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Correlations for Convective Heat Transfer
In many cases it's convenient to have simple equations for estimation of heat transfer coefficients. Below is a collection of recommended correlations for single-phase convective flow in different geometries as well as a few equations for heat transfer processes with change of phase. Note that all equations are for mean Nusselt numbers and mean heattransfer coefficients. The following cases are treated:
1. 2. 3. 4. 5. 6. 7. 8. • • Forced Convection Flow Inside a Circular Tube Forced Convection Turbulent Flow Inside Concentric Annular Ducts Forced Convection Turbulent Flow Inside Non-Circular Ducts Forced Convection Flow Across Single Circular Cylinders and Tube Bundles Forced Convection Flow over a Flat Plate Natural Convection FilmCondensation Nucleate Pool Boiling List of Symbols References

1 Forced Convection Flow Inside a Circular Tube

All properties at fluid bulk mean temperature (arithmetic mean of inlet and outlet temperature). Nusselt numbers Nu0 from sections 1-1 to 1-3 have to be corrected for temperaturedependent fluid properties according to section 1-4. \

Correlations for Convective Heat Transfer By: Dr. BernhardSpang Presented at The Chemical Engineers’ Resource Page, www.cheresources.com

1-1 Thermally developing, hydrodynamically developed laminar flow (Re < 2300) Constant wall temperature:

(Hausen) Constant wall heat flux:

(Shah) 1-2 Simultaneously developing laminar flow (Re < 2300) Constant wall temperature:

(Stephan) Constant wall heat flux:

which is valid over the range 0.7 < Pr < 7or if Re Pr D/L < 33 also for Pr > 7. 1-3 Fully developed turbulent and transition flow (Re > 2300) Constant wall heat flux:

(Petukhov, Gnielinski)

where Constant wall temperature: For fluids with Pr > 0.7 correlation for constant wall heat flux can be used with negligible error.
Correlations for Convective Heat Transfer By: Dr. Bernhard Spang Presented at The Chemical Engineers’ ResourcePage, www.cheresources.com

1-4 Effects of property variation with temperature Liquids, laminar and turbulent flow:

Subscript w: at wall temperature, without subscript: at mean fluid temperature Gases, laminar flow: Nu = Nu0 Gases, turbulent flow:

Temperatures in Kelvin

2 Forced Convection Flow Inside Concentric Annular Ducts, Turbulent (Re > 2300)
Dh = Do - Di

All properties atfluid bulk mean temperature (arithmetic mean of inlet and outlet temperature).

Heat transfer at the inner wall, outer wall insulated:

(Petukhov and Roizen) Heat transfer at the outer wall, inner wall insulated:
Correlations for Convective Heat Transfer By: Dr. Bernhard Spang Presented at The Chemical Engineers’ Resource Page, www.cheresources.com

(Petukhov and Roizen) Heat transfer atboth walls, same wall temperatures:

(Stephan)

3 Forced Convection Flow Inside Non-Circular Ducts, Turbulent (Re > 2300)
Equations for circular tube with hydraulic diameter

4 Forced Convection Flow Across Single Circular Cylinders and Tube Bundles

D = cylinder diameter, um = free-stream velocity, all properties at fluid bulk mean temperature. Correction for temperature dependent fluidproperties see section 4-4. 4-1 Smooth circular cylinder
Correlations for Convective Heat Transfer By: Dr. Bernhard Spang Presented at The Chemical Engineers’ Resource Page, www.cheresources.com

(Gnielinski) where

Valid over the ranges 10 < Rel < 107 and 0.6 < Pr < 1000 4-2 Tube bundle

Transverse pitch ratio

Longitudinal pitch ratio

Void ratio

for b > 1

for b < 1 Nu0,bundle =fANul,0 (Gnielinski)

Nul,0 according to section 4-1 with

instead of Rel.

Arrangement factor fA depends on tube bundle arrangement.

Correlations for Convective Heat Transfer By: Dr. Bernhard Spang Presented at The Chemical Engineers’ Resource Page, www.cheresources.com

In-line arrangement:

Staggered arrangement:

Correlations for Convective Heat Transfer By: Dr. Bernhard Spang...