Modeling of heat transfer from an electrically heated rotating helix in a circular cylindrical channel filled with a biomass moving at a constant velocity

Abstract

The increasingly popular use of screw conveyors for thermo(chemical) processing of food or waste requires modeling the temperature distribution inside such a device. The purpose of this work is to demonstrate the temperature distribution around an electrically heated rotating helix inside a circular cylindrical channel of infinite length filled with a homogeneous biomass moving at a constant velocity in the axial direction. The non-stationary problem of temperature distribution is solved by replacing the real heat source with continuously distributed point sources, expansion of the given and required functions into a Fourier series over angular coordinate and applying integral Fourier and Laplace transforms over axial coordinate and time, respectively. The exact solution of the problem is represented as the product of the energy source determined by the Joule heat and the influence function in the form of the Fourier-Bessel series, which depends on the thermodynamic characteristics of substance and its velocity, radius, pitch and angular velocity of the helix. The temperature field consists of two components, one proportional to the time and the other forming the micro-structure of the temperature profile. On the basis of numerical calculations the analysis of space–time microstructure of the temperature field in the channel is provided. It is shown that in time the temperature undergoes low-amplitude quasi-monochromatic oscillations, the period of which is determined by the angular velocity of the spiral. The spatial temperature distribution has a plateau-like character formed by the geometry of the helix. In particular, the conditions under which the resonant amplification of the amplitude of temperature fluctuations occurs are established.