Abstarct: Improvement the heat transfer parameters and increasing the thermodynamic efficiency for more and better cooling were made necessary by growing development of industry. Nowadays, industry is able to manufacture the systems with high congestion of computer chips. These setups need to new and helpful method for cooling due to the production of heat in the small surface. The micro-channel heat sink with different surfaces and materials is one of the systems that can be used for cooling in these cases. In this research, a circular micro-channel from a thermal heat sink that is imposed to constant heat flux is evaluated. With considering the Bingham plastic fluid in the micro-channel for surface cooling, the effective parameters on the heat transfer and entropy generation were discussed. The results and different parameters such as improvement of heat transfer and thermodynamic efficiency were also compared with the Newtonian fluid in each section. The results of this study showed that the Newtonian fluid is more effective in the heat absorption on the surface than of Bingham plastic fluids. It is also concluded from the entropy generation analysis that the Newtonian fluid has more thermodynamic efficiency than of Bingham plastic fluids due to less entropy generation which can be considered by the researchers. Moreover, the analysis of the slip liquid flow on the surface channel illustrated that with increasing the slip coefficient of fluid, the fluid capacity to absorb the heat from the surface is increased and the generation of entropy is significantly decreased.