Abstract
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.