Nusselt number for flow perpendicular to arrays of cylinders in the limit of small Reynolds and large Peclet numbers

Abstract

The problem of determining the Nusselt number N, the nondimensional rate of heat or mass transfer, from an array of cylindrical particles to the surrounding fluid is examined in the limit of small Reynolds number Re and large Peclet number Pe. N in this limit can be determined from the details of flow in the immediate vicinity of the particles. These are determined accurately using a method of multipole expansions for both ordered and random arrays of cylinders. The results for N/Pe1/3 are presented for the complete range of the area fraction of cylinders. The results of numerical simulations for random arrays are compared with those predicted using effective-medium approximations, and a good agreement between the two is found. A simple formula is given for relating the Nusselt number and the Darcy permeability of the arrays. Although the formula is obtained by fitting the results of numerical simulations for arrays of cylindrical particles, it is shown to yield a surprisingly accurate relationship between the two even for the arrays of spherical particles for which several known results exist in the literature suggesting thereby that this relationship may be relatively insensitive to the shape of the particles.

Mass transfer coefficients for laminar longitudinal flow in hollow-fibre contactors

“…The above choice for the exclusion radius R was made by Dodd et al (1995) who showed that the effectivemedium approximation based on this value of R agrees very well with the results of rigorous computations for the mobility of integral membrane proteins in bilipid membranes, modelled as suspensions of disks. Subsequently, Wang & Sangani (1997), Sangani & Mo (1997), and Spelt et al (2001) have used a similar model for estimating properties of suspensions of disks and spheres. The computational results presented in figure 2 corresponded to hard-disk random configurations.…”

Finite Point Low Mach Number Algorithm for Unsteady Nonisothermal Flows Application to the Study of Reactive Flow Past a Thin Catalytic Wire

“…As a final remark, it is worth noting that Eqs. (10)- (14) could have been written in terms of pressure instead of density. However, in this case the pressure equation, obtained after the continuity equation, would read…”

“…(21) is evaluated by performing an additional time derivative in Eqs. (10)- (14) leaving out the terms that contain second order spatial derivatives. Finite point formulations are well suited to be used in combination with Lax-Wendroff time integration schemes because it is straightforward to compute higher order spatial derivatives after expression (20).…”

“…Regarding the specific issue of the low-Mach-number flow of a reacting mixture past catalytic wires, Sangani and Acrivos [13] studied analytically the limit of simultaneously small Reynolds and Peclet numbers, while Wang and Sangani [14] dealt with the small Reynolds and large Peclet numbers. More recently, Vera and Liñ nan [15] have also addressed analytically the diffusion controlled combustion of a reacting mixture past a two-dimensional array of catalytic wires in the low Peclet number regime.…”

Acoustic Probe for Solid-Gas-Liquid Suspension

“…This includes the calculations of the force on a particle in fixed beds, effective viscosity and elasticity of random suspensions , the Nusselt number for heat transfer from an array of cylinders (Wang and Sangani 1997), and the diffusivity of proteins in bilipid membranes . The effective medium theory is also applied to the light scattering problem, a problem which is quite similar to the acoustic problem of interest here; and its predictions are shown to compare well with experiments on the light scattered by suspensions (Ma et al (1990)).…”