A Mathematical Analysis to Design a Sugarcane Juice Extracting Machine

This paper presents a mathematical analysis to design a sugarcane juice extracting machine. Sugarcane should be crushed to begin extraction of juice easily in the lateral direction. Extraction of juice from sugarcanes uses roller crushers. Axial velocity, transverse velocity and flow rate during crushing of sugarcane are analysed for several parameters by numerical calculations of analytical results. An increase in permeability parameter, Darcy number, reduces the axial velocity as well as the flow rate but enhances the transverse velocity. An increase in the radial dilation parameter also enhances transverse velocity. Hence, high Darcy number and linearly increasing radius of successive rollers are favourable to squeeze out juice easily from sugarcanes. More appropriately, it is concluded that the first pair of rollers will mainly act as crusher but extraction will begin in the true sense when it passes through the next pairs of rollers with less spacing in between the pairs. The first pair of rollers with pointed teeth is suggested.