# Blunt Body

Correlation to calculate HTC in forced convection in case of crossflow conditions over a body. This correlation supports several shapes of the body in crossflow.
Type
Body in Crossflow Nu
Subtype
Body in Crossflow
Table 1. Inputs List
Index UI Name (.flo label) Description
1 Shape

(SHAPE_ID)

Shape of the body in the cross flow.

The shapes available in the correlation are mentioned in the Formulation section.

2 Velocity Input Type

(VEL_ID)

Methods available for the user for velocity input:
• Chamber
• User Input
• RPM based

Further discussions are in the Formulation section.

3 Velocity

(FLOW_VEL)

This is activated only if User Input is selected as the “Velocity Input Type”. It takes the user input velocity.
4 Characteristic Length

(CHAR_LEN)

The characteristic length/diameter of the fluid flow. “d” in the Formulation section.

(OUTER_R)

The stator outer radius. This is activated only if RPM Based is selected as the “Velocity Input Type”.

If “Auto”, then Outer Radius = 0.5 * Characteristic Length.

6 Tip Speed Ratio

(TIP_SPD_RATIO)

The frame tip speed ratio, user-defined.
7 HTC Multiplier

(HTC_MULT)

A constant multiplier to scale the value of heat transfer coefficient obtained from the correlation.

## Formulation

This correlation uses a Nusselt number that can be found in references 1, 2, and 3. A linear interpolation is used if the Re is in the transitional regime.

Reynolds Number:

With:

${V}_{ext}$ : The external fluid velocity.

$d$ : The characteristic length/diameter of the fluid flow.

${\mu }_{T}$ : The external fluid flow viscosity, at the film temperature.

$\rho$ : The external fluid density.

Chamber This is the default method. This takes the velocity that is calculated in the fluid chamber attached to the convector.
User Input In this method, you can directly input the velocity.
RPM Based This method requires the outer radius and tip speed ratio for calculation of the velocity. It is further explored in Formulation section. With:

$\omega$ : The angular speed of the rotor.

$OR$ : The outer radius.

$TipSpeedRatio$ : The user-defined tip speed ratio.

Nusselt’s number:

Shape Name in GUI Shape Demonstration Re C m
Square 2.5*103 – 8*103 0.180 0.699
5*103 - 105 0.102 0.675
Rhombus 5*103 - 105 0.25 0.588
Horizontal Ellipse 2.5*103 – 1.5*104 0.25 0.612
Vertical Ellipse 3*103 – 1.5*104 0.096 0.804
Horizontal Hexagon 5*103 - 105 0.156 0.638
Vertical Hexagon 5*103 – 1.95*104 0.162 0.638
1.95*104 - 105 0.0395 0.782
Thick Vertical Plate 3*103 – 2*104 0.264 0.66
Thin Vertical Plate 4*103 – 1.5*104 0.232 0.731
Horizontal Triangle 3*103 – 2*104 0.246 0.61
Cylinder This follows Churchill-Bernstein convection correlation. For more information, see Heat Transfer Coefficients (HTC) Correlations and view the section Churchill-Bernstein (Cylinder in Cross Flow).
Table 2. Output List
Index .flo label Description
1 TNET Thermal network ID which has the convector where this correlation is used.
2 CONV_ID Convector ID which is using this correlation.
3 SHAPE Shape of the body in cross flow.
4 CHAR_LEN Characteristic length.
5 OUTER_R Only appears if RPM Based velocity type is selected. Displays the value of outer radius used in the calculations.
6 TIP_SPD_RATIO Only appears if RPM Based velocity type is selected. Displays the value of tip speed ratio used in the calculations.
7 VELOCITY The velocity used in the calculations.
8 PR Prandtl number.
9 RE Reynolds number.
10 NU Calculated Nusselt number.
11 HTC Calculated heat transfer coefficient.

## Heat Transfer Correlation References

1. Petit J.P., Transfert de chaleur et de masse, Cours de l’Ecole Centrale de Paris.
2. Incropera, F. and Dewitt, D. Fundamentals of Heat and Mass Transfer, 6th Edition, John Wiley & Sons, 2006.
3. Jakob, M., Heat Transfer, Vol. 1, Wiley, New York, 1949.