In this article investigation has been conducted on the effects of Hall parameter, rotation parameter and Joule heating on the entropy generation of fully developed electrically conducting Poiseuille flow. The coupled system of ordinary differential equations for the flow are obtained, non-dimensionalised and solutions are constructed by Adomian decomposition technique. The effects of Hall current, Ion-slip, Joule heating and magnetic parameters on the velocity, temperature, entropy generation and Bejan number are explained and shown graphically. The results indicate that fluid entropy generation is induced by increase in Hall current, rotation and Joule heating parameters. Furthermore Bejan number is accelerated by Hall current, rotation, Magnetic and Joule heating parameters which signifies that heat transfer irreversibility dominates entropy generation.