In this paper, we present a theoretical study of flow and heat transfer by transient fret convection in a vertical cylinder filled with granular product. The cylinder is opened at the extremities and heated with uniform heat flux density. Two models are used : two-temperatures model and one-temperature model. The mathematical models are solved numerically by the method of finite domains. The numerical simulation has allowed us to determine the time-space evolution of temperatures and pressure. In order to test the validity of the one-temperature model and thus the validity of the local equilibrium hypothesis we have made two types of comparisons : comparison between local values of solid temperature and fluid temperature obtained by the two temperatures model; and comparison between the values obtained by the two models of outlet convected heat flux and outlet flow rate of fluid.