The effect of a nonlinear temperature dependent Prandtl-number on heat transfer of fully developed flow of liquids in a straight tube

If Nu_o is the Nusselt Number for a temperature-independent Prandtl number Pr, and Nu the Nusselt number for a temperature dependent Prandtl number, it is usual to define the correction factor Nu/Nu_o=C. A correction factor which has been defined in this form has, up to now, only been expressed as a function of two characteristic Pr numbers. Thus it was simply assumed that the Pr number was a linear function of the temperature. Fluids with very large Pr numbers show a (T;Pr) relationship which deviates considerably from a linear one. This leads to a very large difference (up to 70%) between the calculated and the measured values of the Nusselt number. In the following study we shall determine a so-called curvature parameter of the (T;Pr) curve and obtain a semi-empirical formula for C. This formula has a deviation from the actual relationship many times smaller than that of the formulae for a linear (T;Pr) relationship.

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Zusammenfassung Ist Nu_o die Nusseltzahl bei temperaturunabhangiger und Nu die Nusseltzahl bei temperaturabhangiger Prandtlzahl Pr, so ist es üblich, mit Nu/Nu_o=C den Korrekturfaktor zu bezeichnen. Ein in dieser Form definierter Faktor C ist bisher als Funktion nur zweier charakteristischer Pr-Zahlen ausgedrückt worden. Es wurde somit nur eine lineare Abhängigkeit von der Pr-Zahl von der Temperatur T vorausgesetzt. Flüssigkeiten mit großen Pr-Zahlen weisen eine (T;Pr)-Charakteristik auf, die sehr stark von der linearen abweicht. Sehr große Abweichungen (bis — 70%) der gerechneten von den gemessenen Nu-Zahlen sind eine Folge davon. In vorliegender Arbeit bilden wir mit einer dritten charakteristischen Pr-Zahl einen sogenannten Krümmungsparameter der Kurve (T;Pr) und leiten eine semiempirische Formel für C ab, die um ein großes Vielfaches kleinere Fehler aufweist, als die Formeln für den linearen (T;Pr)-Verlauf.

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Nomenclature

Material constants c_p specific heat at constant pressure [J/kgK] - k heat conductivity [W/mK] - density [kg/m³] - a temperature diffusivity, a=k/c_p [m²/s] - dynamic viscosity [Ns/m²] - kinematic viscosity [m²/s] Fluid dynamics D inner diameter of the tube [m] - L length of tube [m] - w mean speed of fluid [m/s] Heat transfer h coefficient of heat transfer [W/m²K] - T absolute temperature [K] - T_b bulk temperature (corresponding to the adiabatic mixing temperature) [K] - T_w tube wall temperature [K] - T_f=(T_b+T_w)/2 film temperature [K] - T=T_b-T_w temperature forcing difference of heat transfer [K] Characteristic quantities without dimensions Re=wD/ Reynolds number - Pr=/a Prandtl number - Nu=hD/k Nusselt number - related temperature - related Prandtl number - curvature parameter of the Prandtl number Various - C=Nu_b/Nu_o correction factor according to Eq.(5) - p exponent in Eq.(6), (a), (8) and (16) Indices o corresponding to the quasi-isothermal heat transfer - b,w,f with reference to quantities, including physical properties which correspond to the temperatures T_b, T_wor T_f - Pr,k,, for quantities calculated corresponding to the Prandtl number, the thermal conductivity coefficient, the density or the dynamic viscosity - H,C for heating or cooling exp for quantities calculated from experimental data     

Retrieval of transverse relaxation time distribution from spin-echo data by recurrent neural network

Inversion of transverse relaxation time decay curve from spin-echo experiments was carried out using Hopfield neural network, to obtain the transverse relaxation time distribution. The performance of this approach was tested against simulated and experimental data. The initial guess, necessary for the integration procedure, was established as the analytical Laplace inversion. Together with errors in the simulated data, inversion was also carried out with errors in this initial guess. The probability density function, calculated by the neural network, is used in multiple sclerosis diagnostics.     

Enantioselectivity in Ni(II) Schiff-base complexes derived from amino-acids and (S)-o-N-(N-benzylprolyl)aminobenzophenone: molecular structure of several chiral Ni(II) Schiff-base complexes, circular dichroism and molecular mechanics studies

Several Ni(II) complexes derived from (S)-o-N-(N-benzylprolyl)aminobenzophenone ((S)-BBP) and amino acids of general formula [Ni((S)-BBP-L-(or D-)-aa)] were prepared. The crystal and molecular structures of [Ni((S)-BBP-Gly)], [Ni((S)-BBP-L-Ser)] and [Ni((S)-BBP-L-aaIm)](aaIm =L-2-amino-3-(imidazol-1-yl)propanoate were determined by X-ray diffraction analysis. In the three complexes the nickel atoms display a square-planar coordination and the overall structure around the metal indicates that the entire Schiff-base ligands form quite rigid frameworks. Molecular mechanics calculations were carried out for complexes [Ni((S)-BBP-Gly)], [Ni((S)-BBP-Ser)] and [Ni((S)-BBP-aaIm)] containing either the L- or D-amino acid forms, and the factors controlling the stereoselectivity are discussed. Several other [Ni((S)-BBP-L-aa)] complexes are also prepared and their circular dichroism spectra in solution and of the solids dispersed in KBr disks are measured and discussed. In agreement with other studies in solution with similar [Ni((S)-BBP-aa)] complexes, the Cotton effects for the bands with lambda(max) at 520--530 nm are positive when the amino acids have the L-configuration at the alpha-carbon. The same is observed in this work for the solid-state CD spectra of all compounds.     

Thermal, pressure and light switchable spin-crossover materials

This article reviews the most relevant chemical and structural aspects that influence the spin-crossover phenomenon (SCO). Special attention is focussed on the recent development of SCO coordination polymers. The different approaches currently being explored in order to achieve multifunctionality in SCO materials are discussed.     

Graphical analysis of electrochemical impedance spectroscopy of two consecutive irreversible electron transfers. 2. Zinc anodic dissolution in acid media

The graphical analysis of the impedance plots is used in the study of the electrodic systems that take place through two consecutive single electron transfers. The zinc anodic dissolution is studied by using this procedure. The characteristic points easily allow us to explain and to simulate the impedance behavior of this electrodic system according to the steady-state potential and the roughness of the working electrode. The direct procedure for parametrical identification from the graphical analysis allows us to reduce the time needed for an impedance experiment. This graphical analysis is suggested for studying thin coated galvanized steels.     

New chromogenic probes into nanoscopic pockets in enhanced sensing protocols for amines in aqueous environments

[structure: see text] A new sensory MCM-41-based material for the colorimetric sensing and discrimination of amines has been developed.     

Investigation of the negative thermal expansion mechanism of zeolite chabazite using the pair distribution function method

We have used the pair distribution function (PDF) method to gain insight into the mechanism of contraction of zeolite chabazite. Using this method we followed how the interatomic distances of the local structure changed with temperature. By optimization of the structure by free energy minimization and using the Reverse Monte Carlo technique we were able to find structural models at low and at high temperatures that agreed quantitatively with our experimental PDFs. From these models we conclude that the mechanism of contraction with temperature cannot involve rocking of the tetrahedra as rigid unit modes as there are distortions of the tetrahedra with temperature (indicating internal vibrations) and also that the mechanism of contraction probably involves a mode that translates along the Si-O3-Si-O4-Si linkages inside of the D6R of zeolite chabazite.     

Low-molecular-weight poly(alpha-methyl beta,L-malate) of microbial origin: synthesis and crystallization

Low-molecular-weight poly(alpha-methyl beta,L-malate) made of approximately 25-30 units was prepared from microbial poly(beta,L-malic acid) by treatment with diazomethane. The thermal characterization of the polymalate methyl ester was carried out and its crystalline structure was preliminary examined. Its ability to crystallize both from solution and from the melt was comparatively evaluated.