Numerical study of non-darcy forced convection in a packed bed saturated with a power-law fluid

The objective of the present work was to perform a detailed numerical study of laminar forced convection in a channel packed with an isotropic granular material and saturated with a power-law fluid. Hydrodynamic and heat transfer results are reported for the configuration in which the channel walls are isothermal. The flow in the porous medium was modeled using a modified Brinkman-Forchheimer-extended Darcy model for power-law fluids, which takes into account the non-Darcy effects of inertia and boundary as well as the effects of variable porosity and thermal dispersion. Parametric studies were conducted to study the effects of particle diameter, power-law index, and Reynolds number. The results indicate that as the particle diameter decreases or as the power-law index decreases, the velocity and temperature gradients near the wall increase, which leads to an increase in Nusselt number, and these effects are enhanced as the Reynolds number increases; i.e., when the inertia and thermal dispersion effects become significant. The effects of particle diameter are more pronounced for large particle diameter (D_p > 0.01), whereas the effects of power-law index are more significant for shear-thinning fluids (n < 1). Finally, the increase in pressure drop in the channel due to the presence of the porous medium was found to be more significant with shear thickening fluids (n > 1).