Velocity distributions in a plate heat exchanger channel

The development of a Laser Doppler Anemometer technique to measure the velocity distribution in a commercial plate heat exchanger is described. Detailed velocity profiles are presented and a preliminary investigation is reported on flow behaviour through a single cell in the channel matrix. The objective of the study was to extend previous investigations of plate heat exchanger flow patterns in the laminar range with the eventual aim of establishing the effect of flow patterns on heat transfer performance, thus leading to improved plate heat exchanger design and design methods. Accurate point velocities were obtained by Laser Anemometry in a perspex replica of the metal channel. Oil was used as a circulating liquid with a refractive index matched to that of the perspex so that the laser beams were not distorted. Cell-by-cell velocity measurements over a range of Reynolds number up to ten showed significant liquid mal-distribution. Local cell velocities were found to be as high as twenty seven times average velocity, contrary to the previously held belief of four times. The degree of mal-distribution varied across the channel as well as in the vertical direction, and depended on the upward or downward direction of flow. At Reynolds numbers less than one, flow zig-zagged from one side of the channel to the other in wave form, but increases in Reynolds number improved liquid distribution. A detailed examination of selected cells showed velocity variations in different directions, together with variation within individual cells. Experimental results are also reported on the flow split when passing through a single cell in a section of a channel . These observations were used to explain mal-distribution in the perspex channel itself.

A cautionary note on methods of comparing programmatic efficiency between two or more groups of DMUs in data envelopment analysis

In some applications of data envelopment analysis (DEA) there may be doubt as to whether all the DMUs form a single group with a common efficiency distribution. The Mann-Whitney rank statistic has been used to evaluate if two groups of DMUs come from a common efficiency distribution under the assumption of them sharing a common frontier and to test if the two groups have a common frontier. These procedures have subsequently been extended using the Kruskal-Wallis rank statistic to consider more than two groups. This technical note identifies problems with the second of these applications of both the Mann-Whitney and Kruskal-Wallis rank statistics. It also considers possible alternative methods of testing if groups have a common frontier, and the difficulties of disaggregating managerial and programmatic efficiency within a non-parametric framework. © 2007 Springer Science+Business Media, LLC.

Programmatic efficiency comparisons between unequally sized groups of DMUs in DEA

Data envelopment analysis (DEA) is a popular non-parametric technique for determining the efficiency of a homogeneous set of decision-making units (DMUs). In many practical cases, there is some doubt if the all the DMUs form a single group with a common efficiency distribution. The Mann-Whitney rank statistic has been used in DEA both to test if two groups of DMUs come from a common efficiency distribution and also to test if the two groups have a common frontier, each of which are likely to have important but different policy implications for the management of the groups. In this paper it is demonstrated that where the Mann-Whitney rank statistic is used for the second of these it is likely to overestimate programmatic inefficiency, particularly of the smaller group. A new non-parametric statistic is proposed for the case of comparing the efficient frontiers of two groups, which overcomes the problems we identify in the use of the Mann-Whitney rank statistic for this purpose. © 2005 Operational Research Society Ltd. All rights reserved.

Application of nanoimprinting technique for fabrication of trifocal diffractive lens with sine-like radial profile

The fabrication of submicron-height sine-like relief of a trifocal diffractive zone plate using a nanoimprinting technique is studied. The zone plate is intended for use in combined trifocal diffractive-refractive lenses and provides the possibility to form trifocal intraocular lenses with predetermined light intensity distribution between foci. The optical properties of the designed zone plate having the optical powers 3 D, 0, -3D in the three main diffraction orders are theoretically and experimentally investigated. The results of the theoretical investigations are in good agreement with experimental measurements. The effects of the pupil size (lens diameter) as well as the wavelength-dependent behavior of the zone plate are also discussed.

Transition in plane parallel shear flows heated internally

The stability of internally heated inclined plane parallel shear flows is examined numerically for the case of finite value of the Prandtl number, Pr. The transition in a vertical channel has already been studied for 0≤Pr≤100 with or without the application of an external pressure gradient, where the secondary flow takes the form of travelling waves (TWs) that are spanwise-independent (see works of Nagata and Generalis). In this work, in contrast to work already reported (J. Heat Trans. T. ASME 124 (2002) 635-642), we examine transition where the secondary flow takes the form of longitudinal rolls (LRs), which are independent of the steamwise direction, for Pr=7 and for a specific value of the angle of inclination of the fluid layer without the application of an external pressure gradient. We find possible bifurcation points of the secondary flow by performing a linear stability analysis that determines the neutral curve, where the basic flow, which can have two inflection points, loses stability. The linear stability of the secondary flow against three-dimensional perturbations is also examined numerically for the same value of the angle of inclination by employing Floquet theory. We identify possible bifurcation points for the tertiary flow and show that the bifurcation can be either monotone or oscillatory. © 2003 Académie des sciences. Published by Elsevier SAS. All rights reserved.