Gnielinski Combo

Description

A duct flow correlation that accounts for laminar and turbulent flow. This correlation is like the Gnielinski combo correlation found in tube elements, but the correlation described in this section can also be applied to convectors that are not associated directly to tube elements.

Type: Mixed Laminar-Turbulent Duct Nu
Subtype: Gnielinski Combo

Table 1. Input List
Index	UI Name (.flo label)	Description
1	Flow Element (FLOW_ELM)	ID for flow element that is used for the mass flow rate and other correlation inputs. If AUTO, the correlation must be applied to a convector that is connected to a fluid chamber that has only 1 flow element entering this chamber. The ID of this flow element is used. The element can be of almost any type although some types do not have geometric inputs that can be obtained with the AUTO option of the remaining inputs.
2	Hydraulic Diameter (HYD_DIA)	Passage hydraulic diameter. If AUTO, the hydraulic diameter of the flow element from input 1 is used.
3	Flow Area (FLOW_AREA)	Passage flow area. If AUTO, the area of the flow element from input 1 is used. If the area from the flow element is not available, the passage is assumed circular, and the hydraulic diameter is used to calculate the area.
4	Wall Roughness (WALL_RGH)	The passage wall roughness (equivalent sand grain). If AUTO, the wall roughness of the flow element from input 1 is used.
5	Inlet Effects (INLET_EFF)	Option for heat transfer inlet effects. 1: No inlet effects. 2: Abrupt local or uniform average inlet effects. 3: Abrupt average inlet effects. 4: Uniform local inlet effects. 5: Between uniform average and local inlet effects. 6: Between abrupt average and local inlet effects.
6	Entrance Length (ENTR_LEN)	Distance from the start of the heat transfer area to the boundary layer start. Used in the inlet effects calculation. If AUTO, the length of the flow element from input 1 is used.
7	Laminar-to-Transition Re (RE_LAM)	Reynolds number where the Laminar regime of flow ends and the Transitional regime starts. If AUTO, the global transition Re is used (default=2185).
8	Transition-to-Turbulent Re (RE_TURB)	Reynolds number where the Transitional regime of flow ends and the fully Turbulent regime starts. If AUTO, the global transition Re is used (default=2415).
9	HTC Multiplier (HTC_MULT)	A constant multiplier to scale the value of heat transfer coefficient obtained from the correlation.

Formulation

This correlation uses a Nusselt number equation by Hausen (Ref 1 and 2-eq 8.56) for laminar flow and a correlation from Gnielinski (Ref 2-eq 8.62 and 3) for turbulent flow. A linear interpolation is used if the Re is in the transitional regime.

Reynolds number:

$R e = \frac{\dot{m} D_{h}}{A r e a μ}$

For Re <= RE_LAM:

$N u_{l a m} = 3.66 + \frac{0.0688 * G z}{1 + 0.4 * G z^{2 / 3}} w h e r e G z = \frac{D_{h}}{x} R e P r$

For Re >= RE_TURB:

$N u_{t u r b} = \frac{(R e - 1000) * 0.5 * P r * f}{1 + 12.7 * \sqrt{0.5 * f} * (P r^{.6666} - 1)} w h e r e f = f a n n i n g f r i c t i o n f a c t o r$

$H T C = \frac{N u * k}{D_{h}} w h e r e k = f l u i d c o n d u c t i v i t y a t f i l m t e m p e r a t u r e$

Table 2. Output List
Index	.flo label	Description
1	TNET	Thermal network ID, which has the convector where this correlation is used.
2	CONV_ID	Convector ID, which is using this correlation.
3	FLOW_ELM	Flow element from input 1 or automatically selected.
4	FLOW	Mass flow rate used in Re calculation.
5	HYD_DIA	The hydraulic diameter used in the HTC calculations.
6	RGH_RATIO	Roughness Ratio (wall roughness/hydraulic diameter) used to calculate a friction factor.
7	FRIC_FANNING	Fanning friction factor.
8	INLET_HMULT	HTC multiplier due to inlet effects (boundary layer start).
9	RE	Reynolds number.
10	NU	Calculated Nusselt number.
11	HTC	Calculated heat transfer coefficient.

Heat Transfer Correlation References

Hausen, H., Z. VDI Beih. Verfahrenstech., 4, 91, 1943.
Incropera, F. and Dewitt, D. Fundamentals of Heat and Mass Transfer, 6th Edition, John Wiley & Sons, 2006.
Gnielinski, V., New equations for heat and mass transfer in the turbulent flow in pipes and channels, (Jahrestreffen der Verfahrensingenieure, Berlin, West Germany, Oct. 2-4, 1973.) Forschung im Ingenieurwesen, vol. 41, no. 1, 1975, p. 8-16. In German.