THE RATE OF HEAT CONDUCTION FROM A HEATED SPHERE TO A PACKED BED OF PASSIVE SPHERES
Title:
THE RATE OF HEAT CONDUCTION FROM A HEATED SPHERE TO A PACKED BED OF PASSIVE SPHERES
Author:
Chang, E.Y. Acrivos, A.
Appeared in:
Chemical engineering communications
Paging:
Volume 58 (1987) nr. 1-6 pages 165-170
Year:
1987
Contents:
We calculate the rate of heat conduction, Q, from a heated sphere with constant surface temperature to a packed bed, consisting of equal sized passive spheres of a different thermal conductivity than that of the matrix, whose temperature far away from the heated sphere is constant. If the passive spheres are much smaller than the heated one, the composite may be viewed as an effective continuum with conductivity k*, and hence Q equals the corresponding rate of heat conduction in the absence of the passive spheres multiplied by the ratio of k* to the thermal conductivity of the matrix. Here, we examine the case in which the passive spheres are of the same size as the heated one via an effective continuum technique, which approximately accounts for the depletion of inclusion density near the surface of the heated sphere by introducing a position dependent effective conductivity. The results thus obtained are shown to be in good agreement with the experimental data thus demonstrating that systems which are not macroscopically homogeneous can still be described approximately by means of an effective continuum theory provided that the latter is appropriately modified.
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