Forced convection heat flow in a cylindrical packed bed is examined numerically. The bed is filled with saturated spherical beads porous media and is exposed to a constant wall heat flux. Besides the energy equation, the generalized from. of the momentum equation including the non-Darcian effects such as the variable porosity, flow inertia, and viscous friction is considered, and the finite difference method is used.
The results have been obtained numerically for sphere beads (3≤ d ≤8 mm diameter), ratio of the particle diameter to the pipe radius 0.05 ≤ D ≤0.5, and nondimensional pressure gradient B up to 108. The non-Darcian effects have a significant influence on the behavior of the temperature, thermal entry length. and Nusselt number across and at the channel wall. The channeling phenomenon near the walls enhanced the thermal communication between the fluid/solid matrix. composite and the walls. This fact yielded an overall 21 percent increase in the value of the Nu in the fully developed region, compared to the value predicted when the Darcy model was used. The results gives complete information about the flow structure and heat transfer for the expressed ranges of parameters. Also, useful correlations reporting the dependence of the thermal entry length on the problem parameters (d, D, B) were reported. A direct dependence of the thermal entry length on Re exists and gives the same correlation that obtained for the pure fluid flow case:
XE ͠= 0.1 Re
To verifY the numerical results a comparison have been done with the numerical results obtained by Poulikakos and Renken [11], Kays and Crawford [26] and Petukhov [27]. The comparison shows a very good agreement for the presented results and proves the validity of the model.