An electrically conducting and magnetically influenced three-dimensional flow of modified nanofluid between two rotating disks is investigated in this study. Nanometer-size particles of two distinct materials (Al2O3, Ag) suspended in water in the hybrid nanofluid are considered. The Joule heating effects, mixed convection, chemical factor, and exponential heating are considered in this study. The physical problem under these assumptions is transformed into a system of equations. To convert partial differential equations (PDEs) into systems of ordinary differential equations (ODEs), the suitable similarity variables are introduced. The reduced system is numerically solved using bvp4c, a well-known higher-order algorithm. The effects of significant variables on the profiles of velocity, temperature, and concentration are depicted graphically. We have chosen the pertinent parameters in the specific intervals; [Formula: see text][Formula: see text][Formula: see text][Formula: see text][Formula: see text], [Formula: see text][Formula: see text][Formula: see text] and [Formula: see text]. The interactions between a number of significant factors, including skin friction and Nusselt and Sherwood numbers at the higher and lower disks, are shown in tables. The results demonstrate that the local skin fraction decreases as the mixed convection factor is increased, which physically increases the heat transmission rate between the two discs. Furthermore, as the magnetic field and radiation number rise, the rate of heat transfer at the lower and top discs decreases. The numerical results in the form of a table are compared with the available literature, and our results beat the previously published work. The results described here are desirable choices for thermal uses such as automotive cooling systems, solar thermal systems, engineering, medical areas, heat sinks, or current energy storage since they have demonstrated higher thermal characteristics and stability than simple nanofluids (NFs). In Table 6, a comparative numerical study is presented for the various of state variables with the available literature, where the present study is validated.