<p>The advanced cooling technologies, biomedical engineering and in different energy systems heat transfer presents its pivotal role. In this regard, micropolar fluid has a significant contribution due to its vast applications. The present study explores the free convection behavior of a micropolar hybrid nanofluid, using water as the base liquid and incorporating diamond and copper as the solid nanoparticles. Additionally, the thermal relaxation effect is accounted for by the inclusion of Cattaneo-Christov heat flux in the energy equation and the impact of Darcy-Forchheimer inertial drag with an irregular heat sink/source. In particular, the non-Newtonian behavior with rotational effect and Couple stress is crucial for the flow in micropolar fluids is highly relevant for applications in cooling systems for microelectronics. The dimensional complex system is converted into a corresponding non-dimensional form with a suitable choice of similarity rules. The flow profiles equipped with different phenomena are solved utilizing the spectral quasi-linearization method. The effective properties of several contributing factors likely, micropolarity, thermal relaxation, magnetic, porosity, inertial drag, particle concentration, non-uniform heat source/sink, etc. are presented through graphs and elaborated via validation and convergence of the methodology used in this article. The results highlight the interaction between thermal relaxation and micro-channel effects demonstrating heat transfer capabilities of the hybrid nanofluid. Further, the heat transfer rate enhances for the higher thermal radiation and the impact is reversed for the enhanced heat source along with thermal relaxation parameter.</p>