The production of thermoplastic pellets using underwater die-face pelletizers is a widespread process in the thermoplastics compounding industry. One major challenge in this process is pellet agglomeration, which occurs when the polymer is pliable or easily deformed under heat. To tackle this issue, the non-Newtonian flow of a polymer, along with the turbulent flow of heating oil and heat transfer through the die, are modeled using three-dimensional (3D) computational fluid dynamics (CFD) calculations in ANSYS Fluent. The computational model is validated by comparing its predictions of temperature and pressure using two models with and without a slip method, to experimental measurements from an industrial-scale pelletizer, resulting in a maximum error of <3 % for temperature and <16 % for pressure. The efficiency of the underwater die pelletizer is typically evaluated based on the rate at which it produces pellets. Minor variations in operational parameters, such as the inlet mass flow rate and temperature of the polymer, the temperature of the heating oil, and the water temperature, can greatly affect the quality of the final product. Firstly, contours of pressure, velocity and temperature are presented to understand their impact on pellet agglomeration. However, to more specifically link pellet quality, i.e. pellet agglomeration rate, to the input conditions, the study develops a non-dimensional parameter called the pellet agglomeration number (PAN), as a non-linear function of three other non-dimensional numbers: Reynolds number, Euler number, and a non-dimensional temperature. The values of PAN at the exit and inlet are shown to correlate well with the experimentally measured pellet agglomerations, thereby demonstrating the usefulness of PAN in not only differentiating between good and bad pellet quality but also determining apriori the appropriate operating conditions leading to fewer pellet agglomerations in commercial pelletizers.