Continuum models for the role of the interstitial fluid with respect to mass and heat dispersion in a fixed bed are discussed. It is argued that the departures from local equilibrium and not the concentration and temperature gradients as such should be considered dispersion in the fluid flowing through a packed bed. An essential feature of the model is that mass and heat dispersion flux vectors are taken to be state variables additional to concentration and temperature; their values characterize the departures from local equilibrium. The differential equations for the dispersion model are of the hyperbolic type and they require fundamentally different boundary conditions compared to the usual conditions for the conventionally used diffusion type models. The new model avoids the physical drawbacks inherent to the diffusion models. It provides a new physical interpretation of the scatter in point temperature measurements and of the temperature drop observed near the reactor wall under conditions of heat transfer through the wall. A part of the temperature drop and the temperature scatter are direct consequences of the macroscopic local thermal nonequilibrium state of the fluid. The results predicted by the new model and diffusion model are essentially equivalent in case of slow processes in reactors with large tube-to-particle diameter ratios. Otherwise the diffusion model does not have a solid physical basis and may not be valid for predictive purposes because of the influence of chemical reaction on the transport parameters.