transient 2-d heat conduction analysis

8/6/2019 Transient 2-D Heat Conduction Analysis

1/22

Transient 2-D heat conduction

analysis of a flat plate

Submitted by:

Aman Raj Verma

Bhovad PriyankaK.Kiran Sagar

Mobia Hangu

A.V.Kotesh

Yash Guha


2/22

ABSTRACT

A two dimensional transient analysis of a rectangular flat

plate with a constant heat generation on one side and

free convection on other sides has been carries out.

The analysis has been done using the finite

difference method applied across a two dimensional grid

spread across the flat plate.

The method has

been extended to the typical case of the rectangular fins.

The modelling has been used to compare fins with

different parameters and materials.


3/22

Schematic of problem


4/22

ASSUMPTIONSThe plate has been assumed to have the following

boundary conduction-

Constant heat flux through one side of the plate.

Free Convection at the other two edges, and insulation at

the fourth side.Following are the theoretical assumptions in order to

simply the analysis.-

The heat flux vectors are confined to a plane i.e. onlytwo-dimensional heat conduction is considered.

The material is isotropic

The thermal heat conductivity of the metal is constantwith temperature.


5/22

Numerical analysis


6/22

General analysis of a node

K*(x/2)*t*(T-(0,3) Ti(0,2))/( y/2) + K*t*(y)*(T-(1,2) T

i(0,2))/( x/2) +

K*(x/2)*t*(T-(0,1) Ti(0,2))/( y/2) +[ h *(y)*t*(Ta T

i(0,2)) ] + {q* y}+

{2*h*(x/2)*(Ta Ti(0,2))* y }

= vcp(Ti+1(0,2) Ti(0,2))/ t


7/22

Temperature Equations


8/22

Results

The following graph are being plotted, using

different materials and different time intervals

for

temperature profile,

average temperature and

thermal distortion of the fins.


9/22

Temperature profile of a Cu plate with constant heat

generation at 500s

00.01

0.020.03

0.040.05

0.060.07

0.080.09

0. 1 0

0.05

0. 1

0.15

0.2

0.25

0. 3

0.35

49

49.5

50

50.5

51

51.5

52

Width

Temperature profile of a flat Cu plate with constant heat ge neration at 500s

Length

Temperature


10/22

Temperature contour of a Cu plate with constant heat

generation at 500s

Length

Width

Contour of temperatrue of a flat Cu plate with cons tant heat generation

0 0.01 0 .02 0.03 0 .04 0 .05 0.06 0 .07 0.08 0 .09 0.10

0.05

0.1

0.15

0.2

0.25

34.6

34.7

34.8

34.9

35

35.1


11/22

Comparison of Temperature profiles of a Cu after 500 &

700s

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.1

0. 2

0.3

0. 4

40

45

50

55

60

65

width

Length

temperature of a flat Cu plate with constant heat gene ration at 500 ,700s

temperature


12/22

Comparison of Temperature profiles of a Cu for

different heat generations.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0. 10

0.1

0.2

0.3

0. 4

30

35

40

45

50

55

60

65

70

75

Width

Length

Temperature of C.I. at two different heat gene ration

Temperature


13/22

Schematic of heat transfer in fins


14/22

Comparison of Temperature profiles ofAl fin at

different times 400, 700s

0 0 .01 0.02 0.03 0.04 0 .05 0 .06 0.07 0.08 0.09 0.1 00.1 0.2

0.3 0.429.5

30

30.5

31

31.5

32

Width

Length

Temperature of same Al fin at 400,700s

Temperature


15/22

Comparison of steel and Aluminum fins. The one with

large variation is for Steel

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.1

0. 2

0. 3

0. 4

28

29

30

31

32

33

34

35

Width

Length

Comparison between Steel & Aluminium

Temperature


16/22

Comparison ofAverage surface Temperature with time

for Al (above) & C.S.

0 100 200 300 400 500 600 700 80027

27.5

28

28.5

29

29.5

30

30.5

31

Time

Temperature

Average temperature of different metal fins Al and C.S .

Aluminium

Carbon Steel


17/22

Comparison of Temperature profiles of for different fin

thickness 2 mm, 5 mm(above) for same heat flux

00.01

0.020.03

0.040.05

0.060.07

0.080.09

0.1

0

0.05

0.1

0.15

0.2

0.250.3

0.35

28

30

32

34

36

38

40

42

Temperature profile for different thickness 2mm ,5mm for same he at flux


18/22

Thermal distortion of an Aluminum plate Black- initial,

Blue- Distorted

-0.06 -0.04 -0.02 0 0.02 0 .04 0.06-0. 2

-0.15

-0. 1

-0.05

0

0.05

0.1

0.15

0.2

Length

Width

Thermal distortion of Aluminium


19/22

Comparison of average Temperature of different fin

thickness with respect to time 5mm (above) and 2mm

0 200 400 600 800 1000 120025

30

35

40

45

50

55Average temperature of the plate for different thickness

Time

Averagesurfacetemperature

2 m m

5 m m


20/22

Conclusion

Each fin has its own capacity to act as a heat sinkdepending on parameters like thermal conductivity,specific heat capacity and thickness of the fin.

From the Transient temperature profiles the thermaldistortions have been obtained which can be used forhigh temperature applications.

It can be extended to any applicationinvolving a rectangular plates. It can also be extendedto cuboids if the situation can be reduced to anapproximate two dimensional model, like plane walls.


21/22

Applications

The method can be extended to the typical

case of the rectangular fins which act as heat

sinks and are used to enhance cooling of IC

engines, pumps, PCBs, power transistors, etc.

It can also be extended to cuboids if the

situation can be reduced to an approximate

two dimensional model, like plane walls.


22/22

Thank you

transient 2-d heat conduction analysis

Documents