**4. Conclusions**

*MRE* <sup>¼</sup> <sup>1</sup> *n* X*n i*¼1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� � <sup>s</sup>

*RE*<sup>2</sup> *i*

1 *n* X*n i*¼1

*The errors of the predicted results of different heat transfer correlations. Data in this figure come from Ref. [11]. (a) comparison among Jackson correlation, Bae correlation and Li & Bai correlation; (b) comparison among Morky correlation, Yu correlation, Kuang correlation and Li & Bai correlation; (c) comparison between Cheng*

**Correlation** *MRE***/%** *RMSE***/%** Mokry et al. [9] 44 96 Bae et al. [10] 63 279 Jackson [23] 130 180 Cheng et al. [20] 94 148 Yu et al. [21] 10 163 Kuang et al. [22] 65 113 Li and Bai [11] 27 32

*RMSE* ¼

*Advanced Supercritical Fluids Technologies*

**Figure 8.**

**Table 3.**

**82**

*correlation and Li & Bai correlation.*

*The statistics of the present and existing correlations.*

*REi* j j (48)

(49)

The approach to establishing the heat transfer correlations of supercritical fluids is a critical issue since the correlations play very important role in the design and optimization of the systems and devices. In this chapter, we have discussed the principles and applications of the heat transfer correlations of supercritical fluids. The modeling approaches of the correlations of supercritical fluid heat transfer are reviewed, including the nondimensional parameters applied on the modification of the empirical correlations and the "equivalent buoyancy-free flow method" used for the semiempirical correlations.

Then we introduce a new physically based semiempirical correlation which is based on the momentum and energy conservations in the mixing convective flow. Considering the mechanism of heat transfer deterioration, a physical model characterizing the redistribution of the shear stress under the combined effect of buoyancy and flow acceleration was obtained. Then the model about the heat transfer coefficients under the influence of the reduced shear stress was derived by the energy integration equation within the thermal boundary layer. Based on this, a semiempirical heat transfer correlation was proposed and then verified with a wide range of experimental data. Compared with the existing correlations, the prediction accuracy of this newly developed correlation is significantly improved under the heat transfer deterioration regime. The investigation on the different statistical parameters shows that this semiempirical correlation is superior to the empirical ones.
