Abstract
Commonly based on the liquid diffusion theory, drying theoretical studies in porous materials has been directed to plate, cylinder, and sphere, and few works are applied to non-conventional geometries. In this sense, this work aims to study, theoretically, the drying of solids with oblate spheroidal geometry based on the thermodynamics of irreversible processes. Mathematical modeling is proposed to describe, simultaneously, the heat and mass transfer (liquid and vapor) during the drying process, considering the variability of the transport coefficients and the convective boundary conditions on the solid surface, with particular reference to convective drying of lentil grains at low temperature and moderate air relative humidity. All the governing equations were written in the oblate spheroidal coordinates system and solved numerically using the finite-volume technique and the iterative Gauss–Seidel method. Numerical results of moisture content, temperature, liquid, vapor, and heat fluxes during the drying process were obtained, analyzed, and compared with experimental data, with a suitable agreement. It was observed that the areas near the focal point of the lentil grain dry and heat up faster; consequently, these areas are more susceptible to the appearance of cracks that can compromise the quality of the product. In addition, it was found that the vapor flux was predominant during the drying process when compared to the liquid flux.
Highlights
Water is the main constituent present in high concentrations in fresh foods, which considerably influences the palatability, digestibility, and physical structure of the food
Due to the fact that few works studied coupled heat and mass transfer in solids with complex shape [18,24,25,26,27]; that during the drying process of agricultural products with low moisture content, the predominant mass flux is the vapor flux, and the equilibrium boundary condition does not accurately reflect the physical phenomenon of heat and mass transport on the surface of the grain; this work aims to study the transfer of heat and mass in oblate spheroidal porous materials using mathematical modeling based on the non-equilibrium thermodynamics
In the mathematical formulation, the following assumptions were adopted: (a) The solid is homogeneous and isotropic; (b) Mass transfer in the single particle occurs by diffusion of liquid and vapor, under decreasing drying rate; (c) At the beginning of the drying process, the distributions of the moisture and temperature content are considered uniform and symmetrical around the z-axis; (d) The thermophysical properties are variable during the drying process and dependent on the position and moisture content inside the material; (e) Volume shrinkage negligible; (f) No capillarity effect; (g) Moisture transfer inside the solid by liquid and vapor diffusion, and evaporation and convection on a solid surface; (h) Heat transfer inside the solid by conduction, evaporation, and convection on a solid surface
Summary
Water is the main constituent present in high concentrations in fresh foods, which considerably influences the palatability, digestibility, and physical structure of the food. The deterioration that occurs in food is practically influenced in one way or another by the concentration and mobility of water inside it [1]. The removal of water from solid foods is used as a way to reduce water activity by inhibiting microbial growth, avoiding its deterioration. Water removal has become of great importance in reducing the costs of energy, transport, packaging, and storage of these foods [2]. Most of the methods of food preservation are based on the reduction in water mobility by the use of humectants materials and freezing, and by physical removal of water through osmotic dehydration, drying, evaporation, or lyophilization [3]. The main idea is to decrease the amount of water in the product to acceptable levels and maintain the physical-chemical and sensory properties of agricultural products in order to increase the shelf life of the products
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