Heat Transfer Coefficients (HTC) Correlations

The following sections describe the available heat transfer correlations (HTCs) in Flow Simulator. Correlation equations and literature references are included. All HTC options appear in the 1D-Thermal Convection Resistor. In addition, the duct flow HTC options appear in the Tube/Pipe flow elements and the Advance Orifice flow element.

Nomenclature: Subscripts:
Nu: Nusselt Number lam: Laminar Regime
Re: Reynolds number turb: Turbulent Regime
Pr: Prandtl multiplier tran: Transition Regime
: Dynamic Viscosity

Heat Transfer Correlations:

Lapides-Goldstein:

Dittus-Boelter:

Sieder-Tate:

Gnielinski:

Bhatti-Shah:

External Heat Transfer:

The following section lists cross flow convection and free convection configurations that are available in Flow Simulator. These options are primarily used by connecting a 1D Thermal Convection Resistor to an internal chamber in the flow path.

Colburn (Plate in Cross Flow):

Incropera (Plate in Cross Flow)

The flat plate correlation based on Incropera (reference 4) calculates an average Nusselt number for the laminar flow over the entire plate, or the mixed laminar and turbulent flow over the plate. The plate is assumed to have a constant surface temperature.

For Re < ~500,000:(1)
N u a v e r a g e _ l a m i n a r = 0.664 * ρ *   V * L μ 0.5 * P r 0.333 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGobGaamyDa8aadaWgaaWcbaWdbiaadggacaWG2bGaamyzaiaa dkhacaWGHbGaam4zaiaadwgacaGGFbGaamiBaiaadggacaWGTbGaam yAaiaad6gacaWGHbGaamOCaaWdaeqaaOWdbiabg2da9iaaicdacaGG UaGaaGOnaiaaiAdacaaI0aGaaiOkamaabmaapaqaa8qadaWcaaWdae aapeGaeqyWdiNaaiOkaiaacckacaWGwbGaaiOkaiaadYeaa8aabaWd biabeY7aTbaaaiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaaGimai aac6cacaaI1aaaaOGaaiOkaiaadcfacaWGYbWdamaaCaaaleqabaWd biaaicdacaGGUaGaaG4maiaaiodacaaIZaaaaaaa@5E1D@
For Re > ~500,000:(2)
N u a v e r a g e _ m i x = 0.037 * ρ *   V * L μ 0.8 871.0 * P r 0.333 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGobGaamyDa8aadaWgaaWcbaWdbiaadggacaWG2bGaamyzaiaa dkhacaWGHbGaam4zaiaadwgacaGGFbGaamyBaiaadMgacaWG4baapa qabaGcpeGaeyypa0ZaamWaa8aabaWdbiaaicdacaGGUaGaaGimaiaa iodacaaI3aGaaiOkamaabmaapaqaa8qadaWcaaWdaeaapeGaeqyWdi NaaiOkaiaacckacaWGwbGaaiOkaiaadYeaa8aabaWdbiabeY7aTbaa aiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaaGimaiaac6cacaaI4a aaaOGaeyOeI0IaaGioaiaaiEdacaaIXaGaaiOlaiaaicdaaiaawUfa caGLDbaacaGGQaGaamiuaiaadkhapaWaaWbaaSqabeaapeGaaGimai aac6cacaaIZaGaaG4maiaaiodaaaaaaa@6118@

Where:

L=Plate length in crossflow direction MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGmbGaeyypa0JaamiuaiaadYgacaWGHbGaamiDaiaadwgacaGG GcGaamiBaiaadwgacaWGUbGaam4zaiaadshacaWGObGaaiiOaiaadM gacaWGUbGaaiiOaiaadogacaWGYbGaam4BaiaadohacaWGZbGaamOz aiaadYgacaWGVbGaam4DaiaacckacaWGKbGaamyAaiaadkhacaWGLb Gaam4yaiaadshacaWGPbGaam4Baiaad6gaaaa@5988@

V=fluid crossflow velocity MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGwbGaeyypa0JaamOzaiaadYgacaWG1bGaamyAaiaadsgacaGG GcGaam4yaiaadkhacaWGVbGaam4CaiaadohacaWGMbGaamiBaiaad+ gacaWG3bGaaiiOaiaadAhacaWGLbGaamiBaiaad+gacaWGJbGaamyA aiaadshacaWG5baaaa@4F10@

ρ=fluid film density MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHbpGCcqGH9aqpcaWGMbGaamiBaiaadwhacaWGPbGaamizaiaa cckacaWGMbGaamyAaiaadYgacaWGTbGaaiiOaiaadsgacaWGLbGaam OBaiaadohacaWGPbGaamiDaiaadMhaaaa@4A2E@

μ=fluid film viscosity MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaH8oqBcqGH9aqpcaWGMbGaamiBaiaadwhacaWGPbGaamizaiaa cckacaWGMbGaamyAaiaadYgacaWGTbGaaiiOaiaadAhacaWGPbGaam 4CaiaadogacaWGVbGaam4CaiaadMgacaWG0bGaamyEaaaa@4C1B@

P r = f l u i d   P r a n d t l   N u m b e r MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGqbGaamOCaiabg2da9iaadAgacaWGSbGaamyDaiaadMgacaWG KbGaaiiOaiaadcfacaWGYbGaamyyaiaad6gacaWGKbGaamiDaiaadY gacaGGGcGaamOtaiaadwhacaWGTbGaamOyaiaadwgacaWGYbaaaa@4BDA@
Note: Valid for 10 < Re < 108, Pr > 0.6
Churchill-Bernstein (Cylinder in Cross Flow):

McAdams (Vertical Prism in Free Convection):

Horizontal Plate in Free Convection:

Churchill-Chu(Horizontal Cylinder in Free Convection):

Where:

Gr: Grashof number

Douter: Cylinder outside diameter

ρ: Fluid bulk density

μ: Fluid film viscosity

GRAV: Earth Gravity

β: Fluid bulk compressibility factor

Note: Valid for 106 < (Gr*Pr) < 1012

Turbulent Duct Flow Entrance Effects

The following entrance effects correlations compute an HTC multiplier called Hm. HTC multiplier has limits and must be greater than unity. The Local option resolves heat transfer correctly for all x locations along the axial length of a pipe. The Averaged options use total pipe length L as the input. They correctly predict overall heat transfer, but not local temperature variation.

Abrupt Contraction, Local x

Uniform Bellmouth, Local x

Abrupt Contraction, Averaged L

Uniform Bellmouth, Averaged L

Uniform Blend, Local x

Uniform Blend, Averaged L

Laminar Duct Flow HTC correlations

The following Laminar HTC options are available in Flow Simulator. It is worth noting that Laminar HTCs depend on distance from inlet x, and thus do not need a special Entrance Effects multiplier.

Muzychka-Yovanovich:

Hausen: