The flow and heat transfer induced by an exponentially shrinking sheet with hybrid nanoparticles are investigated comprehensively in this paper. Nanoparticles are considered due to their unusual characteristics such as extraordinary thermal conductivity, which is significant in advanced nanotechnology, heat exchangers, material sciences, and electronics. The main objective of this research is to enhance heat transportation. The flow model is first transformed and simplified to a system of ordinary differential equations utilizing non-dimensional quantities and similarity functions. Then, the desired system is solved with the help of the Runge–Kutta numerical method and the shooting technique in MATLAB script. The results show that a stronger porosity parameter raises the temperature while diminishing the velocity. Additionally, they emphasize that augmentations in the magnetic parameter, Eckert number, radiation parameter, and the volume fractions of titanium dioxide and silver nanoparticles are all proportional to the temperature profile.