An efficient empirical model for microwave-induced average temperature of liquid cylindrical reactants

Microwave-assisted chemical reactions have become very popular in preparative chemistry due to many advantages such as accelerated reaction rate, higher chemical yield and lower energy use. In dedicated equipment, however, the microwave units operate as "black boxes" keeping the role of the thermal effects in microwave-assisted chemical processes somewhat obscure. To address this issue, in this paper, we propose a simple mathematical model for computing microwave-induced temperature in a three-media cylindrical structure representing a core element of a typical microwave reactor with the reactant assumed to be stirred by convection flows. The model determines the average temperature of the reactant for the known absorbed microwave power and heating time. To illustrate its functionality, the model is used to compute time-temperature characteristics of water, ethanol, and methanol heated in the batch reactor MiniFlow 200SS. The curve calculated for water appears to be in an excellent agreement with an experiment. This confirms the hypothesis on temperature homogenization in liquid reactants in batch reactors due to convection and suggests that modeling can be helpful in clarifying and quantifying the details of microwave-assisted chemical processes.