Abstarct: Development the heat transfer parameters and incrementing the thermodynamic efficiency for higher and better cooling were made necessary by increasing improvement of industry. Nowadays industry is able to manufacture the system with more swarm of computer chipsets, and so need to new way of cooling due to the productuin of heat at the limited area. The micro-channel and nano-channel heat sink with various surfaces is a good equipment which can be used for cooling. In this study, the steady-state fully-developed laminar flow of non-Newtonian power-law sluids is examined in a circular microchannel without and with slip boundary condition and under an imposed constant wall heat flux and also iso thermal wall temperature. Effects of slip as well as the hydrodynamic and thermal key parameters on heat transfer and entropy generation are investigated. The result reveal that increasing the Brinkman number and the flow behaviour index both lead to increasing the entropy generation and decreasing the Nusselt number. An increase in the slip coefficient leads to an increase in both the Nusselt number and Bejan number, whereas it gives to a decrease in entropy generation. And also the results of this study showed that the pseudo-plastic fluid is more effective in the heat absorption on the surface than of Newtonian and dilatant fluids. It is concluded from entropy generation analysis the the shear thinning fluids has more thermodynamic efficiency that of Newtonian and shear thickening fluids due to less entropy generation.