Finite element analysis of modified N-S equations coupled with energy transfer for Hybrid Nanofluid flow in complex domains

Abstract: A theoretical and computational finite element study of modified Navier-Stokes Equations coupled with energy conservation governing the flow and heat transfer in complex domains with hybrid nanofluid$(HNF)$ is carried out. The apriori error estimates providing the convergence analysis for the finite element scheme is derived in the $H^1$ norm. A detailed parametric analysis on the physics related to flow and heat tranfer for different governing parameters such as: hybrid nano-particle volume fraction $(\phi),$ Rayleigh Number $(Ra)$, Prandtl Number$(Pr)$, and the length of heat source has been reported. The use of hybrid nano-particles leads to the enhancement of heat conduction both in L and H shaped domains. While a butterfly flow pattern with a multi-cellular structure is noticed in H-shaped domain, the flow in L-Shaped domain depicts a boundary layer feature with primary, secondary and tertiary co-rotating and counter rotating cells.