Natural Convection Nusselt numbers

11202016, 05:35 PM
(This post was last modified: 12132016 12:56 PM by Ángel Martin.)
Post: #1




Natural Convection Nusselt numbers
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 E5 for horizontal Cylinder/Sphere. Here a fourthdegree polynomial approximation is used as follows: 1.a. Vertical Plate / Cylinder: Nu = 0.161771563 + 0.127972027 Ra + 1.153845962 E2 Ra^2  2.797201424 E3 Ra^3 + 4.662002506 E4 1.b. Horizontal Cylinder / Sphere: Nu = 5.949883478 E2 + 01274378392 Ra + 9.986887925 E3 Ra^2 + 2.865190955 E4 Ra^3 + + 2.185315948 E5Ra^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. 

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