<p>In the contemporary context, the demand for efficient and effective products is crucial, particularly those reliant on non-Newtonian characteristics and the presence of solid nanoparticles. The ongoing investigation aims to elucidate the impact of dissipative heat in the Williamson hybrid nanofluid flow through two parallel microchannels embedded in a permeable medium. The fluid, being electrically conductive, is enriched with carbon nanotube (CNT) nanoparticles, examining the combined effects of single-wall carbon nanotube (SWCNT) and multi-wall carbon nanotube (MWCNT) on flow dynamics. However, these are useful in several applications such as advanced cooling in electronic devices and high-performance computing systems, designing microchannel-based biomedical devices, solar thermal collectors and microreactors, cooling of microelectronics, etc. The formulated model is simplified through appropriate transformation rules, and it is noteworthy that the analytical solution is derived using the differential transform method (DTM). The study presents a visual representation of the significant factors in the problem, while the simulated rate coefficients are detailed in a table. Ultimately, the key findings underscore the role of dissipative heat, as indicated by the Eckert number, in enhancing the heat transport phenomenon. Additionally, the concentrations of CNT nanoparticles impede both shear and heat transmission rates, influenced by the combined effects of magnetisation and permeability.</p>