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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.

convection_eq_1

Eq. (1)

 

convection_eq_2

Eq. (2)

 

convection_eq_3

Eq. (3)

 

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

Constant wall temperature:

convection_eq_4

(Hausen)Eq. (4)

 

Constant wall heat flux:

convection_eq_5

(Shah)Eq. (5)

 

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

Constant wall temperature:

convection_eq_6

(Stephan)Eq. (6)

 

Constant wall heat flux:

convection_eq_7

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:

convection_eq_8

(Petukhov, Gnielinski)Eq. (8)

where: convection_1

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:

convection_eq_9

Eq. (9)

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

Gases, laminar flow:

Nu = Nu0

Eq. (10)

Gases, turbulent flow:

convection_eq_11

Eq. (11)

Temperatures in Kelvin.


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

convection_2

Dh = Do - Di

convection_3

convection_4

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

 

Heat transfer at the inner wall, outer wall insulated:

convection_eq_12

(Petukhov and Roizen)Eq. (12)

Heat transfer at the outer wall, inner wall insulated:

convection_eq_13

(Petukhov and Roizen)Eq. (13)

Heat transfer at both walls, same wall temperatures:

convection_eq_14

(Stephan)Eq. (14)


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

Equations for circular tube with hydraulic diameter:

convection_eq_15

Eq. (15)

 

convection_eq_16

Eq. (16)

 

convection_eq_17

Eq. (17)





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