Laminar forced convection flow of nanofluids in a rectangular micro-channel has been numerically studied. The study is carried out to investigate the flow and heat transfer characteristics of hybrid single walled carbon nanotube (SWCNT) and Copper (Cu) nanofluid in a micro-channel. Hybridization of SWCNT and Cu nanoparticles are varied with different proportions such as 50%-50%, 70%-30%and 30%-70%using sphericity based effective thermal conductivity evaluation. A two-dimensional multiphase mixture model has been developed and the effects of Reynolds number, nanoparticles mixture volume concentration on the flow and heat transfer characteristics of hybrid (SWCNT+Cu) nanofluids are reported. The accuracy of present numerical model has been validated with the experimental and numerical results available in the literature. The results show that the average convective heat transfer coefficient increases with increase in Reynolds number. It is also observed that 1 vol.%hybrid nanofluid (0.7 vol.%SWCNT+0.3 vol.%Cu) significantly enhances the average convective heat transfer coefficient than that of pure water. Moreover, the multiphase mixture approach showed better enhancement in terms of heat transfer when compared with single phase homogenous model. The study concludes that hybrid nanofluids with suitable volume concentration of carbon (SWCNT) nanoparticles can be used as modern working fluid based on cooling requirement. Further, hybridizing nanoparticles at higher volume concentrations will minimize the working fluid cost and also enhances the heat transfer characteristics in comparison with pure metal based nanofluids.