This work assesses the influence of transport phenomena on the growth of Yarrowia lipolytica 2.2ab (Yl2.2ab) and protease production during Solid-State Fermentation (SSF) in a bench-scale wall-cooled tubular bioreactor packed with substrate-based pellets derived from agro-industrial residues. Our engineering methodology, in a novel manner, includes: (i) developing a new pseudo-heterogeneous model, (ii) identifying and quantifying the impact of all transport phenomena on microbial kinetics, (iii) elucidating how fluid dynamics enhances heat and mass transfer processes, and hence microbial kinetics, and (iv) determining the operational and geometric parameters for optimal bioreactor performance. As main results: (i) all transport phenomena occurring within the bench-scale bioreactor are fundamental for its reliable simulation and will be essential for its scale-up, and (ii) the maximum production of proteases, 420 U kgDS‐1−1, is achieved under the following operational conditions: a tube to particle diameter ratio of 5.6, a bath temperature of 45°C, an inlet airflow rate of 1 L min−1, and inlet fluid temperature of 43 °C. Finally, the pseudo-heterogeneous model is assessed by describing SSF-based observations from the literature, appropriately predicting the performance of Yl2.2ab in a bench-scale bioreactor. These results pave the way for future exploration of Yl2.2ab in SSF within larger-scale packed-bed bioreactors.