EXTENSION OF SCHUMANN''S THEORY TO THE CASE OF LOW THERMAL DIFFUSIVITY OF SOLID PARTICLES

Two simultaneous partial integro-differential equations which determine the transient heat transfer in a packed bed are introduced instead of Schumann''s equations which assume high thermal diffusivity and uniform temperature within the solid particles. These equations are useful for cases of both high and low thermal diffusivity of the solid. An approximate analytical solution for low Biot number is derived from the equations by neglecting all terms after the first in one of the equations. The analytical solution is similar to Furnas'' except for the definition of variables, and it is mathematically proved that the variables are also identical in the case of infinite thermal diffusivity of the solid. Procedure of numerical calculation for rigorous solution is given for a set of operating conditions, and computed solution for Biot number =1, 2, 3, 4, 5, are graphically presented. The theoretical results agree well with experimental results in the cooling of a column of eggs.