Numerical simulation of conduction heating in conically shaped bodies

A 2-dimensional energy balance approach was used to model temperature distribution in conduction heated conically shaped bodies. A numerical solution by finite differences to the second order partial differential equation for heat conduction served as basis for the model. The cone was divided into small volume elements. The inner elements were concentric rings of rectangular cross section while those at the side surfaces had triangular cross-sections. Energy balance equations for the volume elements were solved explicitly. Acrylic of known thermal properties was used to fabricate cones in 3 different geometries and sizes, varying from a frustum to a point cone. Every cone had 3 or 4 thermocouples (36 gauge, T type) inserted at different locations. Heat penetration tests were carried out in a water bath with constant and variable water temperatures. Experimental temperatures at different locations within the cones agreed well with temperatures predicted by the model. Use of the model to predict the location of the slowest-heating point or “cold point” under different processing conditions was also demonstrated.