Heat Transfer in a Packed Bed at Moderate Values of the Reynolds Number

Results are given of an experimental investigation of the coefficient of wall heat transfer of a round tube filled with a packed medium formed by monodisperse glass spheres of different diameters $(d_p = 0.9$, $3.2$, $8.9$ mm$)$ in a stabilized region of heat transfer under conditions of filtering of water and aqueous solution of glycerin. A two-layer model of heat transfer is used to calculate the contribution made by the heat resistance of the flow core and of the wall zone using the measured coefficients of heat transfer and temperature profiles across the packed bed. The form of dependence for the effective coefficient of thermal conductivity is determined. Data are given of the measurement of the coefficient of wall heat transfer of annular channel filled both with a single layer of spheres with packing of two types (cubic and rhombohedral) and with several layers of spheres with random packing in a stabilized region of heat transfer under conditions of filtering of water. It is demonstrated that, in the case of inertial mode of filtering of liquid through the packed bed, the values of the Nusselt number both in the tube and in the annular channel correspond to the relation $\text{Nu}_e \propto (d_e/D)\text{Pe}_2^{1/2}$. A semi-empirical correlation is suggested, which generalizes well our experimental data (and the data of other authors) on heat transfer in the tube and in the annular channel. A theoretical model is suggested, according to which the variation of heat transfer is defined by the behavior of the effective coefficient of thermal conductivity $\lambda_{\text{ef}}/\lambda_f \propto \text{Pe}_d^{1/2}$associated with the predominant contribution made to convective heat transfer by the transport processes in vortex cells with closed lines of flow.