Soret-Dufour driven unsteady MHD bioconvective tetra-hybrid nano-additives over rotating disks with varying thermophysical property

• The tetra-hybrid nanofluid, which combines four nanoparticles, Al 2 O 3 - Cu- SiO 2 -TiO 2 is investigated to enhance thermal and rheological properties for industrial applications. • Al 2 O 3 and Cu are chosen due to their high thermal conductivity and SiO 2 and TiO 2 for their stabilizing effects. • Dufour and Soret effects helps to understand how temperature and concentration gradient are related. • The magnetic field combined with the porous medium enhances control over fluid flow and heat transfer by introducing electromagnetic forces and affecting permeability. • The fluid is passing through rotating disk which helps in better mixing and improves the convective heat transfer by generating centrifugal forces. • Furthermore, flow and heat transfer estimates are more accurate when temperature-dependent variations in viscosity and thermal conductivity are taken into account • The Akaike Information Criterion and Bayesian Information Criterion are performed for evaluating and selecting the optimal model. Tetra-hybrid nanofluid has major significant due to their advancement in thermal and physical properties. By combining four distinct nanoparticles into base fluid, tetra-hybrid nanofluids exhibit enhanced thermal conductivity, heat transfer efficiency and stability compared to traditional and di- or tri-hybrid nanofluids. The present study investigates the magnetohydrodynamic behavior of an unsteady tetra-hybrid nanofluid past a permeable rotating disk incorporating gyrotactic microorganisms, multiple slip boundary conditions, Soret-Dufour effects and variable viscosity and thermal conductivity. It gives new insights into the factors of these effects on boundary layer, skin friction and Nusselt number, with practical implications for improving thermal management systems while filling gaps not thoroughly investigated in prior studies. The fifth-order Runge-Kutta Fehlberg method in conjunction with shooting technique is used to solve the non-linear ordinary differential equations. It is established that the increase in porosity parameter decreases the velocity profile and increase in Soret number increases the temperature profile. It also found that skin friction decreases by 35 % with increase in variable viscosity parameter and Nusselt number increases by 11 % and 32 % with increase in nanoparticle volume fraction and thermal conductivity parameter respectively. The different distribution models are used for physical quantity data to find the best fit and it was found that the Weibull distribution is suitable for present study. This study helps in understanding the tetra-hybrid nanofluid dynamics by offering a basic for developing efficient solutions in advanced technologies with applications in biomedical engineering, cooling mechanism, wastewater treatment and heat exchangers.