Modelling and simulation of bread leavening to monitor energy consumption in industrial processes

We introduce a mathematical model of bread leavening in a warm chamber by coupling heat transfer, yeast growth, and carbon dioxide production and diffusion with the deformation of baking paste. We analyze the corresponding system of partial differential equations. The system is discretized by using a semi-implicit Euler method and the finite-element method in the time and space domain, respectively. Numerical simulations are employed to identify the energy consumption necessary to achieve a target volume under different settings of the leavening chamber and different concentrations of yeast in the baking paste, thereby providing a tool for the identification of cost-effective protocols.