By using the method of Laplace transform, analytical investigations are performed for combined unsteady electroosmotic, pressure driven and magnetohydrodynamic (MHD) flow of an electrically conducting, incompressible and viscous fluid through a slit parallel plate microchannel under the action of a vertical magnetic field. The velocity profiles for different time and their dependence on several non-dimensional parameters are explained graphically. Based upon the velocity field of steady part, the thermally fully developed heat transfer problem are analyzed by taking the viscous dissipation, the volumetric heat generation due to Joule heating effect and electromagnetic couple effect into account. The exact solution of temperature field is derived subjected to constant wall heat flux condition. The dependence of several dimensionless parameters on temperature and the Nusselt number Nu based on channel height is presented graphically. Finally, the entropy generation analysis of MHD heat transfer is performed. The variations of local and global entropy generations with related parameters are interpreted and the results are discussed. (C) 2015 Elsevier Ltd. All rights reserved.