The laminar forced convective heat transfer in plane microchannel has been investigated numerically. The parallel plates making the boundaries are kept at constant, but different temperatures, which differs from the literature available. The heat transfer in plane Microchannels exposed to a thermal asymmetry are useful to improve the heat dissipation of electronic devices and give a good guidance for the size of the microchannel or nanochannel. The energy equation is solved by separation of variables. Velocity slip condition, temperature jump condition, axial heat conduction are included. The analytical expressions of temperature field and Nusselt number are achieved. Simulation of heat transfer in parallel plates is conducted and it is reveled that in the fully developed region the Nusselt numbers become one. The plane microchannel has larger ability of heat transfer in the thermal entrance region; The length of the entrance increases with the Peclet number. In developing region, the Nusselt numbers of the bottom wall become zero and might experience discontinuities thereby jumping from one to infinite negative. The results when we set the wall symmetry temperature is in good agreement with the results of the classical theory which the Nusselt numbers become 7.54.
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