Numerical study of Cattaneo-Christov heat transfer in MHD Carreau-Yasuda hybrid nanofluid subjected to Buoyancy force

Hybrid nanofluids (HNFs) have potentials applications in automotive industry, heating and cooling systems, biomedical and other fields due to their ability to introduce higher thermal conductivity than standard nanofluids. The purpose of this study is to investigate and compare the thermal transport performance (in the presence of buoyancy force) of two sets of HNFs. The hybrid nanoparticles which is the combination of titanium carbide and aluminium oxide, and the combination of titanium carbide-copper oxide are taken into account. Both types of hybrid nanoparticles are dispersed in C2H6O2$C_{2}H_{6}O_{2}$ as a subjective fluid over a vertical nonlinear stretching sheet embedded in a porous medium. This will be the first study on the MXene base material TiC$TiC$ , making it possible for MXene-based materials to enter the fluid dynamics field. Further, MXene material as heat transporting material is studied less and much more is needed for explore its various aspect. The specific combination of Al2O3-TiC$Al_{2}O_{3}-TiC$, and CuO-TiC$CuO-TiC$ is considered because of their promising thermophysical and thermal transport properties. Moreover, considered combination of nanoparticles and the base fluid form a mixture which has thermal relaxation characteristics due to which its deviates from classical Fourier law of heat conduction. Therefore, instead of conventional Fourier's law of heat conduction, the non-Fourier law of heat conduction is used to formulate the energy equation. It is first time that fhe finite element of method (FEM) is used for such a coupled and nonlinear complex problems of computational fluid dynamics (CFD). The numerical and graphical impacts of magnetic fields, Grashof number, permeable parameter, and thermal relaxation time parameter on velocity, and heat transport are investigated by applying FEM on formulated boundary value problems. In each studied system, increasing the Hartmann number causes an increase the skin friction coefficient and a decrease in the Nusselt number. Moreover, by increasing the thermal relaxation parameter, the temperature of the fluid decreases significantly. The velocity of the modified nanofluids is directly proportional to the Grashof number. The thermal boundary layer thickness (TBLT) and momentum boundary layer thickness (MBLT) of Carreau-Yasuda (CY)-HNF (Set II) is greater than CY hybrid nanofluid (CY-HNF) (Set I) and CY-Nanofluid (NF), respectively. We believe that the current research work provides new insights to improve the heat transport of nanofluid using appropriate combination of hybrid nanoparticles for practical application.