Longitudinal thermal conductivity data were obtained experimentally by means of the frequency response technique.
Water flowing in packed beds were studied, too, because of the scarcity of data on liquids. Glass, steel, hollow celluloid spheres and quartz sand were used as packings, and k_L, k_L values were obtained as a function of (Re)_p.
The data gave average Peclet number (Pe)_h of about 1.0.
For the purpose of comparison of the thermal conductivity with diffusivity, measurements of longitudinal diffusivity were carried out by using residence-time curves.
The results indicate that longitudinal thermal conductivity and diffusivity depend on the similar longitudinal mixing of fluids.

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Experiments were conducted to determine the values of E_z and E_r which are dispersion coefficients of fluid in a gaseous fluidization and a liquid fluidization, respectively. Various kinds of solid particles, 1480mesh in size, (Cf. Table 1) were fluidized in three glass tubes having diameters of 6.7, 9.9 and 12.1cm, respectively. As a tracer fluid, ammonia or hydrochloric acid solution was used. The value of E_z was obtained by Gilliland et al's back-mixing method, and the value of E_r by Hanratty et al's method. The results are given in Tables 2 and 3. Based on these experimental data, Eqs. (19) and (20) were derived, to express the values of Ez in gaseous fluidization, and Eq. (21), to express those of Er in gaseous fluidization. It was difficult to Ez in obtain good correlation in the case of the liquid fluidization, but approximate values of E_z and E_r were derived from Eqs. (22) and (23), respectively.
A theoretical equation, Eq. (2), was derived to represent the distribution of the concentrations of the tracer material introduced constantly from a point at the center of the bottom of the bed. Mixing efficiency, M, of fluid in the bed was defined by Eq. (3) on the basis of the dispersion of concentrations. Values of M, as calculated from Eq. (12), proved to be 5080% in the case of the gaseous fluidization and 1050% in that of the liquid fluidization, which served to make clear the extent of the mixing of fluid quantitatively.
Experimental work was carried out in an attempt to evaluate the fraction void, ε, in fluidized beds, and the expressions were obtained as in Eqs. (15)(17) for liquid fluidization, and as in Eq. (18) for gaseous fluidization.

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Concerning the subjects of the radial mixing of particles in the liquid fluidization, Eq. (10) has been theoretically derived to represent the mass of tracer particles displaced in lateral direction in a given time under batch-unsteady state.
The particles (2032 mesh) of marble, fire brick and lime stone were fluidized with water at 20°C, in the rectangular fluidized bed shown in Fig. 3, and the values of E_rp were evaluated from Eq. (10). Experimental results are given in Table 2, and the plotting as shown in Fig. 4 has led to the expression of E_rp as in Eq. (15).
In order to determine the values of longitudinal dispersion coefficient of solid particles, E_zp, on the basis of Eq. (17) which represents residence-time curve of tracer particles, the experimental work was carried out on the fludization of solid particles, given in Table 1, in water (20°C) in a glass tube (I. D. 7.1cm). From the experimental results, Fig. 6 was obtained and the expression of E_zp was given as in Eq. (24).
Magnitudes of the transient radial-and longitudinal-mixing of solid particles were theoretically derived as in Eqs. (28) and (32), respectively. The expression of the mixing efficiency of solid particles, M_p, is given by Eq. (34). As the result it has been concluded that the values of M_p increase in accordance with the increase in the values of Re_m and θ_h.

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