Heat transfer to small cylinders and flat strips immersed in a fluidized bed

Fluidized bed heat treating systems have been used to heat treat low carbon steel wires for a number of years. Extending this application to high carbon steel wires and metal straps has been implemented with very little success due to the lack of knowledge of heat transfer coefficients or, alternatively, Nusselt number for small cylinders and flat strips. The objective of this study was to provide reliable data for predicting a suitable Nusselt number for small horizontal cylinders and flat strips at various orientations under conditions typically encountered in heat treating fluidized bed systems. In this study, resistively heated small cylinders and flat strips ranging in diameter from 1.27 to 9.53mm and in width from 6.25 to 25.4mm respectively were immersed in a 311mm in diameter lab-scale fluidized bed. The bed consisted of fine alumina oxide sand of mean particle size ranging from 145 to 330[micro]m fluidized by air at ambient temperatures. The fluidized bed unit was capable of fluidizing rates ranging from 0.14 to 23 G/Gmf. The cylinder and flat strip samples were positioned horizontally in the bed. The flat strip samples were rotated around the length's center axis in 15° increments from a 0° horizontal position to a 90° vertical position. The results showed that published correlations over-predict small cylinder Nusselt numbers over the entire fluidizing range; furthermore, their trends did not agree. Flat strip results demonstrated highest heat transfer rates at a vertical position. A correlation that predicts the mean Nusselt number within ±15% for both geometries was developed for operating conditions covered by the experiments.

Heat transfer to small cylinders and flat strips immersed in a fluidized bed

Fluidized bed heat treating systems have been used to heat treat low carbon steel wires for a number of years. Extending this application to high carbon steel wires and metal straps has been implemented with very little success due to the lack of knowledge of heat transfer coefficients or, alternatively, Nusselt number for small cylinders and flat strips. The objective of this study was to provide reliable data for predicting a suitable Nusselt number for small horizontal cylinders and flat strips at various orientations under conditions typically encountered in heat treating fluidized bed systems. In this study, resistively heated small cylinders and flat strips ranging in diameter from 1.27 to 9.53mm and in width from 6.25 to 25.4mm respectively were immersed in a 311mm in diameter lab-scale fluidized bed. The bed consisted of fine alumina oxide sand of mean particle size ranging from 145 to 330[micro]m fluidized by air at ambient temperatures. The fluidized bed unit was capable of fluidizing rates ranging from 0.14 to 23 G/Gmf. The cylinder and flat strip samples were positioned horizontally in the bed. The flat strip samples were rotated around the length's center axis in 15° increments from a 0° horizontal position to a 90° vertical position. The results showed that published correlations over-predict small cylinder Nusselt numbers over the entire fluidizing range; furthermore, their trends did not agree. Flat strip results demonstrated highest heat transfer rates at a vertical position. A correlation that predicts the mean Nusselt number within ±15% for both geometries was developed for operating conditions covered by the experiments.

Temperature induced friction increase in friction test and forming demonstrator for sheet metal forming

High process stability is needed in sheet metal forming industry. This can be achieved by predicting and controlling the transient process and temperature variation, especially at start of production. In this connection, the temperature induced friction changing plays a significant role because it leads to product failures. The handling of the transient friction effects is currently done reactively, based on the individual experience of the machine operators. In future, those transient effects need to be controlled. This paper shows initially an analysis of the temperature induced friction increase in a well-known and proven flat strip drawing test. Different tribological systems were tested at tool temperatures between 20 and 80 °C. The temperature increase results in a higher friction of up to 77 %. Several influences on friction increase will be presented. These friction influences were verified afterwards with a heated forming demonstrator under laboratory conditions.

Flat strips, Bowen–Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces

Let$X$be a proper, geodesically complete CAT($0$) space under a proper, non-elementary, isometric action by a group$\unicode[STIX]{x1D6E4}$with a rank one element. We construct a generalized Bowen–Margulis measure on the space of unit-speed parametrized geodesics of$X$modulo the$\unicode[STIX]{x1D6E4}$-action. Although the construction of Bowen–Margulis measures for rank one non-positively curved manifolds and for CAT($-1$) spaces is well known, the construction for CAT($0$) spaces hinges on establishing a new structural result of independent interest: almost no geodesic, under the Bowen–Margulis measure, bounds a flat strip of any positive width. We also show that almost every point in$\unicode[STIX]{x2202}_{\infty }X$, under the Patterson–Sullivan measure, is isolated in the Tits metric. (For these results we assume the Bowen–Margulis measure is finite, as it is in the cocompact case.) Finally, we precisely characterize mixing when$X$has full limit set: a finite Bowen–Margulis measure is not mixing under the geodesic flow precisely when$X$is a tree with all edge lengths in$c\mathbb{Z}$for some$c>0$. This characterization is new, even in the setting of CAT($-1$) spaces. More general (technical) versions of these results are also stated in the paper.

Two-Dimensional Free Convection Heat Transfer Below a Horizontal Hot Isothermal Flat Strip

Convection heat transfer below a horizontal, hot, and isothermal strip of infinite length and width of 2L embedded in fluids with different Prandtl number (Pr) and Nusselt number (Nu) is analyzed with the aid of integral method. A new concept is utilized to determine the boundary layer thickness at the strip's edge, which is based on matching the flow rate of the boundary layer below the strip at its edge and the flow rate of the plume, which forms after the heated fluid detaches from the strip's edge. In addition to these novelties, a numerical model is developed to verify the analytical framework, and an excellent agreement is observed between the analytical and numerical models.