This study concentrates on heat transmission and momentum in the hydromagnetic flow of hybrid nano-dusty fluid over the thermal plate with radiation, Newtonian heating wall conditions, and heat sink/source. The outcome of this investigation finds application in wastewater management, groundwater treatment, soil remediation, magnetic separation, air pollution, biomedical diagnostics, continuous casting, and environmental engineering. MAPLE Software is used to solve flow-controlling equations numerically. The influence of physical parameters on the dust and fluid phases due to uniform lifting and sudden lifting of the thermal plate are compared by preparing graphs and tables. The obtained outcomes are validated. This study concludes that the fluid velocity and temperature are more significant in uniform lifting than the sudden lifting of the thermal plate. An increase in particle concentration, magnetic field, particle relaxation time, and porosity parameter results in growth in shearing stress with time. The fluid phase has a higher flow velocity and temperature than the dust phase. The temperature field is more in the fluid phase than the dust phase and is augmented with nanoparticle enhancement.