Heat transfer phenomena in a finite circular channel with biomass transported by a rotating shaftless screw heated by an electric current

In this work, we simulate heat transfer in a finite cylindrical circular chanell filled with biomass as pseudo-liquid moving with constant velocity by means of a shaftless screw rotation. The screw acts as a heat source due to the Joule-Lenz effect. The channel lateral surface is thermally insulated, and the Newton boundary conditions are fulfilled at the ends of the channel. To solve this new initial-boundary value problem, the method of expanding the desired temperature into a Fourier-Bessel series over angular and radial variables, as well as the integral Laplace transform over time, was used. The problem in the transforms is solved by replacing the unknown functions in such a way that inhomogeneous ordinary differential equations are transformed into homogeneous differential equations. As a result, an exact solution of the problem was obtained in the field of originals. A detailed numerical analysis of the spatial and temporal characteristics of the temperature field was performed. It is shown that due to the absence of the internal shaft of the screw with its additional reflective surface, the amplitudes of temperature oscillations in the quasi-stationary regime are quite weak, on the order of 0.02 K. However, they are clearly manifested when analyzed in certain directions, especially at appropriately selected velocities of the screw rotation and rectilinear movement of biomass.