Realisation of mathematical conditions ensuring smooth transition of heat and mass transfer at the boundaries of solids and liquids

The drying process involving heat and mass transfer at solid-liquid interfaces is fundamental in various industries such as food, pharmaceuticals and textiles. One of the most challenging aspects of this phenomenon is to ensure smooth heat and mass transfer at solid-liquid interfaces, as discontinuities in boundary conditions can lead to inaccurate results and complicate process control. This study is devoted to the formulation of mathematical conditions that ensure a smooth transition at solid-liquid interfaces in a combined drying process. A transition state model based on Fourier and Fick equations is proposed to describe heat exchange and moisture diffusion in a food product. The modelling takes into account the thermophysical properties of the material, the heat transfer coefficient and the operating conditions of the system. Fundamental theories and mathematical methods required for effective modelling to improve the understanding and control of drying processes are also discussed.