Thermo-convection driven Sodium Alginate-based Darcy–Forchheimer EMHD Williamson hybrid nanofluid flow with varying thermal distribution

A computational investigation is furnished to explore the responses of a Darcy–Forchheimer EMHD Williamson flow of a Sodium Alginate $({\mathrm{\text{C}}}_6{\mathrm{\text{H}}}_9{\mathrm{\text{NaO}}}_7)$-based Ag-Al₂O₃ hybrid nanofluid passing over a vertically exponentially stretching cylinder emerged through a porous region. The prime focus of this research is to encompass the inclusion of nonlinear variations in heat distribution, Newtonian boundary heating (NBH) effects, and the influence of thermo-convection alongside suction effects. Key parameters, including thermal buoyancy, Darcy porous medium effects, heat source/sink effects, Biot number, variable thermal index, and thermal convection factor, are comprehensively analyzed as these combining factors can play a crucial role in optimizing the efficacy of several systems such as heat exchanger, material processing and geothermal system that involve the concept of thermo-transportation mechanism. The physical flow dynamics are modeled, employing suitable similarity transformations, and subsequently translated into a dimensionless form. The ensuing collection of modified nonlinear ordinary differential equations is solved by employing the Bvp4c solver bundled into the MATLAB program. Several parameters are scrutinized through graphical presentations to elucidate their impacts on the velocity curve, temperature curve, skin friction coefficient, and Nusselt index. It is worth mentioning that the heat distribution profile significantly escalated for the rising values of several factors such as electric field parameter, varying thermal index, Biot number and shape factor, but the reverse is the pattern with suction and thermo-convection effect. Also, the thermal transportation rate at the proximity of the vertical cylindrical wall appears to exhibit an increment of about an average of 47% in SA-based Williamson hybrid nanofluid compared to Williamson fluid for thermo-convective effect, NBH, and thermal buoyancy. Furthermore, the proximate shear stress rate appears to be amplified by approximately 39% in Williamson hybrid nanofluid when contrasted with Williamson fluid for electric field parameter and thermo-convection effect alongside the raised Darcy–Forchheimer factor.