# Fin Channel

## Description

Flow Simulator uses a variety of heat transfer correlations to model the heat exchange phenomenon in flow and thermal networks. The correlation types available in Flow Simulator for modeling convection through Fin Channels are discussed below.

(i) Fin Channel Free Convection (Natural Convection)
Used to model heat exchange between fin channels and the free stream fluid through Natural Convection.
Type
Free Convection NU
Subtype
Fin Channel Free Convection
Table 1. Input List
Index UI Name (.flo label) Description Mandatory/Not Mandatory
1 Channel Orientation (ORIENT) Orientation of the channels.
There are two options:
• Horizontal
• Vertical
Mandatory

Based on the channel orientation, the correlation for HTC changes. Refer to the Formulation section for more details.

2 Axial Length of fin (LENGTH)) Length of the fins in the fin channel. Mandatory
3 Height of fin (HEIGHT) Height of the fins in the fin channel. Mandatory
4 Spacing between fins (SPACE) Spacing between the two fins. Mandatory
5 Thickness of fins (FIN_THK) Thickness of fins in the fin channel. Mandatory
6 Number of fins (Number) Total number of fins. Mandatory
7 HTC Multiplier (HTC_MULT) A constant multiplier to scale the value of the heat transfer coefficient obtained from the correlation. Not Mandatory

Default value is 1.0.

## Formulation

The expression of the heat transfer coefficient for a vertical fin channel of axial length L and spacing S, subjected to Free Convection, is given by (Ref. 1 and 2): Where,

L = Axial length of the fin.

H = Height of the fin.

S = Spacing between two fins.

r = Characteristic length, Fin hydraulic radius (2LS / 2L+S).

α = Channel Aspect Ratio (S/L).

The expression of the heat transfer coefficient for a horizontal fin channel of axial length L and spacing S, subjected to Free Convection, is given by (Ref. 1 and 3):
For Spacing > 2 in, the correlation is given by (Ref. 3):(1)
$Nu=0.54*{\left(Gr*Pr\right)}^{0.25}$

Where,

S = Characteristic length (spacing between the fins).

Gr = Grashoff number based on the characteristic length (S).

Pr = Prandtl number at film temperature (TFluid-Stream + TWall / 2).

The heat transfer coefficient from Nusselt number is obtained as:(2)

Where, k = Thermal conductivity of the fluid at film temperature (TFluid-Stream + TWall / 2).

Table 2. Output List
Index .flo label Description
1 TNET Thermal network ID, which has the convector where this correlations is used.
2 CONV_ID Convector ID, which is using this correlation.
3 ORIENTATION User-defined motor orientation.
4 FIN_LEN User-defined fin length.
5 FIN_HGHT User-defined fin height.
6 FIN_SPCE User-defined spacing between two fins.
7 FLOW_VEL Fluid velocity calculated/auto-retrieved for the model.
8 CHRTSC_LENGTH Characteristic length used in the computation of HTC.
9 TOT_AREA Total fin channel area for convection.
10 CHNL_GR Channel Grashoff number.
11 CHNL_PR Channel Prandtl number.
12 HTC Heat transfer coefficient calculated as per the correlation.

## Heat Transfer Correlation References

1. Staton, David A., and Andrea Cavagnino. "Convection heat transfer and flow calculations suitable for electric machines thermal models." IEEE transactions on industrial electronics 55, no. 10 (2008): 3509-3516.
2. Van De Pol, D. W., and J. K. Tierney, "Free convection Nusselt number for vertical U-shaped channels, J. Heat Transfer. Nov 1973, 95(4): 542-543.
3. Jones, Charles D., and Lester F. Smith. "Optimum arrangement of rectangular fins on horizontal surfaces for free-convection heat transfer.", J. Heat Transfer. Feb 1970, 92(1): 6-10.