Microwave-Convective Processing of Whipped Bread: Mathematical Modeling

Abstract

Whipped yeast-free bakery products require effective energy supply to dough in order to optimize energy consumption, baking time, and quality. This article introduces a verified mathematical model of microwave and convective baking for whipped bread based on heat and mass exchange equations. A full-scale experiment to verify the calculations involved dough samples with a humidity of 56 ± 1%. The samples underwent microwave and convective processing until the temperature in the crumb center reached 98 ± 1°C. The mathematical model was formalized as energy and mass conservation equations, which made it possible to consider baking as a non-stationary process of heat and mass transfer of moisture in an isotropic incompressible continuous medium in the diffusion approximation. The equation took into account the unstable phase transition boundary. The practical verification showed the mean error for microwave baking as 14.5% in temperature and 18.2% in moisture content. For convective baking, the results included 12.6% in temperature and 9.7% in moisture content. The mathematical model proved adequate to the real processes of heat and mass transfer. The error in calculating the temperature and moisture content fields was sufficient tooptimize the process. The physical and mathematical model of the baking process made it possible to evaluate the effect of technological variables on the temperature and moisture concentration fields in the dough samples. The mathematical model and the computational experiment can be used to identify static and dynamic characteristics of baking as an object of automatic control, i.e., to identify optimal control channels and actions, as well as to adjust the automatic control system to specific quality indicators.