Fitting a Correlation Clause Samples

Fitting a Correlation. The closure model is formulated in the form of a correlation for the particle-based Nusselt number. This correlation is derived from a refitting of the widely used ▇▇▇▇ correlation (▇▇▇▇, 1978), which is valid for a mono-disperse bed of particles. The refitting is done by changing three coefficients of the ▇▇▇▇ correlation, similar to the approach chosen by Deen et al. (2014). Thus, the original ▇▇▇▇ correlation is re-written in the form: − (7 − 10 + 52) = 0.2 (7 − 10 + 52) + 0.7(1.33 − + 2) 1/3 0 2 The three coefficients (0, 1, 2) are obtained by fitting the particle-based Nusselt number calculated from fully resolved simulations. For the data shown in Figure 7, we obtain 0 = 1.118 1 = −2.066 2 = 1.197 It is worth to notice that ▇▇▇▇ (1978) obtained the following coefficients instead: 0 = 0.7 1 = −2.4 2 = 1.2, while Deen et al. (2014) obtained the coefficients: 0 = 0.17 1 = −2.31 2 = 1.16