Nowadays, there is great attention given to solar collectors (SCs) for their important applications based on the advantages of nanotechnology and solar radiation. Hybrid nano°uid (HNF) is our ¯rst option due to its thermophysical properties that help in improving the overall performance, unlike other nano°uids. This paper gives a detailed novel analysis of SCs with the existence of Newtonian, power-law HNF in unsteady conditions and a three-dimensional model under the consideration of Brownian motion and thermophoresis parameter. In this research, the group transformation method (GTM) and similarity transformation steady state °uid dynamics are used to transform the mathematical model into a simpler system. This coupled system of ordinary di®erential equations with the related functions, dimensionless entropy generation and Bejan number is achieved at two cases of power-law index. The impact of involved parameters on velocity pro¯le, temperature distribution, concentration ¯eld, entropy output of the system and Bejan number is depicted prominently by various graphs