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Natural Convection Nusselt numbers - Ángel Martin - 11-20-2016 05:35 PM
Natural Convection Nusselt numbers. [ NATCNV ]
From the author’s Engineering Collection, included in the ETSII4 module
This program calculates the Nusselt dimensionless number and the film coefficient (h) in a natural convection situation for the following three cases:
• Vertical plate or cylinder
• Horizontal plate
• Horizontal Cylinder or Sphere.
The program requires the Grashof (Gr) and Prandtl (Pr) numbers - or each of their constituent factors when they’re not known to obtain the needed values. Then its product (i.e. the Raileigh number, Ra) is used as a criteria for the different sections of the boundary layer conditions, as follows:
Gr = [ g beta. L^3 (Tp - Tinf) ] / nu^2
Pr = mu. Cp / Kf
Ra = Gr * Pr
Case 1: LowLimit < Ra < 1 E4
With the low limit being 0.1 for vertical plates/Cylinders, or 1 E-5 for horizontal Cylinder/Sphere. Here a fourth-degree polynomial approximation is used as follows:
1.a. Vertical Plate / Cylinder:
Nu = 0.161771563 + 0.127972027 Ra + 1.153845962 E-2 Ra^2 - 2.797201424 E-3 Ra^3 + 4.662002506 E-4
1.b. Horizontal Cylinder / Sphere:
Nu = 5.949883478 E-2 + 01274378392 Ra + 9.986887925 E-3 Ra^2 + 2.865190955 E-4 Ra^3 +
+ 2.185315948 E-5Ra^4
Case 2: 1 E4 < Ra < 1 E9
Vertical Plate/Cylinder: Nu = 0.59 / Ra^4
Horizontal Cylinder / Sphere: Nu = 0.525 / Ra^4
Case 3: 1 E9 < Ra < 1 E12
For all cases covered in the program: Nu = 0.129 / Ra^3
Finally the film coefficient is calculated using the definition expression as function of the thermal conductivity (K) and the characteristic dimension (length or diameter) of the body:
h = Nu K / L
Note that this program makes use of the "UNIT Conversion" Module for the utility functions "*Y/N" and "KEY?" to offer the menu choices.