We thank Dr. Yu for his discussion on two papers 1,2 of ours on thermal dispersion in porous media that appeared in the Journal of Heat Transfer. Dr. Yu rewrites our correlations established performing a series of numerical experiments as follows:
Like these expressions, our expressions (0) and (0) fail as the porosity approaches unity. They may also fail under the other limiting condition, namely, since the permeability–porosity relationship is different there. The porosity range in which our correlations are valid may be judged by reexamining Fig. 8 in our paper 1, where the coefficients are plotted against the abscissa variable to find possible correlations. The errors become large as the porosity approaches zero. Also, in the range close to the origin (i.e. , the coefficients reduce to values too small to elucidate a functional relationship. Thus, we presume that our correlations given by (0), (0), (0) and (0) are valid only for a limited porosity range, say, It should also be noted that neither (0) nor (0) can be used beyond this range, since neither of them has been designed to account for the asymptotic behavior that Dr. Yu presumed in his discussion.
As in Figs. 9 in Ref. 1 and Fig. 4 in Ref. 2, the high Peclet number correlations are found in good accord with available experimental data. This substantiates the validity of our correlations. However, sufficient experimental data are not available for the low Peclet number range with which Dr. Yu is mostly concerned. For this range, we simply repeat that the correlations are consistent with those for packed beds reported by Koch and Brady 3.