Abstract
AbstractA new model is developed for the transient thermal response of a packed bed, using the method of spatial averaging. Equations for the average temperature of the fluid and the solid phase are derived from the point equations for thermal energy in each phase. The new model exhibits some unusual convective and dispersive coupling between the equations for the average fluid and solid temperatures. The response of the model equations to a pulse disturbance is analyzed. It is found that after a sufficiently long time has elapsed, the temperature pulses for the fluid and solid phases will be separated by a constant distance and will spread or disperse about their centroids at an equal rate. The pulse separation predicted by the new model equations is larger than that predicted using more conventional analyses of heat transfer in packed beds. Effective thermal conductivities measured under steady state conditions can differ significantly from those observed in transient experiments due to the spread in temperature pulses caused by heat exchange between phases. Estimates are made of the magnitude of the more important terms affecting longitudinal and lateral effective thermal conductivities under flow conditions, in order to make possible a direct comparison between theory and experiment in a companion paper.
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