Analysis of non-stationary temperature field generated by a shaftless screw conveyor heated by Joule–Lenz effect

The non-stationary problem of temperature distribution in a circular cylindrical channel of infinite length filled with a homogeneous biomass material moving with a constant velocity in the axial direction was investigated. The heat source was a shaftless helical screw (or auger), which was heated with an electric current due to the Joule–Lenz effect and rotated uniformly around the axis of symmetry of the channel. Similar problems arise in the thermal processing of biomaterials using screw conveyor in pyrolysis and mass sterilization and pasteurization of food products. The problem is solved using the expansion of given and required functions in Fourier series over angular coordinate and integral Fourier and Laplace transforms over axial coordinate and time, respectively. As a result, the temperature field is obtained as the sum of two components, one of which, global, is proportional to time, and the other, which forms the microstructure of the temperature profile, is given by Fourier–Bessel series. The coefficients of the series are determined by the integrals calculated using the Romberg method. Based on the numerical calculations, the analysis of the space-time microstructure of the temperature field in the canal was performed. A significant dependence of the features of this microstructure on the geometric, kinematic and thermodynamic characteristics of the filling biomass and the screw was revealed.