The objective of this article is to explore the thermosolutal transmission rates with hydromagnetic Fe3O4-H2O nanofluid and Fe3O4-Cu-H2O hybrid nanofluid flow in a partially heated wavy porous enclosure with a plus-shaped baffle. A portion of length b on the bottom border is heated and soluted uniformly, while the rest portions of the bottom wall are assumed as adiabatic. The side curved borders are considered as cold and low concentration, while the adiabatic condition is imposed in the upper flat border. A plus-shaped cold baffle is located at the geometric center of the chamber. The porous cabinet is filled with a radiative Fe3O4-H2O nanofluid and Fe3O4-Cu-H2O hybrid nanofluid. The streamfunction (ψ)- vorticity (ζ) form incorporating the energy and species transport equations of coupled Navier-Stokes governing equations are solved by an efficient compact scheme. We have validated our in-house computational code with reliable published numerical and experimental works. This work explores the impacts of various well-defined parameters such as Rayleigh number (104≤Ra≤106), Hartmann number (0≤Ha≤40), Darcy number (10−4≤Da≤10−2), buoyancy ratio (N=1), Lewis number (1≤Le≤20), radiation parameter (1≤Rd≤10), heater size (0.2≤b≤0.8), volumetric heat source/sink coefficient (−10≤Q≤10) and solid volume fraction (0.0≤ϕhnp≤0.04) of the hybrid nanofluid. We have found that for the change in the radiation parameter (Rd) from 1 to 10, energy transfer is improved by 150.67% for Fe3O4-Cu-H2O hybrid nanofluid and 149.80% for Fe3O4-H2O nanofluid whereas solutal transfer is diminished by 4.76% and 4.83%, respectively. Our result revealed that Fe3O4-Cu-H2O hybrid nanofluid is more useful than Fe3O4-H2O nanofluid in the case of double diffusion.