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Fins are the extended surfaces through which heat transfer takes place by conduction and convection to keep the base surface cool. Fins of various configurations are presently used ranging from automobile engines to cooling of chip in a computer. Fins used presently are solid with different shapes but in the present research such solid fins are compared with solid fins having maximum of 10 numbers of embossing’s that further increases the surface area for maximum heat transfer. Importance in this research is given to variation of temperature along the length of the fins which in turn gives rate of heat transfer. Thus this research is under taken to increase the efficiency of fins (by extracting heat from the base surface) which is highly demanded today for air cooled engines, compressors, refrigerators etc. In the present research, SOLID70 element and SURF152 elements are used for FE analysis. Methodology involves 3D rectangular fin modelling and meshing, creation of surf elements for the modeling, applying the boundary conditions and source temperature, applying the material property (aluminum) to obtain the steady state thermal contours. FEA results are finally compared with analytic and experimental values for validity. In the present research, a solid rectangular aluminum fin and the same rectangular fin with 2, 4, 8 and 10 embossing’s were compared through finite element analysis for its temperature distribution along the length. FEA analysis of the present research showed that fins having embossing’s were more efficient compared to that a simple solid fin. Hence it is concluded from the present research that embossing’s at preferred locations further increases the rate of heat transfer. From the present analysis it is concluded that the mathematical and FEA for a solid rectangular fin without embossing’s are converging within ±1.2°C and rectangular fin with 10 embossing’s is converging within ±1.4°C and hence the validity.

The basic law that governs the convective heat transfer is Newton’s law of cooling given by:

Q = h A ( T s − T f ) ,Watts (1)

where: T_{s}: the surface temperature ˚C; T_{f}: the fluid temperature ˚C; h: the convective heat transfer coefficient w/m^{2} ˚C; A: surface area, m^{2}.

Note that in the above equation, film coefficient of heat transfer or the convective heat transfer coefficient “h” is very important which mainly depends on the type of the surface, size, shape, its temperature, surface finish etc. Most of the research, mathematical analysis and dimensional analysis are confined in finding “h”. In addition to the above, for fins, the temperature distribution along its length also becomes important.

The expulsion of overabundance warmth from framework parts is fundamental to abstain from harming impacts of overheating. Thusly the improvement of warmth exchange is a vital subject of warm designing [

Balances are utilized to improve convective warmth move in an extensive variety of designing applications and offer a handy method for accomplishing a substantial aggregate warmth exchange surface range without the utilization of an over the top measure of essential surface zone [

Along these lines, fins must be intended to accomplish most extreme warmth expulsion with least material use considering the simplicity of the balance fabricating. The change in warmth exchange coefficient is ascribed to the restarting of the warm limit layer after every interference [

In the examination of warmth trade, cutting edges are surfaces that stretch out from a thing to manufacture the rate of warmth trade to or from nature by growing convection. The measure of conduction, convection, or radiation of an article chooses the measure of warmth it trades [

Finally, it is well known that major heat transfer from the fin is by convection and performance of a fin is evaluated by its efficiency and effectiveness.

There are various examination related to warmth trade and weight drop of channels with pin cutting edges, which are limited to stick parities with round or couple of different cross territories. The genuine warmth trade takes by two modes i.e. by conduction took after by convection. Heat trade through the solid to the surface of the solid happens through conduction whereas from the surface to the surroundings happens by convection. Further warmth trade may be by normal convection or by obliged convection.

Bayram Sahin and Alparslan Demir [

Metzger et al., [

Fins are the extended surfaces through which heat transfer takes place by conduction and convection. In the present investigation the surface area is further increased by providing embossing’s at preferred locations in the solid fin. This in turn increases effectiveness and efficiency of the fin. So far no attempt has been made to provide embossing’s in the solid aluminum fin to increase the surface area and hence the present research was under taken to fill the void.

In the present research, SOLID70 element and SURF152 elements are used for FE analysis. Methodology involves 3D rectangular fin modelling and meshing, creation of surf elements for the modeling, applying the boundary conditions and source temperature, applying the material property (aluminum) to obtain

the steady state thermal contours. Finally the temperature distribution results of solid fin are compared with that of solid fin with 10 embossing’s at preferred locations along the length of the fin.

The most popular energy balance equation used to find the heat transfer through fins mathematically (for steady state condition) is given by:

Q = h p K A ( C 2 − C 1 ) (2)

where Q: rate of hear transfer, watts, h: convective heat transfer coefficient w/m^{2} ˚C; P: the perimeter of the fin, m, K: thermal conductivity, w/m ˚C; A: area, m^{2} and C_{1}; C_{2} are constants obtained by applying the limits.

Above equation is modified to find temperature distribution based on the tip condition.

Equation below is used to find analytically the fin temperature over a distance with given boundary conditions [

T ( X ) = T ∞ + ( T b − T ∞ ) ∗ N r D r (3)

where,

N r = cosh m ( L − x ) + ( h m k ) + sinh m ( L − x )

D r = cosh m L + ( h m k ) + sinh m L

Correlations given below are used to find the heat transfer coefficient using dimensional analysis for vertical plate [

N u L = h ∗ L k = C ( g β L 3 v a ∗ ( T s − T ∞ ) ) n (4)

where,

h = C ∗ k L ( g β L 3 v a ∗ ( T s − T ∞ ) ) n = F K constant ∗ ( T s − T ∞ ) n

(where c = 0.59, n = 0.25).

For analysis and comparison purpose, rectangular aluminum fin with 2, 4, 8 and 10 embossing’s was considered but for discussion only fin with 10 embossing’s is presented in the present paper.

Mathematically, the heat transfer coefficient is calculated using the vertical plate correlation using the following correlation.

h p s = h ∗ ( 1 + 0.75 ∗ 1130.9 1696.45 ) = 2.28 (5)

It is observed from

Analytic calculation to find temperature at distance x | ||||||
---|---|---|---|---|---|---|

L, Length of the fin | 0.15 m | |||||

w, width of the fin | 0.1 m | |||||

t, thickness of the fin | 0.015 m | |||||

h, heat transfer coeff. | 5.489 w/m^{2}-k (for Al) | |||||

p, perimeter | 0.23 m | |||||

Ac, cross section Area | 0.0015 m^{2} | |||||

k, thermal conductivity | 236 w/m-k (for Al) | |||||

m | 1.888 | |||||

T base | 200˚C | |||||

T infinity | 20˚C | |||||

L (inm) | X (in m) | Numerator | Denominator | Theta (a)/theta (b) | T(x), ˚C | |

0.15 | 0 | 1.0439 | 1.0439 | 1.0000 | 200.0 | |

0.015 | 1.0358 | 1.0439 | 0.9923 | 198.6 | ||

0.03 | 1.0286 | 1.0439 | 0.9823 | 197.4 | ||

0.045 | 1.0222 | 1.0439 | 0.9792 | 196.3 | ||

0.06 | 1.0166 | 1.0439 | 0.9738 | 195.3 | ||

0.075 | 1.0118 | 1.0439 | 0.9692 | 194.5 | ||

0.09 | 1.0078 | 1.0439 | 0.9654 | 193.8 | ||

0.105 | 1.0047 | 1.0439 | 0.9624 | 193.2 | ||

0.12 | 1.0023 | 1.0439 | 0.9601 | 192.8 | ||

0.135 | 1.0008 | 1.0439 | 0.9586 | 192.6 | ||

0.15 | 1.0000 | 1.0439 | 0.9579 | 192.4 | ||

supply of 40 watts, a solid rectangular fin reaches a temperature of 192.4˚C at the tip. From

Figures 7-10 show the FE modelling for geometry, meshing, steady state thermal contour and heat flux for a rectangular fin containing 10 embossing’s.

It is observed from

From

It is finally observed that the mathematical and FEA of rectangular fin with 10

embossing’s are converging within ±1.4˚C and hence the validity of FEA with mathematical and experimental analysis.

It is observed from the present research that keeping the base (root) temperature at 200˚C with power supply of 40 watts, a solid rectangular fin reaches a temperature of 192˚C at the tip whereas the same fin with 10 embossing’s reaches 179˚C at the tip. This shows that rectangular fin with embosing’s removes more heat compared to that of a solid fin. It is also observed from the research that this temperature fall is gradual from fin with 2, 4, 8 and 10 embossing’s. Thus the heat removal gradually decreases with increase in embossing’s. Heat flux also follows the same pattern along the length of the fin as that of the temperature.

In the present research it is also observed from the mathematical and FEA that a solid rectangular fin without embossing’s is converging within ±1.2˚C and rectangular fin with 10 embossing’s is converging within ±1.4˚C and hence the validity.

Author thank the Govt. sponsored R&D center, HMSIT, Tumkur, INDIA for extending its facilities for carrying out the research and to Mr. J. Joy Gideon, Research Asst. of the R&D center for assisting in graphics, typing and final setting of this research paper.

Hemanth, J. and Yogesh, K.B. (2018) Finite Element Analysis (FEA) and Thermal Gradient of a Solid Rectangular Fin with Embossing’s for Aerospace Applications. Advances in Aerospace Science and Technology, 3, 49-60. https://doi.org/10.4236/aast.2018.33004