The convective drying of agricultural materials is an energy-intensive process, and optimizing dryer design is critical for improving efficiency and product quality. This study presents a comprehensive heat and mass transfer model for the convective drying of alfalfa leaves in a rotary drum dryer. Freshly harvested leaves with an initial moisture content of approximately 70% (w.b.) were used as the test material. The proposed system features a simplified drum design aimed at enhancing process efficiency while reducing equipment complexity. The primary objective was to reduce the moisture content of alfalfa leaves to below 50% to ensure their quality during subsequent storage and transportation. To determine the optimal operating conditions, the kinematics of leaf motion inside the rotating drum and the associated heat and mass transfer phenomena were investigated through analytical modeling, numerical simulation, and experimental studies on a laboratory-scale physical model. An analytical model was developed to establish relationships between transverse kinematic characteristics (detachment condition, Froude number, drum inclination angle), average longitudinal velocity, and residence time. Numerical simulations based on the Navier–Stokes equations (continuity, momentum, and energy) provided detailed moisture content distributions within individual leaves under varying airflow orientations and drying durations. The novelty of this work lies in the integrated determination of optimized operating parameters through combined analytical, numerical, and experimental approaches. A regression model relating final moisture content to key process variables (air velocity, temperature of 60 °C, drum rotation frequency and mass of loaded material) was developed from experimental data, yielding practical recommendations for the design and operation of rotary drum dryers for alfalfa and similar agricultural materials.