  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.
