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.

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.