The advancement of heat transportation is a significant phenomenon in nuclear reactors, solar collectors, heat exchangers, and electronic coolers; and it can be accomplished by choosing a nanofluid as the functional fluid. Nanofluids have improved thermophysical properties, due to their great progress in engineering and industrial applications. Therefore here, the significance of exponential space‐related heat source (ESHS) on radiative heat motivated Sakiadis two‐phase flow over a moving plate is analyzed for a particulate nanoliquid (CuO–H2O). The impact of the haphazard motion of nanoparticles is analyzed through the Koo–Kleinstreuer–Li model. On applying a similarity transformation to the governing equations, a set of ordinary differential equations is obtained and numerically solved. Through the perception of graphs, the behavior of the velocity and temperature constraints for diverse values of effective parameters is decoded. The results show that the temperature of both phases (dust and fluid) improves with the ESHS aspect. Also, the heat transport rate/friction factor enhances/declines with the concentration of dust particles.