Predicting temperature range in food slabs undergoing short-term/high-power microwave heating

Abstract

A closed-form solution to the heat equation, derived for one-dimensional microwave-heated slabs, is presented. The microwave energy distribution used in the heat equation is obtained from Maxwell’s equations. Therefore, the potential exists of standing waves of microwave energy within the food. This phenomenon contributes to the nonuniform temperature pattern characteristic of microwave heating but is often neglected in theoretical predictions of temperatures. The solution allows temperature to be calculated as a function of thermal, geometric and dielectric properties of the food being heated and is valid for all microwave power levels and durations of heating. Previous work allowed such a solution only if very long durations and very low power levels of microwave heating were used. That the solution is closed-form allows its implementation in spreadsheet format. Simplifications to the closed-form solution that retain the standing wave phenomenon are shown. Their accuracy, however, is limited to approximately 40 s of heating. Results from the full closed-form solution, using parameters measured in beef, show that the range of temperatures experienced by a microwave-heated beef slab is a sensitive function of slab width and time, with ranges as great as 50°C. It is shown that thermal insulation at the slab faces slightly increases the temperature range. Another feature of the theoretical solution is the extreme sensitivity of temperature range to slab width in the 1–3 cm width interval, with decreasing sensitivity as slab widths increase beyond 4 cm. Sensitivity increases, however, as time increases, regardless of slab width. Lastly, a time-invariant temperature range minimum is seen in the 3–4 cm slab width interval.