Fully developed mixed convection flow in an open-ended vertical parallel plate microchannel is theoretically examined by using a perturbation series method. Asymmetrically or symmetrically applied uniform heat fluxes are assumed to apply at channel walls. The analysis included viscous dissipation in the fluid as well as the velocity slip and the temperature jump at the wall. The effects of mixed convection parameter, Knudsen number, Brinkman number and ratio of wall heat fluxes on the Nusselt number. It is disclosed that increasing the mixed convection parameter decreased Nu for the macroscale case while it increased Nu for the microscale case. It is also disclosed that increasing rarefaction decreases the effect of viscous dissipation on the Nusselt number. (C) 2017 Elsevier Ltd. All rights reserved.