The Mathematical Modeling, Diffusivity, Energy, and Enviro-Economic Analysis (MD3E) of an Automatic Solar Dryer for Drying Date Fruits

Abstract

Date fruit drying is a process that consumes a significant amount of energy due to the long duration required for drying. To better understand how moisture flows through the fruit during drying and to speed up this process, drying studies must be conducted in conjunction with mathematical modeling, energy analysis, and environmental economic analysis. In this study, twelve thin-layer mathematical models were designed utilizing experimental data for three different date fruit varieties (Sakkoti, Malkabii, and Gondaila) and two solar drying systems (automated solar dryer and open-air dryer). These models were then validated using statistical analysis. The drying period for the date fruit varieties varied between 9 and 10 days for the automated solar dryer and 14 to 15 days for open-air drying. The moisture diffusivity coefficient values, determined using Fick’s second law of diffusion model, ranged from 7.14 × 10−12 m2/s to 2.17 × 10−11 m2/s. Among the twelve thin-layer mathematical models, we chose the best thin drying model based on a higher R2 and lower χ2 and RMSE. The Two-term and Modified Page III models delivered the best moisture ratio projections for date fruit dried in an open-air dryer. For date fruit dried in an automated solar dryer, the Two-term Exponential, Newton (Lewis), Approximation diffusion or Diffusion Method, and Two-term Exponential modeling provided the best moisture ratio projections. The energy and environmental study found that the particular amount of energy used varied from 17.936 to 22.746 kWh/kg, the energy payback time was 7.54 to 7.71 years, and the net CO2 mitigation throughout the lifespan ranged from 8.55 to 8.80 tons. Furthermore, economic research showed that the automated solar dryer’s payback period would be 2.476 years.