Two cases of the transient conjugate heat transfer in fluid-particle systems are analysed. The first refers to the single rigid spherical particle at particle Reynolds numbers greater than one. The subject of the second is the assemblages of rigid spherical particles at low particle Reynolds numbers, i.e. Re less than or equal to 20. In this case the classical cell models are used to describe the hydrodynamics. In both cases the momentum and the heat balance equations are solved numerically. The velocity field is assumed to be steady, axisymmetric and laminar. The finite difference methods are used for discretization. The single particle problem is solved for Re = 10 (50), Re = 100.0, and a wide domain of variation of the conductivity and volume heat capacity ratios. Simulation results reveal that the conductivity and heat capacity ratios affect the heal transfer remarkably. For the particle assemblages, the analysis is focused on the specific problems of the interphase heat transfer in packed beds at low Peclet numbers. The results show that the theoretical predictions of the unsteady conjugate heat transfer in cell models are not a good description of the packed bed experimental data. (C) 1997 Elsevier Science Ltd.