A mathematical model is developed that predicts three-dimensional, two-phase flow with heat transfer and chemical reaction inside catalytic cracking riser-type reactors.The model consists of the full set of partial-differential equations that describe the conservation of mass, momentum, energy and concentration of chemical species for both phases in the reactor, coupled with empirical correlations concerning interphase friction, interphase heat-transfer and fluid-to-wall frictional forces. The cracking reaction is simulated by a three-lump kinetic model, although this does not represent a limitation of the model.The model can predict the most important engineering design parameters of a riser reactor including pressure drop, catalyst holdup, interphase slip velocity, catalyst acceleration zone, choking behaviour, temperature distribution in both phases and yields distribution all over the reactor.It can also analyse geometry effects, especially in the complex feed injection area, where the cracking reactions are initiated.Τους γονείς μου για την ηθική τους υποστήριξη και τους συναδέλφους μου μεταπτυχιακούς φοιτητές για το ευχάριστο και φιλικό κλίμα που διαμορφώσαμε στο Εργαστήριο Υπολογιστικής Ρευστοδυναμικής.Τέλος θα ήθελα να ευχαριστήσω τη σύντροφο της ζωής μου Νάσια για την αμέριστη συμπαράσταση της, χωρίς την οποία δε θα ήταν δυνατή η ολοκλήρωση της διατριβής αυτής.