The suspension of nanoparticles in fluid influences several properties of the resulting fluid. Many production and manufacturing applications need knowledge of the heat transference mechanism in nanofluids. The current paper concerns the influence of non-uniform heat source/sink on (MoS2-Go/water flow) hybrid nanofluid flow and (Go/water flow) nanofluid flow in a Darcy-Forchheimer porous medium between two parallel and infinite spinning disks in the occurrence of radiation. The Cattaneo-Christov model is utilized to analyze heat and mass transmission. The Cattaneo-Christov model introduces the time lag factors in the process of heat and mass transmission, known as the thermal relaxation parameter and solutal relaxation parameter, respectively. The governing equations are numerically solved employing the “bvp4c function in MATLAB.” The effect of the primary relevant parameters on the velocity, temperature, nanoparticle concentration, and is graphically depicted. Finally, a table is drawn to show the relationships of various critical factors on the Nusselt number, and Sherwood number. Results reveal that an increase in the thermal relaxation parameter reduces the heat transmission rate at both the upper and lower plate. Furthermore, an increase in the nanoparticle’s volume fraction causes enhancement in thermal conduction, which increases the heat transmission rate at the upper disk. The results of this study will be helpful to many transportation processes, architectural design systems, enhanced oil recovery systems, medical fields that utilize nanofluids, and so on.