Temperature Distribution in a Finite-Length Cylindrical Channel Filled with Biomass Transported by Electrically Heated Auger

Abstract

The heat conduction problem for a cylindrical ring reactor of finite length, filled with biomass, which is transported at a constant speed by means of a rotating screw, is considered. The screw is assumed to be mounted on a circular shaft and is inductively heated by the Joule–Lenz effect. The surfaces of the channel and the shaft are thermally insulated. At the entrance and exit of the channel, boundary conditions of the third kind are formulated. The surface of the screw is replaced by uniformly distributed point heat sources. The problem is solved using the decomposition of the investigated temperature into Fourier–Bessel series over space variables and the integral Laplace transform over time. It is shown that the temperature has a quasi-stationary character with a short-term transient process. A numerical analysis of the spatio-temporal structure of temperature and its relationship with the thermophysical, kinematic and geometric parameters of the screw and biomass was carried out. In particular, it was found that the temperature along the reactor increases almost linearly starting from 400 K. It is shown that as in the case of an infinitely long channel, the condition of space–time resonance of the temperature field is fulfilled here.

Keywords

• auger reactor
• helical screw equipment
• electric heating
• temperature field
• mathematical modelling
• numerical analysis