**5. Conclusion**

A three-dimensional mathematical model, developed using incompressible laminar Navier-Stokes equations of motion, is capable of predicting correctly the flow and conjugate heat transfer in the microchannel heat sink. The microchannel heat sink model consists of a 10 mm long silicon substrate, with rectangular microchannels, 57 µm wide and 180 µm deep, fabricated along the entire length. A finite volume numerical code with a multigrid technique, based on additive correction multigrid (AC-MG) scheme, that is a highperformance solver, was developed to solve the steady incompressible laminar Navier– Stokes (N-S) equations, over a colocated Cartesian grid arrangement. Higher Reynolds numbers are beneficial at reducing both the water outlet temperature and the temperatures within the heat sink, also at the expense of greater pressure drop. By the magnitude of the mean velocities and the Reynolds numbers obtained from the analytical and numerical methods, the agreement between the two methods is quite good and provides sufficient evidence for validation of the numerical method. The variations of the heat transfer coefficient and the Nusselt number along the flow direction is quite small for this type of microchannel heat sink after the thermal entrance lengths. The heat flux along the channel side walls is higher than along the channel top and bottom walls (almost two orders of magnitude larger than those at the top and bottom walls) due to the short distance between the channel side walls and the large velocity gradient present. The temperature is highest at the channel corner; this is due to the low velocity of the flow and the resulting high concentration of heat flux. The results indicate that the thermophysical properties of the liquid can significantly influence both the flow and heat transfer in the microchannel heat sink. The bulk liquid temperature is shown to vary in a quasi-linear form along the flow direction for high fluid flow rates, but not for low flow rates (low Reynolds number).
