ANALYSIS OF FINS WITH DIFFERENT CROSS SECTONS

The fins are generally used to increase the heat transfer rate from the system to the surroundings by increasing the heat transfer area. The fins are generally extended surfaces or projections of materials on the system. The fins are commonly used on small power developing machine as engines used for motorcycles as well as small capacity compressors. They are also used in many refrigeration systems (evaporators and condensers) for increasing the heat transfer rates.

In the present analysis, the fins that are of different cross sections and of same material (aluminium) are considered. The knowledge of efficiency and effectiveness of the fin are necessary for proper design of fins. The main objective of our analysis is to determine the most effective cross section among the various cross sections available. The efficiency and effectiveness of various cross sections are determined experimentally by cross sectional area and volume as constant for each cross section.

The various cross sections, which are adopted, are:

• Triangular
• Square
• Hexagon
• Hollow triangle
• Hollow circular
• Hollow Square

The fins, which are taken in the analysis, are experimented for the condition of fin with insulated end i.e. the fin is short fin with insulated end. Comparison is made among the solid sections and between the hollow and solid sections. The graphs plotted give a clear view of the comparisons. In the experiment, various cross sections of aluminium are taken due to its lightweight and high conductivity and it is most widely used in the industrial applications.

Necessity of fins

The heat that is generated produced or developed in the system that conducts through the walls or boundaries is to be continuously dissipated to the surroundings or environment to keep the system in steady state condition. Large quantities of heat have to be dissipated from small area as heat transfer by convection between a surface and the fluid surroundings. It can be increased by attaching thin strips of metals called fins to the surface of the system.

The fin is generally an extended surface on the system. Whenever the available surface is found to be inadequate to transfer the required quantity of heat with the available temperature drop & convective heat transfer coefficient, the surface area exposed to the surroundings is frequently increased by attachment to protrusions to the surfaces. These protrusions are called fins or spines. Thus, the fins increase the effective area of surface there by increasing the heat transfer by convection.

In the present work, fins, which are of different cross sections and are of the same material (aluminium), are experimented for the following conditions

1. natural convection
2. forced convection
1. Flow of air constant and heat input varies.
2. Flow of air varies and heat input constant.

                   

Study on the effectiveness and efficiency of fin was made in the above conditions. Theoretical and practical heat transfer coefficients are calculated. All the fins experimented are uniform cross section through out the length and are different cross sections. Temperature distributions over the surfaces are plotted. The experiments are carried to find out which of the fin is more effective in transmitting heat from primary surface. In the experiment, there will be two comparisons, one among the solid sections and other between the hollow and solid sectional area and same volume for each cross section. The various cross sections of aluminium, is taken because aluminium, is  a light weight material and has high conductivity and is most widely used in the industrial applications.

Modes of heat transfer

Heat transfer is defined as the transmission of energy from one region to another as a result of temperature gradient takes place by the following three modes

1. conduction
2. convection
3. radiation

Heat transmission occurs as a result of combinations of these modes of heat transfer.

Heat transfer from the surface to fin at its base by conduction. This heat is convected to surrounding atmosphere over the fin surface.

Conduction :

The heat conduction is accomplished by two mechanisms

Ø  by molecular interactions

Ø  by drift of free electrons

By molecular interaction, the energy exchange takes place by kinetic motion or direct impact of molecules. Molecules at a relatively higher energy level impart energy to adjacent molecules at lower energy levels. This type of energy transfer always exists so long as there is a temperature gradient in a system comprising molecules of a solid of gas.

By the drift of free electrons, as in the case of metallic solids. The metallic alloys have a different concentration of free electrons, and their ability to conduct heat is directly proportional to the concentration of free electrons in them.

Convection :

Convection is the transfer of heat within a fluid by mixing of one portion of the fluid with another. Convection constitutes the microform of the heat transfer since macroscopic particles of a fluid moving in space cause the heat exchange. The effectiveness of heat transfer by convection depends largely upon the mixing motion of fluid. Convection is met with in situations where energy is transferred as heat to a flowing fluid at any surface over which flow occurs. The heat flow depends on the properties of fluid and is independent of the properties of the material of the surface. However, the shape of the surface will influence the flow and hence the heat transfer.

Convection is of two types

1. Natural convection: The temperature difference produces a density difference results in mass movements.

2. Forced convection: The motion of the fluid is caused by an external device like pump, compressor.

Important parameters in Analysis of Fins :

The various important parameters in the analysis of fins are

1. Heat transfer coefficient

2. Length of the fin

3. Cross sectional area of the fin

4. Thermal conductivity of fin

5. Efficiency and Effectiveness of fin.

Heat transfer coefficient:

The coefficient of convective heat transfer ‘h’ may be defines as the amount of heat transmitted for a unit temperature difference between the fluid unit area of surface in unit time.

The value of ‘h’ depends on the following factors:

1. Thermodynamic properties

2. Nature of fluid flow

3. Geometry of the surface

4. Prevailing thermal conditions

Length of fin:

The length of fin from the heated surface has a great importance on its effectiveness. As the length of fin increases the temperature indicated for a convective heat flow goes on decreasing. Therefore after a certain length the effectiveness drastically reduces, in addition length is uneconomical and often objectionable. This also makes the end heat losses negligible for along fin hence short fins are used.

Cross sectional area of fin:

For a constant cross sectional area fin, the heat flux decreases towards the end of the fin and so that all cross sections of the fin are not properly utilized. End cross sections are poorly utilized compared with cross section at base. Usually parabolic or elliptical profile fins are preferred where as triangular fin gives maximum heat flow per unit weight with ease of manufacturing.

Thermal conductivity of fins:

Thermal conductivity of solids is by the two modes, lattice vibrations and transport by free electrons. The thermal conductivity of solid increases as the square root of absolute temperature of the solid.

Efficiency and Effectiveness of fin:

The purpose of adding fins to a surface is to increase the surface are available for convective heat transfer to the surrounding fluid. In order to express the heat exchanging capacity of an extended surface relative to the heat exchanging capacity of the primary surface with no fins, it is useful to define fin effectiveness.

Fin effectiveness= (heat transfer with fin)/(heat transfer without fin)

Fin efficiency is defined as the ratio of actual heat transferred to the heat which would be transferred, if entire fin were at base temperature.

Generalised Equation for a Fin and its implications to various cross sections

Generalised fin equation:

The generalized equation which is applicable to all fins of any cross sections is given as

d2θ/dx2 +[1/A(dA/dx)(dθ/dx)]-[hA/Ki)(ds/dx)θ]=0

  

This equation is applied to all extended surface configurations for which one-dimensional assumption is valid. The above equation is modified Bessel equation.

The equation when applied to fins of uniform cross sectional area from base to bed becomes

	d2θ/dx2 – h C/Kθ =0

The solution of the above equation is of the form

θ= B e –mx + d e mx

 

Applying boundary conditions to the above equation, the temperature distribution over the fins is given by

Assuming fin as the one, which is insulated at ends which is the most practical case, for boundary conditions the equation becomes

	θ/θ0 = cosh m (l-x) /cosh ml

Assumptions made in the analysis of heat flow for the finned surfaces

1. Thickness of the fin is small compared with the length and width.
2. Homogenous and isotropic fin material. The thermal conductivity of the fin material is constant.
3. Uniform heat transfer coefficient ‘h’ over the entire fin surface.
4. No heat generation with in the fin itself.
5. Joint between the fin and heated wall offers no bond resistance. Temperature at base of the fin is uniform and equal to temperature t0 of the wall.
6. Thorough generalized education for heat transfer from fins is fairly established. Data on different materials and shapes of fins is available. Hence the present work in proposed to conduct experiments on short fin with insulated end with aluminum as material and different geometric shapes.
7. Steady state heat dissipation.

Experimental study of fins :

In the present work, a comparative study of theoretical heat transfer, experimental heat transfer coefficient, efficiency and temperature distribution on different cross sections is made.

Experimental set up:

The experiment is carried out on fin apparatus. It consists of a rectangular duct one end of which is open and the other end is fitted with a blower. A delivery pipe is provided with an orifice in it. To control the flow of air, valves are fitted to the pipe itself. The flow rate is measured by using water manometer conducted to the orifice of delivery tube. The test fin is placed across the duct. Air flows over its entire length. A heater attached to its head, heats the fin.

The fins are 150mm long and 11.3097 mm² cross sectional area. It is provided with tapered holes to insert thermocouples which are attached to the temperature indicator to indicate the temperature on different locations of the fin.

Experimental Procedure :

Natural convection:

The experimental procedure is

1. Power is switched on and dimmer stat is turned on to a required power input.
2. Here blower is not switched on.
3. Wait about 30 minutes for the fin to reach steady state.
4. After a steady state is ensured the temperature on the fin and ambient air temperatures are read from thermometer using thermo couple selector knob.
5. The above procedure is repeated for different heat inputs and the readings of the different temperature values are noted.

Forced convection:

Case I: Heat input is constant and variable flow rate.

1. Power is switched on and dimmer stat is turned on to a required power.
2. Here blower is switched on and water head is adjusted for required flow rate observing manometer readings.
3. Wait about 40 minutes for the fin to reach steady state.
4. After a steady state is ensured, the temperature on the fin and ambient air temperatures are read from thermometer using thermo couple selector knob.
5. The above procedure id repeated for different flow rates of air by keeping the heat input constant.

Case II: Heat input is varied and flow rate is constant.

1. Power is switched on and dimmer stat is turned on to a required power.
2. Here blower is switched on and water head is adjusted to constant flow rate and heat input varies.
3. Wait about 40 minutes for the fin to reach steady state.
4. After a steady state is ensured, the temperature on the fin and ambient air temperatures are read from thermometer using thermocouple selector knob.
5. The above procedure is repeated for different flow rates of air by keeping the heat input constant.

Precautions :

1. The most important precaution is temperature over the fin is to be noted only after steady state is reached.
2. The power applied to the fin should not exceed 200W.

SPECIFICATIONS OF FIN APPARATUS :

Effective length of each fin =240 mm

Spacing between thermocouples = 30 mm

Diameter of the orifice = 20 mm

Size of duct used = 150mm x 100 mm

Coefficient of discharge for orifice meter = 0.61

Shape of fin:

Side of square fin = 12.7 mm

Side of triangle fin = 17.02 mm

Side of hexagon fin = 6.32 mm

Outer diameter of hollow circular fin = 16.1 mm

Inner diameter of hollow circular fin = 10 mm

Side of hollow square fin = 14.25 mm

Inner side of hollow square fin = 10 mm

Side of hollow triangle fin = 21.02 mm

Inner side of hollow triangle fin = 10 mm

OBSERVATIONS & CALCULATIONS :

FIN: Square (Aluminum)

Condition: Natural Convection

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	100	0.53	----------------	86	81	75	71	69	30	47.11	88.88
2	110	0.60	----------------	115	109	102	96	93	30	47.2	88.72
3	120	0.65	----------------	144	135	127	120	116	30	46.95	88.05
4	130	0.70	----------------	165	156	147	139	135	30	46.84	87.84

FIN: Square (Aluminum)

Condition: Forced Convection (Flow of air varies & heat input constant)

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	120	0.66	20	129	120	109	100	95	30	45.13	84.08
2	120	0.66	30	149	140	126	115	109	30	44.87	83.27
3	120	0.66	40	158	148	139	126	115	30	44.68	82.91
4	120	0.66	50	167	157	146	137	123	30	44.32	82.25

FIN: Square (Aluminum)

Condition: Forced Convection (Flow of air constant & heat input varies)

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	100	0.54	30	82	78	72	66	63	30	45.17	83.19
2	110	0.60	30	108	101	92	84	80	30	45.05	83.68
3	120	0.65	30	133	125	114	104	98	30	44.91	83.47
4	130	0.70	30	151	140	127	116	110	30	44.78	83.32

FIN: Triangle (Aluminum)

Condition: Natural Convection

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	100	0.54	----------------	75	62	55	64	58	30	53.93	88.21
2	110	0.60	----------------	106	85	84	79	68	30	53.37	87.24
3	120	0.65	----------------	131	106	109	95	89	30	53.12	86.88
4	130	0.70	----------------	157	135	128	112	110	30	52.94	86.55

FIN: Triangle (Aluminum)

Condition: Forced Convection (Flow of air varies & heat input constant)

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	120	0.66	20	117	82	73	63	59	30	50.8	83.17
2	120	0.66	30	121	87	77	64	61	30	50.5	82.60
3	120	0.66	40	130	93	83	65	62	30	50.37	82.40
4	120	0.66	50	135	95	81	68	64	30	50.10	81.90

FIN: Triangle (Aluminum)

Condition: Forced Convection (Flow of air constant & heat input varies)

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	100	0.54	30	69	62	59	57	55	30	50.85	83.0
2	110	0.60	30	89	78	74	69	63	30	50.66	82.71
3	120	0.65	30	113	106	98	92	89	30	50.57	82.61
4	130	0.70	30	121	107	105	98	90	30	50.45	82.51

FIN: Hexagon (Aluminum)

Condition: Natural Convection

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	100	0.54	----------------	115	94	84	83	81	30	40.42	90.14
2	110	0.60	----------------	132	109	98	96	91	30	40.43	90.05
3	120	0.65	----------------	152	142	131	117	109	30	40.22	89.69
4	130	0.70	----------------	163	154	149	130	117	30	40.26	89.59

FIN: Hexagon (Aluminum)

Condition: Forced Convection (Flow of air varies & heat input constant)

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	120	0.64	20	96	78	70	68	62	30	40.43	90.04
2	120	0.64	30	136	104	88	86	78	30	40.06	89.23
3	120	0.64	40	146	112	95	93	82	30	39.97	89.11
4	120	0.64	50	152	116	97	95	85	30	39.84	88.81

FIN: Hexagon (Aluminum)

Condition: Forced Convection (Flow of air constant & heat input varies)

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	100	0.54	30	95	86	72	66	63	30	40.16	89.41
2	110	0.60	30	112	109	87	74	72	30	39.72	88.62
3	120	0.65	30	141	133	102	92	86	30	39.73	88.42
4	130	0.70	30	160	152	117	99	90	30	39.69	88.39

FIN: Hollow Circular (Aluminum)

Condition: Natural Convection

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	100	0.54	---------------	110	102	96	89	85	30	42.79	86.95
2	110	0.60	----------------	117	104	94	90	86	30	42.75	86.90
3	120	0.65	----------------	122	113	102	98	90	30	42.77	86.95
4	130	0.70	----------------	128	117	106	99	92	30	42.66	86.85

FIN: Hollow Circular (Aluminum)

Condition: Forced Convection (Flow of air varies & heat input constant)

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	120	0.65	20	102	98	92	88	82	30	43.8	88.8
2	120	0.65	30	106	102	98	91	87	30	43.6	88.29
3	120	0.65	40	114	106	103	98	91	30	43.1	87.5
4	120	0.65	50	120	108	102	99	92	30	42.77	86.9

FIN: Hollow Circular (Aluminum)

Condition: Forced Convection (Flow of air constant & heat input varies)

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	100	0.54	30	106	98	94	89	84	30	43.60	88.29
2	110	0.60	30	110	103	98	94	89	30	43.56	88.34
3	120	0.65	30	114	107	99	95	91	30	43.52	88.24
4	130	0.70	30	122	115	111	102	95	30	43.62	88.34

FIN: Hollow Square (Aluminum)

Condition: Natural Convection

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	100	054	----------------	89	82	79	76	71	30	50.37	86.85
2	110	0.60	----------------	93	87	83	79	74	30	50.32	86.54
3	120	0.65	----------------	99	91	87	82	79	30	50.11	86.01
4	130	0.70	----------------	104	94	89	84	81	30	49.78	85.76

FIN: Hollow Square (Aluminum)

Condition: Forced Convection (Flow of air varies & heat input constant)

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	120	0.65	20	81	77	74	71	69	30	52.00	78.89
2	120	0.65	30	88	82	78	77	72	30	51.27	76.90
3	120	0.65	40	94	89	83	81	79	30	50.63	75.98
4	120	0.65	50	98	92	88	83	81	30	50.33	75.81

FIN: Hollow Square (Aluminum)

Condition: Forced Convection (Flow of air constant & heat input varies)

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	100	0.54	30	87	83	79	77	72	30	51.65	75.50
2	110	0.60	30	91	89	83	81	79	30	51.63	75.46
3	120	0.65	30	96	90	85	80	78	30	51.61	75.43
4	130	0.70	30	102	96	91	86	81	30	51.59	75.4

FIN: Hollow Triangle (Aluminum)

Condition: Natural Convection

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	100	0.54	----------------	73	69	64	62	59	30	53.15	87.75
2	110	0.60	----------------	82	75	71	68	63	30	53.17	87.77
3	120	0.65	---------------	94	86	80	75	69	30	52.93	87.39
4	130	0.70	---------------	108	99	91	87	79	30	52.82	87.20

FIN: Hollow Triangle (Aluminum)

Condition: Forced Convection (Flow of air varies & Heat input constant)

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	120	0.65	20	69	63	59	55	49	30	49.86	80.10
2	120	0.65	30	78	71	68	64	59	30	49.60	79.07
3	120	0.65	40	85	79	73	69	59	30	49.22	78.04
4	120	0.65	50	96	90	88	81	77	30	48.92	78.02

FIN: Hollow Triangle (Aluminum)

Condition: Forced Convection (Flow of air constant & Heat input varies)

Sl no	Voltage (V)	Current (A)	Manometer Reading(mm)	T1	T2	T3	T4	T5	T6	Effectiveness	Efficiency (%)
1	100	0.54	30	97	94	88	85	82	30	48.58	79.36
2	110	0.60	30	102	92	89	87	86	30	48.53	78.12
3	120	0.65	30	107	97	86	85	74	30	47.68	77.89
4	130	0.70	30	112	102	97	92	87	30	47.15	77.67mkl;

GRAPHS :

Graphs are drawn according to the above obtained values for

(i)                   Heat Input Vs Effectiveness

(ii)                 Heat Input Vs Efficiency

Applications of fins:

The use of extended surfaces is of practical importance for numerous applications. The following are the various applications of fin materials.

Air-cooled engine cylinder heads

In case of air-cooled engines for an effective cooling the surface area of the cylinder metal, which is in contact with the air, should be increased. Using fins over the cylinder barrels does this. Either these fins are cast as integral part of the cylinder or separate fins are inserted over the cylinder barrel.

Economizers for steam power plants

The purpose of the economizer is to extract the waste heat of the flue gases to preheat the water before it is fed into the boiler.

Using these fins, it will increase the effective area of economizer pipe through which feed water goes into the boiler. By increasing the defective area, more amounts of flue gases will be exposed to the pipes and more amount of heat is extracted from flue gases. This unit improves the overall efficiency of boiler by reducing fuel consumption.

Radiators of automobiles

The function of radiator is to ensure close contact of the hot water coming out of the engine with the surrounding fluid to ensure high rates of heat transfer from the water to sir thereby increasing the life of the engine. Using extended surfaces more amount of surrounding fluid will be exposed to the radiator tubes thereby increasing the heat transfer rate.

Small capacity compressors

The cooling of compressor is to decrease the work done thereby increasing the efficiency of power plant. By using the extended surfaces, more amount of heat will be dissipated to surroundings thereby increasing the life and efficiency of plant.

Transformers

The heat that is generated in the transformer must be  dissipated to the surroundings otherwise the insulating material, which is provided surroundings the wire is melted and short circuit may occur that will cause the failure of transformer. So using extended surfaces the heat is generated is dissipated to the surroundings effectively thereby increasing the life of the transformer.

The fins are used in the following applications by the addition of the same materials to the systems.

1. In the cooling coils and condenser coils and condenser coils which are used in refrigerators and air conditioners.
2. In the convectors, which are used for steam and hot water heating systems.
3. In the electric motor blades.

OBTAINED VALUES :

S. NO.	CROSS SECTION	EFFECTIVENESS	EFFICIENCY
1.	Square	46.57	85.30
2.	Triangular	52.61	83.17
3.	Hexagon	40.03	89.21
4.	Hollow circular	43.59	88.54
5.	Hollow square	51.25	82.89
6.	Hollow triangular	53.15	81.56

CONCLUSION:

The following considerations are drawn from the experimental results of fins of the various cross sections taken.

1. Effectiveness is more for triangular fin followed by square, and hexagon.

2. In case of hollow sections, hollow triangular fin is more effective.

3. For same cross sectional area and volume hollow cross sections are preferable over solid sections.

4. However the requirements may vary widely in their importance over the type of engine/device/system and its area of applications.

For air craft and Automobile purpose preference will be given to less weight material. In that case aluminum fins is best one because of its additional advantage related to lower cost and weight.

REFERENCES :

v  S C Arora, S Domkundwar ‘ A Course in Heat & Mass Transfer’

v  R K Rajput ‘Heat & Mass Transfer

v  C P Kodandaraman ‘Fundamentals of Heat & Mass Transfer’