This research investigates the Couette-Poiseuille flow and heat transfer of Newtonian and Non-Newtonian fluids through a porous parallel microchannel under the combined effects of bottom wall injection, magnetic field and buoyancy force. Some typical base fluid temperatures are utilized to determine the physical properties of two base fluids: water and ethanol-glycol -water mixture. The full two-dimensional Navier-Stokes along with the energy equations for incompressible power-law fluid flow are solved with efficient numerical methodologies: non-uniform grid, staggered grid, finite volume method (and then QUICK scheme for convective terms) and SIMPLE algorithm. Effects of various regulatory flow parameters (top wall movement based Reynolds number, inlet pressure gradient, injection rate, power-law index, Richardson number, Prandtl number and Hartman number) on velocity components, vorticity, streamline, temperature distribution, heat transfer and entropy generation rate are investigated here. An effort is made to make the classical one-dimensional channel Couette-Poiseuille flow to a two-dimensional flow under the influence of aforesaid parameters. Under the different flow situations considered here, our intention is to explore (i) active zone of entropy generation inside the channel and (ii) individual contributions of irreversibilities due to fluid friction, Joule heating and thermal gradient to the total entropy generation for both Newtonian and non-Newtonian fluids.