Modelling and simulation of volumetric microwave heating : energy conversion and heat transfer

• Main Author: Mthombeni, Goodman
• Published: 2012
• Subjects: Microwave heating > Mathematical models; Heat > Transmission > Mathematical models; Ilmenite
• Online Access: http://hdl.handle.net/10210/6600

M.Tech. === Due to electric (E) and magnetic (H) fields that vary with space (r) and time (t) in the microwave cavity, and due to the inhomogeneous nature of the minerals, heating a mineral in a microwave oven gives an inherently non-uniform temperature distribution. The objective of the project is to introduce a mathematical model that will demonstrate the thermal interaction between ilmenite mineral (FeTiO3) and microwaves. The simulation presents the temperature distribution in the sample based on the conditions imposed on its boundaries. The field distribution in the cavity is simulated, and then the thermal analysis is performed using the lumped thermal capacity model. The temperature distribution in the sample is also simulated using the general heat conduction equation. Finite difference method is used two solve the two-dimensional unsteady heat conduction equation. The simulation of the field distribution in the cavity reveals that there are position of intense electric and magnetic field in the oven. This is demonstrated by experiment 6, where samples are heated at different positions in the oven for the same duration and different temperatures in the samples were measured. Electromagnetic wave propagation was also studied. It became apparent that the electric and magnetic field can not be treated independently from each other, because the changing electric field produces a changing magnetic field and the newly produced changing magnetic field produces a changing electric field, which is an electromagnetic wave. It is also proved that, considering the relationship given by Maxwell's equations, the electric and magnetic fields are not only space out of phase but they are also time out of phase, meaning that the one quantity is leading while the other is lagging. Based on the available mathematical evidence it was suggested to fit the conventional representation of the electromagnetic field, which show the electric field and the magnetic field at right angle to each other and in time phase, to the new representation which would highlight the fact that the electric and magnetic fields are time out of phase. The study of electromagnetic wave propagation has proved that the one-dimensional conventional representation of electromagnetic waves is inadequate. It does not support the fact that there are a number of resonant modes that exists in the cavity which has long been proved and accepted by authors in the field of electromagnetism. This is very much clear when dealing with electromagnetic waves in three dimensional space.