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Encyclopedia > Nusselt number

The Nusselt number is a dimensionless number that measures the enhancement of heat transfer from a surface compared to the heat transferred if just conduction occurred. It is named after Wilhelm Nusselt, a German engineer, who was born 25 November 1882, in Nurnberg, Germany. In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units. ...


Typically, the Nusselt number (Nu) it is used to measure the enhancement of heat transfer when convection takes place.

mathit{Nu}_L = frac{hL}{k_f} = frac{mbox{Convective heat transfer}}{mbox{Conductive heat transfer}} in perpendicular to the flow direction

where

Selection of the significant length scale should be in the direction of growth of the boundary layer. A salient example in introductory engineering study of heat transfer would be that of a horizontal cylinder versus a vertical cylinder in free convection. K value redirects here. ... Convection in the most general terms refers to the movement of currents within fluids (i. ... The heat transfer coefficient is used as a fudge factor in calculating heat transfer in thermodynamics. ... Convection is the transfer of heat by the motion of or within a fluid. ...


Several empirical correlations are available that are expressed in terms of Nusselt number in the elementary analysis of flow over a flat plate etc. Sieder-Tate, Colburn and many others have provided such correlations.


For a local Nusselt number, one may evaluate the significant length scale at the point of interest. To obtain an average Nusselt number analytically one must integrate over the characteristic length. More commonly the average Nusselt number is obtained by the pertinent correlation equation, often of the form Nu = f(Ra, Pr). In fluid mechanics, the Rayleigh number for a fluid is a dimensionless number associated with the heat transfer within the fluid. ... The Prandtl Number is a dimensionless number approximating the ratio of momentum diffusivity and thermal diffusivity. ...


The Nusselt number can also be viewed as being a dimensionless temperature gradient at the surface.


The mass transfer analog of the Nusselt number is the Sherwood number. The Sherwood number (Sh) is a dimensionless number used in mass-transfer operation. ...

Contents

Empirical calculations

Free convection at a vertical wall

Cited as coming from Churchill and Chu[1]


overline{Nu}_L = 0.68 + frac{0.67Ra_L^{1/4}}{left[1 + (0.492/Pr)^{9/16} , right]^{4/9} ,} quad Ra_L le 10^9


Free convection from horizontal plates

For the top surface of a hot object in a colder environment or bottom surface of a cold object in a hotter environment[1]


overline{Nu}_L = 0.54 Ra_L^{1/4} , quad 10^4 le Ra_L le 10^7


overline{Nu}_L = 0.15 Ra_L^{1/3} , quad 10^7 le Ra_L le 10^{11}


For the bottom surface of a hot object in a colder environment or top surface of a cold object in a hotter environment[1]


overline{Nu}_L = 0.27 Ra_L^{1/4} , quad 10^5 le Ra_L le 10^{10}


Forced convection in pipe flow

The Dittus-Boelter equation (for turbulent flow), with n=0.4 for heating of the fluid, and n=0.3 for cooling of the fluid[1]:


Nu_D = 0.023 Re_D^{4/5} Pr^{n}


See also

  • Churchill-Bernstein Equation

In convective heat transfer, the Churchill Bernstein equation is used to estimate the surface averaged Nusselt number for a cylinder in cross flow at various velocities. ...

References

  1. ^ a b c d Incropera, Frank P.; DeWitt, David P.. Fundamentals of Heat and Mass Transfer, 4th Edition, Wiley. p 493
v • d • e
Dimensionless numbers in fluid dynamics
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  Results from FactBites:
 
AE/ME Lab -- Spring 2005 (120 words)
This page is a reformated version of the Nusselt Number uncertainty analysis example that Dr. Daniel Cole constructed for the ME 370 course when he taught it in the Fall of 1996.
Define the functional relationship for the Nusselt number.
Define the relationship for the uncertainty in the Nusselt number.
Heat transfer coefficient - NewMars (354 words)
The Nusselt Number of a thermal interface is a dimensionless analog of the heat transfer coefficient.
However, the Nusselt number can be found using empirical relations for the interface’s materials and geometry as well, and then used to derive the heat transfer coefficient.
Nusselt Number equations for various systems are simply fitted to experimental data, and there is not necessarily any correspondence between them.
  More results at FactBites »


 

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