Development and Validation of the D 2 MCD Family: Dual‐Term Diffusion Models for Coffee Drying

ABSTRACT This study presents the Duque Diffusion Model for Coffee Drying (D 2 MCD), a family of dual‐term diffusive formulations derived from Fick's law with convective boundary conditions. The models were developed to describe the mechanical drying behavior of Coffea arabica L. washed‐processed coffee under variable thermal and psychrometric environments, providing a physically consistent framework that complements classical empirical approaches. The general form of the model expresses the moisture ratio as the superposition of two exponential modes weighted by a time‐stretch integral that accounts for temperature and moisture‐dependent effective diffusivity. Four variants are proposed: D 2 MCD‐Core, the fundamental dual‐term model; D 2 MCD‐XR, which incorporates a reabsorption term through an exponential memory function; D 2 MCD‐Iso, a simplified isothermal version; and D 3 MCD‐T, an extended thermodiffusive formulation coupling heat and mass transfer. Model parameters were estimated using nonlinear least‐squares fitting against experimental data from controlled mechanical drying tests of washed‐processed coffee conducted at 35°C–50°C and 20%–60% relative humidity. The D 2 MCD family achieved high predictive accuracy (RMSE < 0.012 moisture units [wb]) and physically consistent parameter behavior, displaying improved agreement with experimental data compared with classical models such as Page, Midilli, and Henderson–Pabis. The reabsorption module effectively captured transient humidity peaks, while the thermal coupling enhanced performance under nonisothermal conditions. The D 2 MCD framework establishes a unified and flexible basis for modeling mass and heat transfer during coffee drying and can be extended to other agricultural materials and drying configurations.