Marangoni convection plays a significant role in heat transfer in advanced cooling, lubrication, energy harvesting, and environmental systems. This research article, utilizing a passive flow control technique, presents a novel investigation into the Marangoni convective heat transfer flow of nanofluid over an infinite porous disk. The prevailing partial differential equations are transformed into a system of regressed ordinary differential equations with the help of Karman’s transformations. Besides, the numerical solutions to the equations are analyzed with the bvp4c algorithm unified in MATLAB. Apart from that, a well-established Taguchi method has been used to optimize the heat transfer rate. The described model effectively approximates the velocity and temperature behavior patterns within nanofluids. The regression analysis develops an empirical model to estimate key engineering parameters, such as the Nusselt number. The findings reveal that the radial velocity of the fluid increases with a higher strength of the porosity parameter. In contrast, the axial velocity exhibits the opposite behavior and decreases as the porosity parameter strength increases. Also Nusselt number decreases significantly for both porosity parameter and Stefan’s blowing parameter. Apart from that, a well established Taguchi method has been used to optimize the Nusselt number which indicates that the combination of and provides the maximal Nusselt Number. The statistical analysis revels that, Marangoni parameter is maximum and Stefan’s blowing has minimum contribution in the estimation of Nusselt number, which indicates that. This problem have the potential to serve the real life applications like material processing and manufacturing, Environmental and Industrial Processes, cooling and heating process, etc.
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