Approximate computation of heat sources in axisymmetric microwave heating

Microwave radiation offers the very important feature of inducing volumetric heating in a sample that leads to faster processing rates and lower thermal gradients in the heated material than the conventional techniques based on boundary heating. This feature has led to the use of microwaves as heating means in many practical applications, especially related to food technology. Given the importance of microwave heating, the abundance of reported studies in the literature regarding its modeling is not surprising. Microwaves create very complex heat source patterns in the heated material. These patterns can be found from the solution of the Maxwell equations. Although their two(2D) and threedimensional (3D) solutions are feasible1 (but computationally demanding), the one-dimensional (1D) case is usually invoked to attain greater insight on the physics of the problem. The usual 1D approximation refers to the normally irradiated slab2,3 (Cartesian geometry) and the radially irradiated cylindrical sample (axisymmetric case). The latter 1D model has been used to simulate the heating of cylindrical samples in actual microwave ovens based on the dubious assumption that multiple reflections from the oven’s wall lead to an approximately 1D pattern in the sample.4 Recently, it has been experimentally shown that the temperature profile in a rotated cylindrical sample is axisymmetric so the radially irradiated model is appropriate for this case.5 The heat source patterns resulting from the Maxwell equations for the 1D case are not so simple, especially for the case of nonuniform dielectric properties for which a numerical solution is needed. For this reason, several simple expressions for heat sources based on Lambert’s law have been proposed. Although the limits of validity of these expressions for the case of an 1D slab have been extensively studied years ago,6 only recently have the corresponding limits for the axisymmetric geometry been proposed.7 In the present work, the approximate expressions for the heat sources in a radially irradiated cylindrical sample are reviewed and the corresponding validity region for the best one (much wider than that proposed previously7) is given. In addition, criteria for the application of simplified expressions for sources in the case of temperaturedependent dielectric properties are presented for the first time.