**Appendices and nomenclature**


Bo*m*\* the maximum Jackson buoyancy number under a specified working condition Bu Bae and Kim buoyancy parameter *c*1, *c*2, *ck* exponents in the empirical correlations (in **Figure 2**) *cp* specific heat (J kg�<sup>1</sup> K�<sup>1</sup> ) *cp* average specific heat in the thermal boundary layer (=(*Hw* � *Hb*)/(*Tw* � *Tb*)) (J kg�<sup>1</sup> <sup>K</sup>�<sup>1</sup> *Cμ*, *Cμ*<sup>1</sup> the correction coefficients under heat transfer deterioration in the Li and Bai correlation *CA*, *CB*, *Cμ*1, *Cd*, *m*, *n* constants in the Li and Bai correlation *d* inside diameter of the circular tube (m) *f* Fanning resistance coefficient *F*, *F*1, *F*<sup>2</sup> constants in the Cheng correlation *F*0 *VP*1, *F*<sup>0</sup> *VP*2, *F*<sup>0</sup> *VP*<sup>3</sup> the modifications on the variable properties for the "equivalent" buoyancy-free flow *FVP*1, *FVP*2, *FVP*<sup>3</sup> the modifications on the variable properties for the real flow *FVPA* the modification on the variable properties for the acceleration-influenced flow *FVPB* the modification on the variable properties for the buoyancy-influenced flow *g* gravitational acceleration (m s�<sup>2</sup> *G* mass flux (kg m�<sup>2</sup> s �1 ) Gr Grashof number *h* local heat transfer coefficient (kW m�<sup>2</sup> K�<sup>1</sup> *H* enthalpy (kJ kg�<sup>1</sup> ) *kT* the dimensionless number reflecting the expansion of the fluid *lm* the mixing length (m) *m*1, *m*2, *m*4, *n*<sup>2</sup> the exponents in the Jackson's semiempirical model Nu Nusselt number *P* pressure (MPa) Pr Prandtl number Pr*<sup>b</sup>* average Prandtl number across the thermal boundary layer Pr*<sup>t</sup>* turbulent Prandtl number *q* wall heat flux (kW m�<sup>2</sup> ) *r* radial coordinate (m) *R* tube radius (m) Re Reynolds number *T* temperature (K) *X*, *Y* nondimensional parameters in the empirical correlation (in **Figure 2**) *Y*, *Y*1, *Y*2, *Kh*, *KAm*, *Kqm* constants in the Deev correlation *y* distance from the wall (m)

)

*δ* thermal boundary layer thickness (m)

wall units *θ* nondimensional excess temperature *φ* the constant in the Li and Bai correlation *ψ* the functional expression for the acceleration-

*τ* shear stress (Pa)

*Heat Transfer Correlations of Supercritical Fluids DOI: http://dx.doi.org/10.5772/intechopen.89356*

*T* transpose matrix

*B* buoyancy effect

*F, f* forced convection

*pc* pseudo-critical point *w* values at the wall

*l* definition based on the local values

*b* bulk value *max* maximum

*t* turbulence

Fangbo Li, Binbin Pei and Bofeng Bai\*

provided the original work is properly cited.

\*Address all correspondence to: bfbai@mail.xjtu.edu.cn

*A* flow acceleration effect

**Supercripts**

**Subscripts**

**Author details**

**85**

University, Xi'an, China

*δ*<sup>+</sup> nondimensional thermal boundary layer thickness in

*ave* average value over the thermal boundary layer

*BA* combined effect of the buoyancy and flow acceleration

State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

influenced or buoyancy-influenced heat transfer

)

)

### *y* <sup>+</sup> nondimensional distance from the wall

## **Greek symbols**


*Heat Transfer Correlations of Supercritical Fluids DOI: http://dx.doi.org/10.5772/intechopen.89356*

