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

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