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.
Highlights
We consider the problem of determining the rate of heat or mass transfer from particles to the surrounding fluid
Sangani and Acrivos3 used a somewhat different collocation technique to determine the heat transfer rates in square and hexagonal arrays of infinitely long cylinders, while Acrivos et al.4 examined the case of dilute random arrays of spherical particles
The formula is shown to be surprisingly accurate even when applied to the arrays of spherical particles for which several known results exist in the literature
Summary
We consider the problem of determining the rate of heat or mass transfer from particles to the surrounding fluid. Sangani and Acrivos used a somewhat different collocation technique to determine the heat transfer rates in square and hexagonal arrays of infinitely long cylinders, while Acrivos et al. examined the case of dilute random arrays of spherical particles. Both of these studies were concerned with the case of vanishingly small Re and small but finite Pe. In the present study we shall be interested in the opposite limit of Pe, i.e., in the limit of large Pe, the Reynolds number being vanishingly small. The formula is shown to be surprisingly accurate even when applied to the arrays of spherical particles for which several known results exist in the literature
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
