Estimation of Transport Properties

After the differential equations and boundary conditions have been formulated, there remain the problems of evaluating the various coefficients that appear, and carrying out the numerical solution of the equations. The following quantities are required. 

The contribution of other modes of transport to the effective thermal conductivity. 

Differences in Velocity Profiles in Beds of Cylinders and Spheres, at 4 Radial Positions 

With the measurements subject to fluctuations of 20 or 30%, no accurate description of the profile is possible. All that can be said is that with moderate ratios of tube to particle diameter, the maximum velocity is about twice the minimum, and that when the particles are relatively small, the profile is relatively flat near the axis. It is fairly well established that the ratio of the velocity at a given radial position to the average velocity is independent of the average velocity over a wide range. Another observation that is not so easy to understand is that the velocity reaches a maximum one or two particle diameters from the wall. Since the wall does not contribute any more than the packing to the surface per unit volume in the region within one-half particle diameter from the wall, there is no obvious reason for the velocity to drop off farther than some small fraction of a particle diameter from the wall. In any case, all the variations that affect heat transfer close to the wall can be lumped together and accounted for by an effective heat-transfer coefficient. Material transport close to the wall is not very important, because the diffusion barrier at the wall makes the radial variation of concentration small. 

S 1 + 2 V2wdP/6rt [exp (—0r2/dP) ]/i (0r2/dr) in which J1 denotes the first-order modified Bessel function and X and 9 are adjustable parameters. X determines how much higher the velocity is near the wall than at the axis, and 6 determines how flat the profile is 

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Nikhade BP, Pangarkar VG. (2007) A theorem of corresponding hydrodynamic states for estimation of transport properties case study of mass transfer coefficient in stirred tank fitted with helical coU. Ind. Eng. Chem. Res., 46 3095-3100. 

The estimation of transport properties of porous materials has long been a source of interest in both the applied and theoretical arenas. Many practical processes occur in porous media in which transport is particularly critical, the morphological properties of the void network are crucial in determining the performance of the reaction or separation processes in all these situations. 

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