Poiseuille and Nusselt numbers for laminar flow in microchannels with rounded corners

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.This work investigates the frictional and heat transfer behaviour of laminar, fully-developed flow in microchannels with trapezoidal and rectangular cross-section and rounded corners under H1 boundary conditions. The equations of momentum and energy are solved numerically, and the results validated with analytical data, when available. The runs have been carried out for different aspect ratios and nondimensional radii of curvature Rc, with either all sides or three sides heated, one short side adiabatic for rectangular geometries and three sides heated, the longest one adiabatic for trapezoidal geometries. The Poiseuille and Nusselt numbers are reported and show, for the rectangular cross-section heated on all sides, a maximum increase for the highest value of the aspect ratio (β=1) with increments in the Poiseuille and Nusselt numbers of about 11% and 16% respectively for values of Rc * of 0.5, increasing as the geometry approaches the circular duct (12.5% and 21%). The increase is less pronounced as β decreases and also when only three sides are heated (maximum increase of Nu around 10%); in the case of the trapezoidal geometry the effects of rounding the corners are almost negligible (a maximum increase in Nu of around 2%)

Geometrically induced phase transitions in two-dimensional dumbbell-shaped domains

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Association between diverticulosis and colonic neoplastic lesions in individuals with a positive faecal immunochemical test

Background The association between diverticulosis and colonic neoplastic lesions has been suggested, but data in literature are conflicting. This study aimed to investigate such a relationship in patients participating in a colorectal cancer screening program who underwent high-quality colonoscopy.Methods Data from consecutive individuals 50-75 years of age with a positive faecal immunological test were considered. Diverticulosis was categorised as present or absent. The prevalence of neoplastic lesions (adenoma, advanced adenoma, and cancer) between individuals with and those without diverticula was compared. A multivariate analysis was performed.Results Overall, data from 970 consecutive individuals were evaluated, and diverticulosis was detected in 354 (36.5%) cases. At least one adenoma was detected in 490 (50.5%) people, at least one advanced adenoma in 264 (27.2%), multiple adenoma in 71 (7.3%), whilst a cancer was diagnosed in 48 (4.9%) cases. At univariate analysis, the adenoma detection rate in patients with diverticula was significantly higher than in controls (55.9% vs 47.4%; p=0.011). At multivariate analysis, presence of diverticulosis was an independent risk factor for both adenoma detection rate (OR=1.58; 95% CI=1.14-2.18; p=0.006) and advanced adenoma (OR=1.57; 95% CI=1.10-2.24; p=0.013), but not for colorectal cancer.Conclusions In a colorectal screening setting, the adenoma detection rate was significantly higher in individuals with diverticulosis than in controls

Numerical characterization of silicon DC electro-osmotic pumps: the role of the micro channel geometry

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.A numerical analysis of silicon DC open channel EOPs is presented to show which parameters should be taken into account in the design of these devices. Particular attention is paid to the influence of the channel cross-section geometry on pump behavior, especially in relation to the electrical properties of the fluid. Rectangular and trapezoidal, micro and nano channels chemically etched on silicon wafers are considered and a broad range of operative conditions are analyzed. In order to make all the results available, two user-friendly correlations that predict the characteristic curves of the pumps are given as functions of the relevant parameters. The EOP model used to obtain the results is explained extensively, as well as the method used to solve it. A brief discussion on the domain in which it applies is also presented

The effect on the Nusselt number of the non-linear axial temperature distribution of gas flows through commercial microtubes

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.The characteristics of nitrogen convective heat transfer through commercial stainless steel microtubes with inner diameter of 172 μm and 750 μm are investigated both experimentally and numerically. In this work is highlighted that the axial local gas bulk temperature distribution can present a strong nonlinearity along the flow direction especially for microtubes having a small inner diameter and a thick solid wall. It is also demonstrated that the trend of the experimental Nusselt numbers as a function of the Reynolds number can be considered in good agreement with the conventional correlations if the average bulk temperature is calculated by taking into account the axial non-linearity of the gas bulk temperature. This fact explains the low values of the Nusselt numbers obtained in the previous experimental works appeared in literature where the convective heat transfer for gas flows through microtubes has been investigated assuming the gas bulk temperature distribution between the inlet and the outlet of the microtube as linear without verifying this hypothesis.European Community's Seventh Framework Programme (ITN - FP7/2007-2013) under grant agreement no 215504

Optimal design of multi-channel microreactor for uniform residence time distribution

Multi-channel microreactors can be used for various applications that require chemical or electrochemical reactions in either liquid, gaseous or multi phase. For an optimal control of the chemical reactions, one key parameter for the design of such microreactors is the residence time distribution of the fluid, which should be as uniform as possible in the series of microchannels that make up the core of the reactor. Based on simplifying assumptions, an analytical model is proposed for optimizing the design of the collecting and distributing channels which supply the series of rectangular microchannels of the reactor, in the case of liquid flows. The accuracy of this analytical approach is discussed after comparison with CFD simulations and hybrid analytical-CFD calculations that allow an improved refinement of the meshing in the most complex zones of the flow. The analytical model is then extended to the case of microchannels with other cross-sections (trapezoidal or circular segment) and to gaseous flows, in the continuum and slip flow regimes. In the latter case, the model is based on second-order slip flow boundary conditions, and takes into account the compressibility as well as the rarefaction of the gas flow

A Non-Local Mean Curvature Flow and its semi-implicit time-discrete approximation

We address in this paper the study of a geometric evolution, corresponding to a curvature which is non-local and singular at the origin. The curvature represents the first variation of the energy recently proposed as a variant of the standard perimeter penalization for the denoising of nonsmooth curves. To deal with such degeneracies, we first give an abstract existence and uniqueness result for viscosity solutions of non-local degenerate Hamiltonians, satisfying suitable continuity assumption with respect to Kuratowsky convergence of the level sets. This abstract setting applies to an approximated flow. Then, by the method of minimizing movements, we also build an "exact" curvature flow, and we illustrate some examples, comparing the results with the standard mean curvature flow

A second order minimality condition for the Mumford-Shah functional

A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\Gamma)$, $\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.Comment: 30 page