Fully developed laminar mixed convection in uniformly heated pipes

Approximate solutions are carried out for fully developed laminar mixed convection in uniformly heated horizontal pipes. The problem considered is steady state and validity of the Boussinesq approximation is assumed. The analysis reveals that the relevant parameters are the Prandtl number and the product of the Rayleigh number based on temperature gradient along the pipe wall and of the Reynolds number based on pressure gradient along the pipe axis. Solutions for the velocity and temperature fields are obtained by a spectral Galerkin method, which proves capable of giving rapid convergence and, by implication, good accuracy, as demonstrated by the comparison with other numerical predictions. The results are presented in terms of fluid flow patterns, isotherms, and graphs of mass flow rate, local and average Nusselt number for various values of the parameters.

---

Ausgebildete Laminarmischkonvektion in gleichförmig beheizten Rohren

Zusammenfassung Es werden Näherungslösungen für ausgebildete Laminarmischkonvektion in gleichförmig beheizten Rohren angeboten. Die Boussinesq-Approximation geht bei der Ermittlung des Stationärzustandes als Voraussetzung ein. Die Untersuchung zeigt, daß als relevante Parameter die Prandtl-Zahl und das Produkt aus Rayleigh-Zahl (basierend auf dem Temperaturgradienten entlang der Rohrwand) und Reynolds-Zahl (basie-rend auf dem Druckgradienten entlang der Rohrachse) auftreten. Lösungen für die Geschwindigkeits- und Temperaturfelder werden mit Hilfe einer spektralen Galerkinmethode erhalten, die rasche Konvergenz zeigt und auf gute Genauigkeit schließen läßt, wie durch Vergleich mit anderen numerischen Vorhersagen gezeigt werden kann. Die Ergebnisse werden in Form von Strömungsbildern, von Isothermen und von Diagrammdarstellungen des Massenstroms, der lokalen und der gemittelten Nußelt-Zahl als Funktion verschiedener Parameter angeboten.

---

Nomenclature a pipe radius - A, B dummy functions - c specific heat - c _ij normalizing factors - d _ij normalizing factors - f dimensionless stream function - f _ij expansion coefficients forf ^N,M - f ^N,M approximate solution forf - F _ij trial functions forf ^N,M - g acceleration due to gravity - G _ij trial functions forW ^N,M and ^N,M - h local heat transfer coefficient - average heat transfer coefficient - J Jacobian operator - I _i Bessel function of orderi - J _i modified Bessel function of orderi - k thermal conductivity - m mass flow rate - N number of radial modes - M number of circumferential modes - Nu local Nusselt number - average Nusselt number - p pressure - p pressure distribution in the cross section defined by Eq. (2) - P dimensionless pressure - Pr Prandtl number - q heat flux - Q heat flow per unit length - r radial coordinate - R dimensionless radial coordinate - Ra Rayleigh number - Re Reynolds number - T temperature - T temperature distribution in the cross section defined by Eq. (1) - u, v, w radial, tangential and axial velocity - U, V, W dimensionless radial, tangential and axial velocity - w _i,j expansion coefficient forW ^N,M - x dummy variable - z axial coordinate Greek symbols coefficient of thermal expansion - axial pressure gradient - convergence parameter - gradient operator - Laplace operator - ² biharmonic operator - dimensionless temperature - _i,j expansion coefficient for ^N,M - _ij eigenvalues - viscosity - _ij eigenvalues - density - axial temperature gradient - tangential coordinate     

Polyelectrolytes Multilayers to Modulate Cell Adhesion: A Study of the Influence of Film Composition and Polyelectrolyte Interdigitation on the Adhesion of the A549 Cell Line

Polyelectrolyte multilayers (PEMs) with different polycation/polyanion pairs are fabricated by the layer‐by‐layer technique employing synthetic, natural, and both types of polyelectrolytes. The impact of the chemical composition of PEMs on cell adhesion is assessed by studying cell shape, spreading area, focal contacts, and cell proliferation for the A549 cell line. Cells exhibit good adhesion on PEMs containing natural polycations and poly(sodium 4‐styrenesulfonate) (PSS) as polyanion, but limited adhesion is observed on PEMs fabricated from both natural polyelectrolytes. PEMs are then assembled, depositing a block of natural polyelectrolytes on top of a stiffer block with PSS as polyanion. Cell adhesion is enhanced on top of the diblock PEMs compared to purely natural PEMs. This fact could be explained by the interdigitation between polyelectrolytes from the two blocks. Diblock PEM assembly provides a simple means to tune cell adhesion on biocompatible PEMs.

     

Spontaneous separation of charged grains

In 1867, Lord Kelvin described an experiment in which two streams of water droplets were connected so that each stream amplified the charge on the second stream [W. Thomson, Proc. R. Soc. London 16, 67 (1867)]. We present here a complementary effect in flowing grains that spontaneously separates similar and well-mixed grains into two charged streams of demixed grains. This effect has important consequences for industrial and natural processes.