Little is known on the three-dimensional flow of a couple stress Casson fluid conveying nanoparticles when the significance of Lorentz force, chaotic gesture of those minute particles, and thermophoresis are significant. The intent of this investigation is to focus on the flow of such fluid along a horizontal surface due to dual stretching and internal heating. A zero nanoparticle mass flux condition is employed at the surface, which specifies that the nanoparticles’ fraction is submissively measured. The dimensional nonlinear equations are reduced into a system of coupled nonlinear ordinary differential equations by employing scaling analysis and later they are solved numerically. The results are discussed graphically for various emerged physical parameters through different plots. The results in the absence of stretching ratio factor indicate that the heat absorption parameter and Prandtl number accelerate the heat transfer rate. The temperature of the non-Newtonian couple stress fluid is found to be higher than that of viscous case. It may be suggested that the Casson couple stress nanofluid can be substituted for the corresponding viscous fluid in industrial applications for greater heat transfer. The outcomes are closely matched with the studies available in the literature as a limiting case.