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Stator ventilation duct

The air passes through the stator ventilation duct.

Problem Type:
Axisymmetric problem of heat transfer.

Geometry:

ventilation duct

D = 30 mm, L = 4000 mm.

Given:
Speed of air in the channel v = 10 m/s,
Duct surface convection coefficient α = 50 W/K·m2,
Thermal load q = 300 W/m2.

Problem:

Define the air temperature rise.

Solution:

The channel is divided into n sections. The heat flux q from each section is calculated. The consumed energy dQ can be found as:

dQ = q·t, where
q - thermal flux (W),
t - time of air passage through the section (sec.): t = (L / n) / v.

air ventilation duct heating

Then the air temperature rise is calculated as:

dT = dQ / (dV·C·ρ), where
dQ - consumed energy (J),
dV - volume (m3),
C - thermal capacity of air (J / kg·K),
ρ - density of air (kg/m3).

Results:

0-iteration

Section number

Convection temperature, °C

Thermal flux, W

Consumed energy, J

1

0

18.85

0.754

2

0

18.85

0.754

3

0

18.85

0.754

4

0

18.85

0.754

5

0

18.85

0.754

6

0

18.85

0.754

7

0

18.85

0.754

8

0

18.85

0.754

9

0

18.85

0.754

10

0

18.85

0.754

1 iteration

Section number

Convection temperature, °C

Thermal flux, W

Consumed energy, J

1

0

19.95

0.798

2

2.41

18.90

0.756

3

4.82

18.85

0.754

4

7.24

18.85

0.754

5

9.65

18.85

0.754

6

12.06

18.85

0.754

7

14.47

18.86

0.754

8

16.89

18.84

0.754

9

19.30

18.81

0.752

10

21.71

17.74

0.709

2 iteration

Section number

Convection temperature, °C

Thermal flux, W

Consumed energy, J

1

0

19.97

0.799

2

2.55

18.88

0.755

3

4.97

18.85

0.754

4

7.38

18.85

0.754

5

9.80

18.85

0.754

6

12.21

18.85

0.754

7

14.62

18.85

0.754

8

17.03

18.82

0.753

9

19.44

18.47

0.739

10

21.85

18.10

0.724

3 iteration

Section number

Convection temperature, °C

Thermal flux, W

Consumed energy, J

1

0

19.97

0.799

2

2.56

18.88

0.755

3

4.97

18.85

0.754

4

7.38

18.85

0.754

5

9.80

18.84

0.754

6

12.21

18.85

0.754

7

14.62

18.85

0.754

8

17.03

18.82

0.753

9

19.44

18.47

0.739

10

21.81

18.10

0.724

Air temperature rise is dT = 21.81 °C

ventilation duct heat flux

ventilation duct temperature

* Reference: John H. Lienhard IV, John H. Lienhard V, A heat transfer textbook.

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