Editor’s message: cooling evolution for validating microwave heating models

Heating with the purpose of conducting a process is one of the most important non-communication applications of microwaves. Given the importance of the temperature as a variable for designing different systems, such as curing, sintering, drying, or food cooking, there is a great deal of interest in measurement techniques, as well as modeling and simulation. Since it is very important to know the thermal profile and its evolution while heating of materials, there are great efforts in the designing of instruments and devices for temperature measurement, and the development of mathematical models for calculating the heat distribution and temperature profiles. Both, temperature measurement and validation of the models are in the case of microwave heating very difficult. In addition to conduction, convection, and radiation (infrared) mechanisms for heat transfer, in the case of microwaves the generated heat within the sample depends on the electric field profile that depends on the permittivity of the sample, that depends on the temperature, which in turn depends on the electric field and the permittivity. It is impossible to have a homogeneous material, slight differences in composition affect everything else. In most cases, the only available information is the external temperature. This is a common problem in engineering known as the boundary value problem. Heat transfer is described with differential equations, solved either analytical or numerical, to describe the temperature inside the sample. It is possible to insert thermocouples, in the case of conventional heating, to follow thermal evolution, but that is more complicated in the case of microwaves because even when they could sense the temperature correctly, they affect the electric field. Validity of a model depends on the accuracy of the set of equations for describing the involved phenomena often referred to as “Multiphysics”, and the right thermal and electromagnetic characterization of the system, as well as the knowledge of the functional relation of the properties with different variables. However, the thermal profile calculated with such a model requires some sort of validation, and it happens that the inner of the sample cannot be seen. Physical evidence of the achieved temperatures can be found after heating, such as cured zones, phase transformation, or confirmation of molten zones, but in the case of microwaves that information does not allow to build a thermal profile because they could be either thermal sources or thermal absorbers, therefore the possibility of validating a thermal profile is limited. The validation of microwave heating models could be conducted by focusing on the cooling part after the microwaves are shut off so that we have only conduction within the sample with known boundary conditions. We have access to the external temperature, then we can follow that evolution. The idea consists of heating a sample with microwaves at certain conditions and calculating the internal thermal profile of that sample at the same conditions with the model that we want to validate. We cannot see the internal