The effective thermal conductivity k eff for concentric cylinders and concentric spheres is provided in Equations 9.59
Question:
The effective thermal conductivity keff for concentric cylinders and concentric spheres is provided in Equations 9.59 and 9.62, respectively. Derive expressions for the critical Rayleigh numbers associated with the cylindrical and spherical geometries, Rac,crit and Ras,crit, respectively, below which keff is minimized. Evaluate Rac,crit and Ras,crit for air, water, and glycerin at a mean temperature of 300 K. For specified inner and outer surface temperatures and inner cylinder or sphere radii, comment on the heat transfer rate for outer cylinder or sphere radii corresponding to Rac,crit and Ras,crit, respectively.
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Fundamentals Of Heat And Mass Transfer
ISBN: 9780470501979
7th Edition
Authors: Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera, David P. DeWitt