This study presents a numerical analysis of an agitated vessel with a draft tube through the analysis of dimensionless numbers correlations. The heat transfer and fluid mechanics simulation was conducted using ANSYS Fluent software. The simulation used the Sliding Mesh approach and the SST k- \( \omega \) turbulence model to capture the vessel’s fluid flow and heat transfer phenomena. A grid independence study was conducted by varying the number of time steps to obtain an appropriate time step size for the simulation. The convective heat transfer coefficient, as indicated by the mean values of the Nusselt number, was calculated. The local values along the radial coordinate of the heat transfer surface were also determined. These results provide insights into the distribution of heat transfer rates within the vessel, which can help optimize process efficiency and equipment design. The simulation results were analyzed by varying the c and m coefficients in the Nusselt correlation presented as \(Nu= c \ Re^{m} \ Pr^{1/3}\) .  Furthermore, correlations describing the mean Nusselt number at the bottom and wall of the vessel are presented and compared with existing literature, contributing to advancing knowledge in this field.