement has been observed between the analytical and numerical results.

Artificial neural network model and multi-objective optimization of microchannel heat sinks with diamond-shaped pin fins

In this study, laminar, steady-state, incompressible flow with conjugate heat transfer was investigated for one flow passage of a microchannel with staggered diamond-shaped pin fin array. CFD analyzes were performed with OpenFOAM for various configurations and in all cases, the rhomboidal area of each pin fin was kept constant at 0.16 mm2, and the bottom surface of the substrate was subjected to a uniform heat flux of 69.3 kW/m2. Water with temperature-sensitive viscosity was taken as the cooling fluid, and copper with constant thermophysical properties was used for the solid domain. Parametric analyzes have been conducted for various combinations of geometric design variables such as pin fin angle (α), longitudinal pitch-to-diameter ratio (SL/D) and transverse pitch-to-diameter ratio (ST/D) with the flow attribute represented by pin fin Reynolds number (ReD). In the parametric investigations, α ranged from 30∘ to 90∘; ReD ranged from 20 to 100, and SL/D and ST/D were between 2.5 and 4.5. A multi-layer artificial neural network model (ANN), which was coded in Python and trained with parametric CFD results, was utilized to estimate off-design pin fin Nusselt numbers (NuD) and pin fin Poiseuille numbers (PoD), two objective functions representing thermal and hydrodynamic character, respectively. Non-dominated Sorting Genetic Algorithm (NSGA-II) was used to optimize the microchannel configuration, in which the individuals have been evaluated based on the multi-layer neural network prediction model. The constructed multi-layer neural network model predicted NuD and PoD with average errors of 1.39% and 1.02%, respectively. Among all design variables considered, α was found to be the most dominant one on NuD and PoD. Following the genetic algorithm, the majority of the optimal solutions appeared at ST/D around 2.5 and at ReD equal to 20 or 100. Over the entire range of ReD, NSGA-II suggested combinations of optimal α and SL/D yielding 4<NuD<11 and 6<PoD<32 appropriate for thermal or hydrodynamic demands.

Performance Evaluation Criteria for Triangular Microchannels with Smoothed Corners

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.

Laminar Forced Convective Heat Transfer Performance Analysis of Elliptical and Semicircular Microchannels

In this paper, a single-phase fluid flow, and heat transfer characteristics of elliptical and semicircular microchannels using air as a working fluid are analyzed for a range of Reynolds number (). Experiments are performed on aluminum alloy (AlSi10Mg) microchannels, including inlet and outlet manifolds fabricated using three-dimensional printing technology. A numerical model is developed and validated with the experimental results to study the effect of operating and geometrical parameters on the heat transfer performance of the microchannels. It is found that the temperature difference, Poiseuille number, and average Nusselt number in the elliptical microchannel are higher for all the Reynolds numbers. The axial wall conduction significantly affects the temperature distribution in the fluid and wall of the microchannels. The effect of axial conduction weakens with the increase in the Reynolds number. The numerical average Nusselt number increases with Reynolds number for and is higher than the average Nusselt number predicted from the correlation.

Mini-channel heat exchanger optimization using genetic algorithm and multiple-criteria decision making

This study aims to apply an integrated optimization approach that combines Multi-objective Optimization (MOO) and Multiple-criteria Decision-making (MCDM) to optimize a multiport mini-channel having 2D sawtooth micro fins under laminar, transitional, and turbulent flow conditions. Water was considered as working fluid. The Reynolds number (Re), fin height (Hf), fin width (Wf), the number of micro-fins in each mini-channel (N), and the distance between the successive fins (S1) were selected as design and flow parameters and the Nusselt number (Nu) and the Poiseuille number (Po) were selected as objective functions. A Genetic Algorithm based MOO study was conducted using the correlations available in the literature aiming to find the optimum values of design and flow parameters that maximize Nu and minimize Po. Then, the VIsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method was employed to help designers to select an optimum design among the Pareto optimal solution set which is the output of MOO. Finally, the optimization results obtained were compared with those obtained by the 1st Law of Thermodynamics based Performance Evaluation Criteria (PEC). The advantages and disadvantages of these methods were discussed in detail. It is revealed that the integrated approach is a more comprehensive and flexible approach that also covers the results of PEC.

A Study to Investigate the Viscosity Effect on Micro-Confined Fluids Flow in Tight Formations Considering Fluid–Solid Interaction

Understanding different fluids flow behavior confined in microscales has tremendous significance in the development of tight oil reservoirs. In this article, a novel semiempirical model for different confined fluid flow based on the concept of boundary layer thickness, caused by the fluid–solid interaction, is proposed. Micro-tube experiments are carried out to verify the novel model. After the validation, the viscosity effect on the flow rate and Poiseuille number considering the fluid–solid interaction is investigated. Furthermore, the novel model is incorporated into unstructured networks with anisotropy to study the viscosity effect on pore-scale flow in tight formations under the conditions of different displacement pressure gradients, different aspect ratios (ratio of the pore radius to the connecting throat radius), and different coordination numbers. Results show that the viscosity effect on the flow rate and Poiseuille number after considering the fluid–solid interaction induces a great deviation from that in conventional fluid flow. The absolute permeability is not only a parameter related to pore structures but also depends on fluid viscosity. The study provides an effective model for modeling different confined fluid flow in microscales and lays a good foundation for studying fluid flow in tight formations.

On the competition of anti-lift-up mechanism and Reynolds stress mechanism in Spiral Poiseuille flow

This work is devoted to the studies of optimal perturbation and its transient growth characteristics in Spiral Poiseuille flow (SPF). The Poiseuille number [Formula: see text], representing the dimensionless axial pressure gradient, is varied from 0 to 20,000. The results show that for the axisymmetric case, with the increase of axial shear, the peaks of the amplitudes of azimuthal and radial velocities are both shifted towards the inner cylinder, and a second peak appears near the outer cylinder for both velocity components. Viewing the time evolution of azimuthal shear contribution [Formula: see text] and axial shear contribution [Formula: see text] to the kinetic energy growth of the optimal perturbation, while [Formula: see text] is large enough ([Formula: see text], 20,000), the Reynolds stress mechanism in the meridional plane [Formula: see text] is dominant for the transient growth behavior in SPF relative to anti-lift-up mechanism, which is dominant in the absence of axial flow for co-rotating Taylor–Couette flow with wide gap. For the oblique mode with azimuthal wave number [Formula: see text], which becomes the optimal azimuthal mode over a wide range of azimuthal wave number ([Formula: see text]–10) when [Formula: see text] is large enough, the peaks of the amplitudes of azimuthal and radial velocities are both shifted towards the outer cylinder, opposite to the axisymmetric case.

A novel study on a micromixer with Cantor fractal obstacle through grey relational analysis

This paper proposes a multi-objective optimization method for a micromixer with Cantor fractal baffles through grey relational analysis, and evaluates the comprehensive performance of the micromixer through two aspects. The height of the baffle (h), the distance of the baffle (p), the width of the microchannel (L) and the height of the microchannel (H) are selected as design variables, and the orthogonal experiment table L16(44) is obtained. The optimized performance characteristics take into account the mixing index and Poiseuille number. Numerical simulations are used to obtain the results of each experimental design group. We use the grey relational degree as an index to evaluate the comprehensive performance of the multi-objective of the micromixer, and optimize to find a set of optimal design variables. Finally, we judge the influence of the four design variables on the two performance characteristics respectively, so as to obtain the importance of different design variables. The results show that the optimized micromixer, namely CFM-11, has a maximum increase of 23.75% in mixing index and a maximum decrease in Poiseuille number of 34.40%. Among all the parameters, the h and the L have a greater impact on the performance characteristics. This work can provide a good analysis method for multi-objective research and structural optimization related to micromixers.

Fully-developed laminar flow in trapezoidal ducts with rounded corners: a numerical solution and case study

PurposeThis paper aims to numerically solve fully developed laminar flow in trapezoidal ducts with rounded corners which result following forming processes.Design/methodology/approachA two-dimensional model for a trapezoidal duct with rounded corners is developed and conservation of momentum equation is solved. The flow is assumed to be steady, fully developed, laminar, isothermal and incompressible. The key flow characteristics including the Poiseuille number and the incremental pressure drop have been computed and tabulated for a wide range of: sidewall angle (θ); the ratio of the height of the duct to its smaller base (α); and the ratio of the fillet radius of the duct to its smaller base (β).FindingsThe results show that Poiseuille number decreases, and all the other dimensionless numbers increase with increasing the radii of the fillets of the duct; these effects were found to amplify with decreasing duct heights or increasing sidewall angles. The maximum axial velocity was shown to increase with increasing the radii of the fillets of the duct. For normally used ducts in hydrogen fuel cells, the impact of rounded corners cannot be overlooked for very low channel heights or very high sidewall angles.Practical implicationsThe data generated in this study are highly valuable for engineers interested in estimating pressure drops in rounded trapezoidal ducts; these ducts have been increasingly used in hydrogen fuel cells where flow channels are stamped on thin metallic sheets.Originality/valueFully developed laminar flow in trapezoidal ducts with four rounded corners has been solved for the first time, allowing for more accurate estimation of pressure drop.

Computational and Experimental Analysis of an In Vitro Microfluidic Experimental Setup on Testing Molteno, Ahmed Valve and Ex-Press Implants and Their Critical Comparisons

ABSTRACT Purpose/Aim of the study Researchers have investigated glaucoma drainage devices in various in vitro experimental setups to overcome their disadvantages. In this study, it is aimed to perform in vitro analyses of glaucoma drainage devices that are actively utilized for glaucoma treatment. Materials and Methods A new in vitro experimental setup is constructed and the first outcomes of numerical simulations and experimental trials are shared. Firstly, an in vitro experimental setup is designed and simulated in ANSYS Fluent, then assembled/fabricated using microfluidic equipment. Secondly, computational fluid dynamics results are expressed as pressure losses through an Ahmed Valve implant, a Molteno drainage device, an Ex-Press implant for physiological flow rates. Results In the scope of this study, Ahmed Valve (valved), Molteno (non-valved), Ex-Press (orbital shunt) implants are examined numerically using computational fluid dynamics tools. Results are compared with in vitro studies of the proposed experimental setup. Poiseuille and Reynolds numbers versus pressure drop characteristics of tested glaucoma drainage devices are also obtained using in vitro microfluidic experimental setup. In the range of 1.6–2.5 µl/min, Ahmed Valve implant created an active and effective pressure drop of 5.6 to 12 mmHg. Ahmed Valve and Molteno showed similar characteristics in terms of Poiseuille and Reynolds numbers variations with pressure drop across implants. Ex-Press, opposing Molteno and Ahmed Valve gave a reciprocal correlation between pressure drop and Po. Conclusions High resemblances of pressure drops between computational fluid dynamics results and in vitro microfluidic experimental results proved that the setup will be a better choice compared to syringe pump type setups for testing different glaucoma drainage devices at the same conditions. In conclusion, a new glaucoma drainage device should be equipped with a slimmer but larger end plate and a valve mechanism similar to Ahmed Valve in the perspective of intraocular pressure drop performance.

Impact of aspect ratio and thermophysical properties on heat transfer behavior in spiral microchannel

The heat transfer characteristics in spiral microchannels are studied numerically in this present work. Impact of aspect ratios (α = 0.5–2) and Reynolds number (Re = 15–1200) on Poiseuille number (f.Re) and Nusselt number (Nu) is investigated with the help of local flow patterns. Three-dimensional numerical simulations are performed by varying the Reynolds number at the inlet of spiral microchannel supplied with constant heat flux boundary condition and considering thermo-physical property variation. It is observed that, in the Dean flow regime, the Poiseuille number and Nusselt number vary directly with Reynolds number whereas they vary inversely with aspect ratio. However, some non-monotonous variation of Nusselt number is reported in spiral microchannel having aspect ratio equal to unity. This behavior has been explained with the help of merging and splitting of vortices along the flow direction. Interestingly, all the aspect ratio microchannels exhibit comparatively same thermal performance factor but different temperature homogeneity. These findings have direct implication in the design of micro heat sinks and microreactors employing spiral microchannels.

Reduced models of unidirectional flows in compliant rectangular ducts at finite Reynolds number

Soft hydraulics, which addresses the interaction between an internal flow and a compliant conduit, is a central problem in microfluidics. We analyze Newtonian fluid flow in a rectangular duct with a soft top wall at steady state. The resulting fluid–structure interaction is formulated for both vanishing and finite flow inertia. At the leading-order in the small aspect ratio, the lubrication approximation implies that the pressure only varies in the streamwise direction. Meanwhile, the compliant wall's slenderness makes the fluid–solid interface behave like a Winkler foundation, with the displacement fully determined by the local pressure. Coupling flow and deformation and averaging across the cross section leads to a one-dimensional reduced model. In the case of vanishing flow inertia, an effective deformed channel height is defined rigorously to eliminate the spanwise dependence of the deformation. It is shown that a previously used averaged height concept is an acceptable approximation. From the one-dimensional model, a friction factor and the corresponding Poiseuille number are derived. Unlike the rigid duct case, the Poiseuille number for a compliant duct is not constant but varies in the streamwise direction. Compliance can increase the Poiseuille number by a factor of up to four. The model for finite flow inertia is obtained by assuming a parabolic vertical variation of the streamwise velocity. To satisfy the displacement constraints along the edges of the channel, weak tension is introduced in the streamwise direction to regularize the Winkler-foundation-like model. Matched asymptotic solutions of the regularized model are derived.

Numerical calculations on liquid-metal magnetohydrodynamic flow in rectangular channel with wavelike uneven walls

Numerical calculations have been performed on liquid-metal magnetohydrodynamic (MHD) flows in rectangular channels with wavelike uneven walls in order to propose a flow channel in which the MHD pressure drop decreases. The calculations have been carried out for a Hartmann number of 10,000, a wall conductance ratio of 0.05, and channel aspect ratios of 1/4 and 1/9, in order to simulate typical conditions proposed to fusion reactor blankets. In the range examined in the present calculations, the Poiseuille number, which is the product of pressure gradient and Reynolds number, decreases to about half at maximum of that in a corresponding base case, i.e. a rectangular channel with flat walls.

Effect of the hotter groove on the capillary flow enhancement with nanofluids in a microgrooves wick

This work studied the capillary flow enhancement with Fe3O4-water nanofluids in a microgrooves wick when the groove is hotter than the fluid. Capillary-rise experiment was conducted to derive three parameters, ∆Pcap∙K, capillary pressure and Poiseuille number for evaluating the flow on flow driving force and resistance. Results show that the hotter groove promotes the enhancement by making it easier for the nanofluids to induce friction reduction. When the temperature difference between the groove and liquid pool, ∆T is about 15 °C, the nanofluids lead to a 76% increase in ∆Pcap∙K and 42% decrease in Poiseuille number on average, which is 30 and 15 percentage points larger than that for ∆T of zero respectively. Furthermore, it requires optimizing the concentration and ∆T for raising the enhancement with the nanofluids. However, the capillary pressure is slightly affected by the nanofluids when the groove is hotter. At the optimal concentration, the capillary pressure even becomes almost independent of ∆T. The mechanism is explained with how the hotter groove can change the particle migrations that exist in the groove cross-section and determine the wetting and friction reduction of a nanofluid.