This numerical study has been carried out by developing two-phase mixture model with conjugate heat transfer. Pure and hybrid nanofluids (HyNF) with particle as well as base fluid hybridization are used in analyzing the performance of microchannel under forced convection laminar flow. The flow as well as heat transfer characteristics of pure water, copper (Cu), aluminum (Al), single-walled carbon nanotube (SWCNT), and hybrid (Cu + Al, water + methanol) nanofluids with various nanoparticle volume concentrations at different Reynolds numbers are reported. Sphericity-based effective thermal conductivity evaluation is considered in the case of SWCNT nanofluids by using volume and surface area of nanotubes. A significant enhancement in the average Nusselt number is observed numerically for both pure and hybrid nanofluids. Pure nanofluids such as Al, Cu, and SWCNT with 3 vol % nanoparticle concentration enhanced the average Nusselt number by 21.09%, 32.46%, and 71.25% in comparison with pure water at Re = 600. Whereas, in the case of hybrid nanofluids such as 3 vol % HyNF (0.6% Cu + 2.4% Al) and 3 vol % SWCNT (20% Me + 80% PW), the enhancement in average Nusselt number is observed to be 23.38% and 46.43% in comparison with pure water at Re = 600. The study presents three equivalent combinations of nanofluids (1 vol % Cu and 0.5 vol % SWCNT), (2 vol % Cu, 1 vol % SWCNT and 3 vol % HyNF (0.6% Cu + 2.4% Al)) as well as (2 vol % SWCNT and 3 vol % SWCNT (20% Me + 80% PW)) that provides a better switching option in choosing efficient working fluid with minimum cost based on cooling requirement. The study also shows that by dispersing SWCNT nanoparticles, one can enhance the heat transfer characteristics of base fluid containing methanol as antifreeze. The conduction phenomena of solid region cause the interface temperature between solid as well as fluid regions to increase along the length of the microchannel. The developed numerical model is validated with the numerical and experimental results available in the literature.