A finite difference numerical approach for solving slightly compressible, time-dependent, viscous laminar flow is presented in this study. Simplified system of Navier-Stokes equations and energy equation are employed in the study in order to perform more efficient numerical calculations. Fluid flow and heat transfer phenomena in two dimensional microchannels are illustrated numerically in this paper. This numerical approach provides a complete numerical simulation of the development of the fluid flow and the temperature profiles through multi-dimensional microchannels.

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