The present mathematical model discloses the effects of Boussinesq and Rosseland approximations on unsteady 3D dynamics of water-driven hybridized nanomaterial with the movements of nanoplatelets (molybdenum disulfide,
MoS
2
and graphene oxide,
GO
). Variable thermal conditions, namely, VST (variable surface temperature) and VHF (variable heat flux), are opted to provide temperature to the surface. MHD effects have also been used additionally to make the study more versatile. In order to transmute the transportation equations into nondimensionlized forms, similarity transformations have been adopted. The Keller-Box technique has been applied to obtain a numerical simulation of the modeled problem. The convergence of the solution for both VST and VHF cases is presented via the grid independence tactic. Thermal setup against escalating choices of power indices and nonlinear thermal radiation parameter is discussed via graphical illustrations. The rate of heat transaction has been discussed with the growing choices of mixed convection, thermal radiation, and unsteady parameters through various tabular arrangements. It is observed through the present analysis that mixed convection parameter, radiation parameter, temperature maintaining indices
r
,
s
, and unsteady parameter magnify the rate of heat transference under the control of platelet-shaped nanoparticles.