Numerical Solution of Mass Transfer Process during Drying of Apple Slices Using Pseudospectral Method

Introduction Convective air drying is one of the oldest and most popular drying methods. Designing and controlling the convective air drying needs the mathematical description of the moisture transfer during the drying process, known as drying kinetics. Fick’s second law of diffusion can be used for modelling the moisture distribution inside the moist object during drying process. Mathematical modeling of drying process is a very important tool, as it contributes to understand better moisture distributions inside the product which helps designing, improving and controlling drying operation in the food industry. Implementation of the partial differential equations subject to the correspondent initial and boundary conditions is one of the main methods of mathematical modeling to describe the physical phenomena such as moisture transfer during drying. In the recent decades, considerable number of research works have been devoted to numerical solution of mass transfer phenomena during convective drying of food products by using the common numerical solution such as FDMs, FEMs and FVMs. The spectral collocation (pseudospectral) methods is a powerful tool for the numerical solutions of smooth PDEs like mass transfer equations. Pseudospectral methods are able to achieve the high precision with using a small number of discretization points compared to FDMs and FEMs and with low computational time and computer memory. The objective of present research is to simulate the mass transfer phenomena in one dimension during convective drying of apple slices. The validation of the presented numerical model was done by comparing experimental drying data taken from Kaya et al. (2007) and Zarein et al. (2013). For more confirming the numerical approach, a numerical example with the exact solution is provided and the related errors were evaluated. Materials and Methods Estimation of mass transfer coefficients The convective mass transfer coefficient in the surface of the apple slice was obtained according to the relationship presented by Paitil (1988) and Janjai et al. (2008). (1) Estimation of effective moisture diffusivity coefficient Fick’s second law of diffusion was applied to obtain the effective moisture diffusivity coefficient of the apple slices. The analytical solution of this equation can be written as follows (Crank, 1975): (2) In this study, we consider the Pseudospectral methods for solving 1D mass transfer equation. In order to develop the model