Use of sensors for mathematical modeling during the roasting of cocoa beans (Theobroma cacao) of the Chuncho variety

Simple innovations in temperature control during cocoa roasting can help improve the quality of chocolate made by small entrepreneurs in the Andean-Amazonian valleys of Peru. The objective of this research was to evaluate the effect of oven temperature on the temperature of cocoa beans (Theobroma cacao) during roasting, using six mathematical models. Cocoa beans in the amounts of 100 and 200 g were placed in a tray in a conventional electric oven set at 250 degrees C. A K-type thermocouple with its respective reader was introduced in the geometric center of a cocoa bean and another 5 cm from the surface. The readings were recorded every 5 min and exported via Bluetooth to a computer. The temperature data were fitted to the mathematical models of the Concentrated System, Fourier's Law, Peleg, Page, Weibull and Midilli. The convective heat transfer coefficient (h), the thermal diffusivity (alpha), and the constants of the empirical models were determined. The h was 7.04 and 7.74 W/m2 degrees C for the toast of 100 and 200 g, respectively. The alpha was 3.09 x 10-8 and 3.28 x 10-8 m2/s for the 100 and 200 g toast, respectively. The rate constants of the empirical models showed a difference in the roasting of 100 and 200 g. All models represented the experimental data very well, since the values of R2, MRSE and MA%E were close to 1, close to 0 and less than 10%, respectively. The best mathematical model was that of Peleg.