Faculty Advisor or Committee Member

Vadim V. Yakovlev, Advisor




A fundamental problem of microwave (MW) thermal processing of materials is the intrinsic non-uniformity of the resulting internal heating pattern. This project proposes a general technique to solve this problem by using comprehensive numerical modeling to determine the optimal process guaranteeing uniformity. The distinctive features of the approach are the use of an original concept of uniformity for MW-induced temperature fields and pulsed MW energy as a mechanism for achieving uniformity of heating. The mathematical model used to represent MW heating describes two component physical processes: electromagnetic wave propagation and heat diffusion. A numerical solution for the corresponding boundary value problem is obtained using an appropriate iterative framework in which each sub-problem is solved independently by applying the 3D FDTD method. Given a specific MW heating system and load configuration, the optimization problem is to find the experiment which minimizes the time required to raise the minimum temperature of the load to a prescribed goal temperature while maintaining the maximum temperature below a prescribed threshold. The characteristics of the system which most dramatically influence the internal heating pattern, when changed, are identified through extensive modeling, and are subsequently chosen as the design variables in the related optimization. Pulsing MW power is also incorporated into the optimization to allow heat diffusion to affect cold spots not addressed by the heating controlled by the design variables. The developed optimization algorithm proceeds at each time-step by choosing the values of design variables which produce the most uniform heating pattern. Uniformity is measured as the average squared temperature deviation corresponding to all distinct neighboring pairs of FDTD cells representing the load. The algorithm is implemented as a collection of MATLAB scripts producing a description of the optimal MW heating process along with the final 3D temperature field. We demonstrate that CAD of a practical applicator providing uniform heating is reduced to the determination of suitable design variables and their incorporation into the optimization process. Although uniformity cannot be attained using“static" MW heating, it is achievable by applying an appropriate pulsing regime. The functionality of the proposed optimization is illustrated by computational experiments which show that time-to-uniformity can be reduced, compared to the pulsing regime, by up to an order of magnitude.


Worcester Polytechnic Institute

Degree Name



Mathematical Sciences

Project Type


Date Accepted





uniformity of heating, optimization, optimal process, modeling, microwave pulsing, microwave heating, FDTD method, coupled problem, Microwave heating, Mathematical models, Heat, Transmission, Mathematical models, Mathematical optimization