Mathematical Modelling of Heat Transfer in Baking Cookies

Abstract

The process of heat transfer involves the exchange of internal energy between two substances. Along with heat and mass transport phenomena, baking will involve biological processes and physical transformations. Conduction and convection heat transfer is applied in this study. To enhance comprehension of the baking process, a model of heat transfer phenomena in cookies will be developed. Besides, Finite Different Method (FDM) is used to solve the PDE and then plot the temperature and moisture profile. The cookie is considered a cylinder and we divide it into two regions, the outer and central sections. Therefore, this study aimed to discuss the diffusion of water and heat transfer between the central and outer regions of the cookie. The heat and mass transfer inside the butter cookie governed Fourier’s Law and Fick’s Second Law respectively. As the radial distance from the side of the pan increase, the temperature will decrease but the moisture content increase. At the end of the baking process, the whole cookie is at the optimum temperature but does not have the same moisture content. The side of the cookie has lower moisture content than the inner region of the cookie. Hence, a crunchy outside and soft cookie inside can be baked.  The size and mass of the cookie remain constant throughout this research.