Prediction of stagnation point heat transfer for a single round jet impinging on a concave hemispherical surface

This paper deals with a systematic procedure for assessment of fluid flow and heat transfer parameters for a single round jet impinging on a concave hemispherical surface. Based on Scholkemeier's modifications of the Karman-Pohlhausen integral method, expressions are derived for evaluation of the momentum thickness, boundary layer thickness and the displacement thickness at the stagnation point. This is followed by the estimation of thermal boundary layer thickness and local heat transfer coefficients. A correlation is presented for the Nusselt number at the stagnation point as a function of the Reynolds number for different non-dimensional distances from the exit plane of the jet to the impingement surface.

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Bestimmung des Staupunktes bei der Wärmeübertragung für einen einzelnen Strahl, der auf eine konkave halbkugelige Oberfläche trifft

Zusammenfassung Diese Arbeit beschäftigt sich mit dem systematischen Verfahren der Bewertung von Fluidströmungen und Wärmeübertragungsparametern für einen einzelnen runden Strahl, der auf eine konkave halbkugelförmige Oberfläche trifft. Das Verfahren beruht auf Scholkemeiers Modifikation des Karman-Pohlhausen Integrationsverfahrens. Ausdrücke sind für die Berechnung der Impuls-Dicke, der Grenzschichtdicke und der Verschiebungsdicke am Staupunkt hergeleitet worden. Dies ist aus der Berechnung der thermischen Grenzschichtdicke und des lokalen Wärmeübertragungskoeffizienten abgeleitet worden. Es wird eine Gleichung für die Nusselt-Zahl am Staupunkt als Funktion der Reynolds-Zahl für verschiedene dimensionslose Abstände vom Strahlaustrittspunkt bis zum Auftreffpunkt auf die Oberfläche vorgestellt.

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Nomenclature c _p specific heat at constant pressure - d diameter of single round nozzle - h ₀ heat transfer coefficient at the stagnation point - H distance from the exit plane of the jet to the impingement surface - k thermal conductivity - Nu _0.5 Nusselt number based on impinging jet quantities=h _0.50/k - Nu _{0.5, 0} stagnation point Nusselt number=h _{0 0,50}/k - p pressure - p _a ambient pressure - p ₀ maximum pressure or stagnation pressure - p(x) static pressure at a distancex from the stagnation point - R radius of curvature of the hemisphere - Re _J jet Reynolds number=U _Jd/ - Re _0.5 Reynolds number based on impinging jet quantities=u _{m0 0.50}/ - T temperature - T _a room temperature - T _J jet temperature - T _W wall temperature - u velocity component inx andx directions (Fig. 1) - u _m jet centerline (or maximum) free jet velocity: external (or maximum) boundary layer velocity aty= _m - u _m0 arrival velocity defined as the maximum velocity the free jet would have at the plane of impingement if the plane were not there - U _J jet exit velocity - x* non-dimensional coordinate starting at the stagnation point=x/2 _0.50 - x, y rectangular Cartesian coordinates - y coordinate normal to the wall starting at the wall - ratio of thermal to velocity boundary layer thickness= _T/_m - ₀ ratio of thermal to velocity boundary layer thickness at the stagnation point - * inner layer displacement thickness - _0.50 jet half width at the plane of impingement if the plate were not there - _m inner boundary layer thickness atu=u _m - Pohlhausen's form parameter - dynamic viscosity - kinematic viscosity=/ - fluid density - momentum thickness - ₀ momentum thickness at the stagnation point     

Synthesis and applications of a novel supramolecular polymer network with multiple H‐bonded melamine pendants and uracil crosslinkers

A conjugated main‐chain copolymer ( PBT ) consisting of bithiazole, dithieno[3,2‐b:2′,3′‐d]pyrroles (DTP), and pendent melamine units was synthesized by Stille polymerization, which can be hydrogen‐bonded (H‐bonded) with proper molar amounts of bi‐functional π‐conjugated crosslinker F (i.e., two uracil motifs covalently attached to a fluorene core through triple bonds symmetrically) to develop a novel supramolecular polymer network ( PBT/F ). The effects of multiple H‐bonds on light harvesting capabilities, HOMO levels, and photovoltaic properties of polymer PBT and H‐bonded polymer network PBT/F are investigated. The formation of supramolecular polymer network ( PBT/F ) between PBT and F was confirmed by FTIR and XRD measurements. Because of the stronger light absorption, lower HOMO level, and higher crystallinity of H‐bonded polymer network PBT/F , the solar cell device containing PBT/F showed better photovoltaic properties than that containing polymer PBT . The preliminary results show that the solar cell device containing 1:1 weight ratio of PBT/F and [6,6]‐phenyl C₇₁ butyric acid methyl ester (PC₇₁BM) offers the best power conversion efficiency (PCE) value of 0.86% with a short‐circuit current density (J_sc) of 4.97 mA/cm², an open circuit voltage (V_oc) of 0.55 V, and a fill factor (FF) of 31.5%. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Electrical and Dielectric Characteristics of BiSmO3

Physics of the Solid State - The synthesis of the perovskites BiSmO3 was done by the solid-state reaction method. In this communication, the structural and detailed electrical (dielectric,...     

Imidazole derivatives as the organic precursor of ZnO nano particle

N₁-Hydroxy-2,4,5-trisubstituted imidazoles were synthesized starting from 1,2-diketones. The crystal structure of 4,5-dimethyl-2-(3-nitrophenyl)-1H-imidazol-1-ol has been determined. An unusual intermolecular hydrogen bonding through the association of water molecule has been reported. These imidazole derivatives can be thought of as the organic precursor for the synthesis of zinc oxide nano particles.     

Synthesis and applications of cyano‐vinylene‐based polymers containing cyclopentadithiophene and dithienosilole units for photovoltaic cells

Two β‐cyano‐thiophenevinylene‐based polymers containing cyclopentadithiophene ( CPDT‐CN ) and dithienosilole ( DTS‐CN ) units were synthesized via Stille coupling reaction with Pd(PPh₃)₄ as a catalyst. The effects of the bridged atoms (C and Si) and cyano‐vinylene groups on their thermal, optical, electrochemical, charge transporting, and photovoltaic properties were investigated. Both polymers possessed the highest occupied molecular orbital (HOMO) levels of about ?5.30 eV and the lowest unoccupied molecular orbital (LUMO) levels of about ?3.60 eV, and covered broad absorption ranges with narrow optical band gaps (ca. 1.6 eV). The bulk heterojunction polymer solar cell (PSC) devices containing an active layer of electron‐donor polymers ( CPDT‐CN and DTS‐CN ) blended with an electron‐acceptor, that is, [6,6]‐phenyl‐C₆₁‐butyric acid methyl ester (PC₆₁BM) or [6,6]‐phenyl‐C₇₁‐butyric acid methyl ester (PC₇₁BM), in different weight ratios were explored under 100 mW/cm² of AM 1.5 white‐light illumination. The PSC device based on DTS‐CN: PC₇₁BM (1:2 w/w) exhibited a best power conversion efficiency (PCE) value of 2.25% with V_oc = 0.74 V, J_sc = 8.39 mA/cm², and FF = 0.36. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011.     

Synthesis and applications of low‐bandgap conjugated polymers containing phenothiazine donor and various benzodiazole acceptors for polymer solar cells

A series of soluble donor‐acceptor conjugated polymers comprising of phenothiazine donor and various benzodiazole acceptors (i.e., benzothiadiazole, benzoselenodiazole, and benzoxadiazole) sandwiched between hexyl‐thiophene linkers were designed, synthesized, and used for the fabrication of polymer solar cells (PSC). The effects of the benzodiazole acceptors on the thermal, optical, electrochemical, and photovoltaic properties of these low‐bandgap (LBG) polymers were investigated. These LBG polymers possessed large molecular weight (M_n) in the range of 3.85?5.13 × 10⁴ with high thermal decomposition temperatures, which demonstrated broad absorption in the region of 300?750 nm with optical bandgaps of 1.80?1.93 eV. Both the HOMO energy level (?5.38 to ?5.47 eV) and LUMO energy level (?3.47 to ?3.60 eV) of the LBG polymers were within the desirable range of ideal energy level. Under 100 mW/cm² of AM 1.5 white‐light illumination, bulk heterojunction PSC devices containing an active layer of electron donor polymers mixed with electron acceptor [6,6]‐phenyl‐C₆₁‐butyric acid methyl ester (PC₆₁BM) or [6,6]‐phenyl‐C₇₁‐butyric acid methyl ester (PC₇₁BM) in different weight ratios were investigated. The best performance of the PSC device was obtained by using polymer PP6DHTBT as an electron donor and PC₇₁BM as an acceptor in the weight ratio of 1:4, and a power conversion efficiency value of 1.20%, an open‐circuit voltage (V_oc) value of 0.75 V, a short‐circuit current (J_sc) value of 4.60 mA/cm², and a fill factor (FF) value of 35.0% were achieved. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Inflation with an antisymmetric tensor field

We investigate the possibility of inflation with models of antisymmetric tensor field having minimal and nonminimal couplings to gravity. Although the minimal model does not support inflation, the nonminimal models, through the introduction of a nonminimal coupling to gravity, can give rise to stable de-Sitter solutions with a bound on the coupling parameters. The values of field and coupling parameters are sub-planckian. Slow roll analysis is performed and slow-roll parameters are defined which can give the required number of e-folds for sufficient inflation. Stability analysis has been performed for perturbations to antisymmetric field while keeping the metric unperturbed, and it is found that only the sub-horizon modes are free of ghost instability for de-Sitter space.     

Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

In this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE)

Synthesis and Characterization of Reversible Chemosensory Polymers: Modulation of Sensitivity through the Attachment of Novel Imidazole Pendants

Three novel electron donor–acceptor conjugated polymers ( P1 – P3 ) bearing various imidazole pendants have been synthesized. Their excellent photophysical and electrochemical properties make them suitable transduction materials for chemosensing applications. Indeed, polymers P1 – P3 have been found to show remarkable sensing capabilities towards H⁺ and Fe²⁺ in semi‐aqueous solutions. Upon titration with H⁺, polymers P1 and P2 showed hypsochromic shifts of their absorptions and photoluminescence (PL) maxima with enhanced fluorescence intensities. However, P3 showed diminished absorption and fluorescence intensities under similar conditions due to static quenching. The anomalous behavior of P3 compared with P1 and P2 has been clarified in terms of electronic distributions through computational analysis. Furthermore, P3 (K_SV=1.03×10⁷) showed a superior sensing ability towards Fe²⁺ compared with P1 (K_SV=2.01×10⁶) and P2 (K_SV=4.12×10⁶) due to its improved molecular wire effect. Correspondingly, the fluorescence lifetime of P3 was greatly decreased (almost 11‐fold) compared to those of polymers P1 (4.6‐fold) and P2 (6.2‐fold) in the presence of Fe²⁺. By means of a fluorescence on‐off‐on approach, chemosensing reversibilities in protonation–deprotonation and metallation–demetallation have been achieved by employing triethylamine (TEA) and the disodium salt of ethylenediaminetetraacetic acid (Na₂‐EDTA)/phenanthroline, respectively, as suitable counter ligands. ¹H NMR titrations have revealed the unique behavior of P3 compared with P1 and P2 . To the best of our knowledge, there have been no previous reports of Fe²⁺ sensors based on single imidazole receptors conjugated to a main‐chain polymer showing such a diverse sensitivity pattern depending on their attached substituents.