Basic Models of Heat Transfer in Packed Beds

Basic Models of Heat Transfer in Packed Beds 

A packed bed of solid particles usually has poorer heat transfer ability compared with heat transfer in solid. This is true in the case of adsorbent particles. Heat transfer in packed beds of adsorbents can be described by models of varying degrees of simplicity. 

One rigorous model is shown in Fig. 8.2, where temperature difference between fluid and particle is taken into account and temperature distribution in the radial direction in the bed occurs due to heat exchange through the column wall. In such cases a set of equations for heat transfer is given as follows. 

In the above equations, Cpr and Cp denote heat capacities of the fluid and solid phases, pb is the bed density and hp is the heat transfer coefficient between fluid and particles. Transport of heat through the fluid phase in the axial direction and in the radial direction of the bed by conduction are described by the effective thermal conductivities, ka,i and kas, while in the solid phase thermal conduction can be assumed to be isotropic and the effective thermal conductivity ka can be used to express this effect. Q i represents the heat evolution/absorption by adsorption or desorption on the basis of bed volume. This model neglects the temperature distribution in the radial position of each particle, which may seem contradictory to the case of mass transfer, where intraparticle mass transfer plays a significant role in the overall adsorption rate. Usually in the case of adsorption, the time constant of heat transfer in the particle is smaller than the time constant of intraparticle diffusion, and the temperature in the particle may be assumed to be constant. 

The above model is often too complicated hence several simplified versions are given below. 

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