Two Functions Used in the Analysis of Crossflow Exchangers, Regenerators and Related Equipment

a response exhibits a step when t = P and thus t' = t a . The first cross-sectional fluid a lamina that enters at time zero with a temperature of unity sees fluid b at zero temperature. (The wall is "transparent" when its thermal capacitance is zero.) This lamina therefore has a temperature of exp(-AOc). When it reaches its exit plane {x -1) at time /" its temperature is exp (-N), which is the magnitude of the jumps seen in The solution with zero core capacitance is much easier and faster to compute than the Spiga and Spiga solution. It is therefore of interest to estimate the upper range of V a or V b that is reasonable for an exchanger. Suppose that fluid a flows inside tubes. Then for thin wall tubes V a -£>y/(4A) in which D and A are the tube diameter and wall thickness and v is the ratio of the volummetric heat capacities of the fluid and tube materials. This ratio has the exceptionally large value of 1.7 for water and aluminum. Using this material combination gives V a -0.4D/A. Thus an aluminum tube with 25 mm diameter and 1 mm wall thickness gives V a = 10. The parameters V a and V b can, of course, vary over a wide range, but this illustration indicates that the simplicity of the zero core capacitance solution can sometimes be enjoyed with acceptable accuracy. References Anzelius, A., 1926 Introduction This note focuses on the transport in aiding laminar mixed convection flow adjacent to a vertical isothermal surface. The direction of forced flow is taken to be upward for the heated surface. This situation causes the flow to be predominantly forced at the leading edge, primarily natural far downstream, and mixed in the middle. In the intermediate region of mixed convection Merkin (1969) reported a finite difference solution for Pr = 1

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The Laser Interferometer Gravitational-Wave Observatory has performed a third science run with much improved sensitivities of all three interferometers. We present an analysis of approximately 200 hours of data acquired during this run, used to search for a stochastic background of gravitational radiation. We place upper bounds on the energy density stored as gravitational radiation for three different spectral power laws. For the flat spectrum, our limit of Ω_0<8.4×10^(-4) in the 69–156 Hz band is ~10^5 times lower than the previous result in this frequency range

Astrophysically Triggered Searches for Gravitational Waves: Status and Prospects

In gravitational-wave detection, special emphasis is put onto searches that focus on cosmic events detected by other types of astrophysical observatories. The astrophysical triggers, e.g. from gamma-ray and X-ray satellites, optical telescopes and neutrino observatories, provide a trigger time for analyzing gravitational wave data coincident with the event. In certain cases the expected frequency range, source energetics, directional and progenitor information is also available. Beyond allowing the recognition of gravitational waveforms with amplitudes closer to the noise floor of the detector, these triggered searches should also lead to rich science results even before the onset of Advanced LIGO. In this paper we provide a broad review of LIGO's astrophysically triggered searches and the sources they target

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We place direct upper limits on the amplitude of gravitational waves from 28 isolated radio pulsars by a coherent multidetector analysis of the data collected during the second science run of the LIGO interferometric detectors. These are the first direct upper limits for 26 of the 28 pulsars. We use coordinated radio observations for the first time to build radio-guided phase templates for the expected gravitational-wave signals. The unprecedented sensitivity of the detectors allows us to set strain upper limits as low as a few times 10^(-24). These strain limits translate into limits on the equatorial ellipticities of the pulsars, which are smaller than 10^(-5) for the four closest pulsars

Gravitational Waves From Known Pulsars: Results From The Initial Detector Era

We present the results of searches for gravitational waves from a large selection of pulsars using data from the most recent science runs (S6, VSR2 and VSR4) of the initial generation of interferometric gravitational wave detectors LIGO (Laser Interferometric Gravitational-wave Observatory) and Virgo. We do not see evidence for gravitational wave emission from any of the targeted sources but produce upper limits on the emission amplitude. We highlight the results from seven young pulsars with large spin-down luminosities. We reach within a factor of five of the canonical spin-down limit for all seven of these, whilst for the Crab and Vela pulsars we further surpass their spin-down limits. We present new or updated limits for 172 other pulsars (including both young and millisecond pulsars). Now that the detectors are undergoing major upgrades, and, for completeness, we bring together all of the most up-to-date results from all pulsars searched for during the operations of the first-generation LIGO, Virgo and GEO600 detectors. This gives a total of 195 pulsars including the most recent results described in this paper.United States National Science FoundationScience and Technology Facilities Council of the United KingdomMax-Planck-SocietyState of Niedersachsen/GermanyAustralian Research CouncilInternational Science Linkages program of the Commonwealth of AustraliaCouncil of Scientific and Industrial Research of IndiaIstituto Nazionale di Fisica Nucleare of ItalySpanish Ministerio de Economia y CompetitividadConselleria d'Economia Hisenda i Innovacio of the Govern de les Illes BalearsNetherlands Organisation for Scientific ResearchPolish Ministry of Science and Higher EducationFOCUS Programme of Foundation for Polish ScienceRoyal SocietyScottish Funding CouncilScottish Universities Physics AllianceNational Aeronautics and Space AdministrationOTKA of HungaryLyon Institute of Origins (LIO)National Research Foundation of KoreaIndustry CanadaProvince of Ontario through the Ministry of Economic Development and InnovationNational Science and Engineering Research Council CanadaCarnegie TrustLeverhulme TrustDavid and Lucile Packard FoundationResearch CorporationAlfred P. Sloan FoundationAstronom