In the last two decades, many researchers have concentrated on the nanofluid boundary-layer flow over a stretching/shrinking surface. The hybrid nanofluid flows have vast applications and therefore it is necessary to study them under various physical conditions. The present model deals with the flow of MoS2–SiO2/water hybrid nanofluid over a stretching/shrinking surface. The model is developed assuming the presence of Darcy–Forchheimer porous medium; and space- and temperature-dependent heat source/sink. In addition to the linear thermal radiation effect, heat-transfer rate with quadratic thermal radiation effect is also studied, to focus on systems with high temperature differences. The prevailing partial differential equations depicting the modeled problem with the aforementioned effects are transformed via similarity transformations and solved via the “bvp4c” function, which is accessible by MATLAB software. The present numerical results are validated through a comparison with published literature and “bvp5c” and Runge–Kutta–Fehlberg-shooting technique (RKF-shooting technique). The heat-transfer coefficient is seen higher for quadratic thermal radiation than for linear thermal radiation. The streamlines pattern are seen to be curved outside and inside, for stretching and shrinking sheet, respectively. Furthermore, the presence of a magnetic field has a thinning consequence on the velocity boundary-layer region. The results of this study apply to several thermal systems, engineering, and industrial processes, which utilize nanofluid for cooling, and heating processes. © 2022 Begell House Inc.. All rights reserved.