Electromagnetic field distribution and power absorption of 3D spherical objects.

Abstract

Microwave and radiofrequency heating has great promise in many engineering and biomedical applications because of its non-contact, volumetric heat generation and selective heating. However, the heating patterns and temperature distributions are non-uniform and difficult to control. Electromagnetic power absorption guides the heating pattern which is a complex function of dielectric properties, electromagnetic frequencies, size, and shape of the target object. A closed form expression of power absorption with functional relationship with various parameters is obtained for a spherical shaped dielectric object using Maxwell's equations in spherical coordinate. Maxwell's equations are solved using vector potentials and separation of variables. Mathematical tools such as Bessel functions, Legendre Polynomials, infinite series, and complex number expressions are employed in finding the solution. The electromagnetic power absorption is calculated from the knowledge of electromagnetic field within the object using Poynting theorem. The analytical expression of the electric field, magnetic field, and power generation within the sphere are coded in MATLAB and FORTRAN to get numerical results for spherical shaped meat balls of 1.0, 2.0, 3.0 and 5.0 cm radii with varying properties and electromagnetic frequencies of 2800 MHz, 2450 MHz, 915 MHz, and 300 MHz. Origin Labs is utilized to produce 1-D plots and also 2-D polar plots by reading the data text files generated in the FORTRAN program. Results show that the presence of local maxima of electric and magnetic field strength due to the constructive interference of the electromagnetic wave in the target object. The spatial distribution of microwave power absorption follows the trend of electromagnetic field distribution. The locations of local maxima and minima of power absorption and electromagnetic field distributions vary with the radius of the sphere and applied frequencies. The results also show that the strength of the absorbed electromagnetic wave at the 2450 MHz is most non-uniform at the radius of 3 cm nugget. The smallest (1 cm radius) and largest (5 cm radius) dielectric radii show a lower electromagnetic and power generation peak values but a more even distribution of energy overall. Analysis reveals the correlations of propagating wavelength, penetration depth of electromagnetic waves and size of the beef nuggets. Results indicate that the uniform and effective electromagnetic power absorption can be facilitated by proper design of the object of interest and selection of appropriate frequencies. This rigorous analytic investigation will provide significant insight in understanding the power absorption and temperature distribution mechanism for spherical shaped objects under electromagnetic wave (microwave and radiofrequency) treatment.