Multi-Variable Analysis of Thermal and Flow Characteristics in Cylindrical Channels Using Response Surface Methodology

The present study deals with the flow dynamics and heat transfer parameters under laminar flow conditions in the cylindrical tube geometry. The fluid velocity distribution, temperature profile, and exit parameters were analyzed considering the variables of tube length (80–120 mm), entry radius (12–20 mm), and entry temperature (333–413 K). With the help of ANSYS Fluent, Response Surface Method (RSM) and Box-Behnken experimental design (BBD), 46 different scenarios have been analyzed. The results indicate that narrow inlet diameters not only affected the boundary layer formation by increasing the velocity gradients but also linearly increased the exit temperature as the temperature increases. Moreover, as the pipe length increases, it is found that the flow development region elongates and the temperature differences fall. Flow regimes were evaluated through Reynolds and Nusselt numbers, and model accuracy was proven with over 95% regressive coefficient. This study contributes to the determination of the optimal flow and heat transfer conditions in cylindrical pipes. It enriches the literature with good quantitative data about the relationship between geometric and thermal variables and flow behaviors, and provides useful tips for heating units and industrial processes that function with laminar flow delivery.