Mass transfer in creeping flow past periodic arrays of cylinders.

Abstract

MethodCreeping flow past a square and an equilateral triangular array of cylinders and mass transfer between the fluid and the surface of the cylinders were studied theoretically. A numerical solution for the drag coefficient of the cylinders was obtained and found to be in good agreement with the asymptotic analytical solutions for very small and very large values of the dimensionless pitch respectively. Anumerical solution for the Sherwood number was obtained as a function of the Peclet number, the dimensionless pitch, and the number of rows of cylinders in square and triangular arrays. Theoretical predictions for the drag coefficient of the cyh'nders and the Sherwood number were compared with approximate analytical solutions based on the free-surface model by Happel.

A Fundamental Investigation of Gas/Solid Heat and Mass Transfer in Structured Catalysts Based on Periodic Open Cellular Structures (POCS)

“…The Diamond unit cell ( Figure 4 b exhibits two different regimes, namely, a full laminar regime at low flow rate (Re ds ≤ 32) and an unsteady laminar regime at Re ds > 32, according to our fluid dynamic simulations. For 1 ≤ Re ds ≤ 32, a laminar flow regime establishes inside the Diamond unit cell, and such behavior is once again comparable to the behavior of cylinders 49 in cross-flow and in tube banks 50 in the discussed Re range, for which a dependency of the Sherwood number to the Reynolds number raised to the power of 1/3 was found. Such dependency arises for foams as well in the same flow regime.…”

“…The streamlines of the flow field are adherent to the solid surface and axisymmetric with respect to the direction of the flow. Such behavior is in analogy with flow condition around cylinders and in tube banks in the discussed Re range, for which the authors propose a dependency of the Sherwood number to the Reynolds number raised to the power of 1/3. In this work, the best fit of the data set leads to a dependency of the Sherwood number on the Reynolds number raised to the power of 0.35, close to the theoretical value 1/3, which is hereby adopted for the TKKD unit cell in the range of 1 ≤ Re ds ≤ 4.…”

“…Furthermore, this behavior is also associated with creeping viscous flow past cylinders and arrays of cylinders. 49 , 50 The second asymptotic contribution is provided by a dependence of the dimensionless transfer coefficient on the Reynolds number raised to 0.8, which is reported for fully turbulent flow in tube bundles 56 and for a single cylinder in cross-flow in the turbulent flow as well. 49 It should be noted that the superposition of the asymptotic contributions related to the creeping flow and the post-Forchheimer regimes leaded to an apparent dependency of the Sherwood number on the Reynolds number raised to the power of 0.45 in the unsteady laminar regime investigated in this work for 32 ≤ Re d s ≤ 128, as shown in Section 3.2 .…”

Is the surface area of the red cell membrane skeleton locally conserved?

“…Saffman and Delbruck (1975) used the diameter of the whole cell instead. It happens, however, that the choice made here gives the same result as when the force is obtained from calculations on flows past infinite periodic arrays of cylinders (Ishimi et al, 1987). With increasing density of cylinders the last model is to be preferred against the first one.…”

Convective heat transfer for power law fluids in packed and fluidised beds of spheres

“…), su ce it to add here that within the framework of the submerged object model, the simple free surface cell model has been shown to yield satisfactory predictions of macroscopic uid mechanical parameters in a variety of settings. Thus, for instance, the values of drag coe cient and Nusselt number for the ow of Newtonian and inelastic non-Newtonian media over the bundles of circular cylinders (Ishimi et al, 1987;Satheesh et al, 1999;Vijaysri et al, 1999;Dhotkar et al, 2000;Chhabra et al, 2000;Shibu et al, 2001;Mandhani et al, 2002), in beds of spheres (Jaiswal et al, 1991(Jaiswal et al, , 1992(Jaiswal et al, , 1993Kawase and Ulbrecht, 1981;Satish and Zhu, 1992, etc. ) and for the free rise/fall of uid particles (Gummalam and Chhabra, 1987;Gummalam et al, 1988;Jarzebski and Malinowski, 1986;Chhabra, 1998;Zhu, 2001, etc.).…”