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## Correlations for Convective Heat Transfer

Nov 08 2010 01:20 PM | bspang in Heat Transfer Share this topic:
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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 heat transfer coefficients.

Section 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 temperature-dependent fluid properties according to section 1-4.

 Eq. (1)

 Eq. (2)

 Eq. (3)

1-1 Thermally Developing, Hydrodynamically Developed Laminar Flow (Re<2300)

Constant wall temperature:

 (Hausen) Eq. (4)

Constant wall heat flux:

 (Shah) Eq. (5)

1-2 Simultaneously Developing Laminar Flow (Re<2300)

Constant wall temperature:

 (Stephan) Eq. (6)

Constant wall heat flux:

 Eq. (7)

which is valid over the range 0.7 < Pr < 7 or 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) Eq. (8) where:

Constant wall temperature:

For fluids with Pr > 0.7 correlation for constant wall heat flux can be used with negligible error.

1-4 Effects of Property Variation with Temperature

Liquids, laminar and turbulent flow:

 Eq. (9)

Subscript w: at wall temperature, without subscript: at mean fluid temperature.

Gases, laminar flow:

 Nu = Nu0 Eq. (10)

Gases, turbulent flow:

 Eq. (11)

Temperatures in Kelvin.

Section 2: Forced Convection Flow Inside Concentric Annular Ducts, Turbulent (Re > 2300)

 Dh = Do - DiAll properties at fluid bulk mean temperature (arithmetic mean of inlet and outlet temperature).

Heat transfer at the inner wall, outer wall insulated:

 (Petukhov and Roizen) Eq. (12)

Heat transfer at the outer wall, inner wall insulated:

 (Petukhov and Roizen) Eq. (13)

Heat transfer at both walls, same wall temperatures:

 (Stephan) Eq. (14)

Section 3: Forced Convection Flow Inside Non-Circular Ducts, Turbulent (Re > 2300)

Equations for circular tube with hydraulic diameter:

 Eq. (15)

 Eq. (16)

 Eq. (17)