**Supercripts**

Bo*m*\* the maximum Jackson buoyancy number under a specified working condition

*c*1, *c*2, *ck* exponents in the empirical correlations (in **Figure 2**)

*cp* average specific heat in the thermal boundary layer

*FVP*1, *FVP*2, *FVP*<sup>3</sup> the modifications on the variable properties for the

*FVPA* the modification on the variable properties for the acceleration-influenced flow *FVPB* the modification on the variable properties for the buoyancy-influenced flow

*h* local heat transfer coefficient (kW m�<sup>2</sup> K�<sup>1</sup>

*Cμ*, *Cμ*<sup>1</sup> the correction coefficients under heat transfer deterioration in the Li and Bai correlation

(=(*Hw* � *Hb*)/(*Tw* � *Tb*)) (J kg�<sup>1</sup> <sup>K</sup>�<sup>1</sup>

*VP*<sup>3</sup> the modifications on the variable properties for the "equivalent" buoyancy-free flow

> �1 )

> > )

)

*kT* the dimensionless number reflecting the expansion of

*m*1, *m*2, *m*4, *n*<sup>2</sup> the exponents in the Jackson's semiempirical model

Pr*<sup>b</sup>* average Prandtl number across the thermal boundary

*X*, *Y* nondimensional parameters in the empirical correlation

)

(in **Figure 2**)

<sup>+</sup> nondimensional distance from the wall

*Y*, *Y*1, *Y*2, *Kh*, *KAm*, *Kqm* constants in the Deev correlation *y* distance from the wall (m)

*λ* thermal conductivity (W m�<sup>1</sup> K�<sup>1</sup>

*β* thermal expansion rate (K�<sup>1</sup>

*μ* dynamic viscosity (Pa s)

*ρ* density (kg m�<sup>3</sup>

)

)

)

)

)

)

Bu Bae and Kim buoyancy parameter

*CA*, *CB*, *Cμ*1, *Cd*, *m*, *n* constants in the Li and Bai correlation *d* inside diameter of the circular tube (m)

real flow

*g* gravitational acceleration (m s�<sup>2</sup>

the fluid

layer Pr*<sup>t</sup>* turbulent Prandtl number *q* wall heat flux (kW m�<sup>2</sup>

*G* mass flux (kg m�<sup>2</sup> s

Gr Grashof number

*H* enthalpy (kJ kg�<sup>1</sup>

Nu Nusselt number *P* pressure (MPa) Pr Prandtl number

*lm* the mixing length (m)

*r* radial coordinate (m) *R* tube radius (m) Re Reynolds number *T* temperature (K)

*f* Fanning resistance coefficient *F*, *F*1, *F*<sup>2</sup> constants in the Cheng correlation

*F*0 *VP*1, *F*<sup>0</sup>

*y*

**84**

**Greek symbols**

*VP*2, *F*<sup>0</sup>

*cp* specific heat (J kg�<sup>1</sup> K�<sup>1</sup>

*Advanced Supercritical Fluids Technologies*


### **Subscripts**

