This research examines the optimization of thermal enhancement in viscous fluids using statistical and numerical methods. The present study considers the impact of thermophoretic particle deposition on the swirling flow generated by the cylinder’s torsional motion. It is presumed that the cylinder rotates continuously along its axis and that the expansion rate of the cylinder wall is proportional to the position along the axis from the origin. Similarity variables are employed to convert partial differential equations (PDEs) into ordinary differential equations (ODEs), which are subsequently solved using the Runge-Kutta-Fehlberg-4th–5th (RKF-45) order numerical technique. Furthermore, Taguchi-based optimization, in conjunction with sensitivity analysis, is employed to assess the thermal transfer rate. The graphical representation indicates that with a rise in the Reynolds number, both the velocity and thermal profiles decrease, while the concentration profile increases. The Taguchi technique indicates that the third level of the heat source/sink parameter, the second level of the Dufour number, and the first level of the Reynolds number provide optimal circumstances for optimizing the Nusselt number. The analysis forecasts its industrial significance by attaining a maximum heat transfer rate of 4.916537. The Reynolds number (94.76%) has the largest effect on the Nusselt number, while the heat source/sink parameter (1.53%) has the least.
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