Optimization of heat transfer in bi-directional flow of sodium alginate-based ternary hybrid nanofluid over an extending heated surface with velocity slip conditions

The analysis of three-dimensional trihybrid nanofluid flow on a stretchable sheet using variable porous medium and diverse nanoparticles (Cu, CuO, Al₂O₃) in a sodium alginate base fluid has many applications in augmenting thermal transfer processes across numerous engineering systems like optimization of thermal management in electronic components, industrial heat exchangers and energy conversion systems. The inclusion of velocity slips and convective heat transfer has many applications in advanced thermal systems in aerospace, renewable energy and automotive sectors efficient heat dissipation in critical. Therefore, in this article, three-dimensional flows of a ternary hybrid nanofluid flow on a stretchable sheet using variable permeable medium. The velocity slip conditions along with convective thermal transportation are also considered in this article along with thermal radiation and heat source. The present analysis is endorsed with the earlier published results by which the validation of present model and applied technique are confirmed. The results of the current investigation demonstrate that a higher magnetic factor boosted the thermal distribution, while reducing the primary and secondary velocity distributions. A higher Casson factor improved both the primary and secondary velocities. Higher velocity slip factors lowered the primary and secondary velocities. The increased thermal Biot number, thermal radiation parameter improved thermal dispersion. The greater the thermal Biot number, radiative and heat source factors, the higher the thermal transfer rate.