Free and Forced Heat Convection

GROUP T4 MEMBERS ID Shahul Hammed, Mohd Shah 23719567 Zabedi, Muhammad Zahid Yahya, Muhammad Shafiq Noor Hisham, Syahrul Nazreen Tarabykin, Vladimir

F

Mazlan, Muhammad Zuhairi

R DATE OF EXPERIMENT

STUDENT

Abstract

TABLE OF CONTENTS 1

Aim.................................................................................................................. 3

2

Introduction..................................................................................................... 3

3

Theory............................................................................................................. 4

4

Experimental Investigation.............................................................................. 6

5

4.1

Experimental Apparatus............................................................................6

4.2

Procedure.................................................................................................. 6

Results............................................................................................................. 8 5.1

Sample Calculations.................................................................................. 8

5.2

Calculated Results and Graph.................................................................10

5.2.1

Experiment 1.................................................................................... 10

5.2.2

Experiment 2.................................................................................... 11

6

Discussion of Results..................................................................................... 12

7

Conclusion..................................................................................................... 13

8

References..................................................................................................... 13

1 AIM This experiment aims to investigate the heat transfer rate by natural and forced convection from surfaces with and without fins and also to determine the temperature profile along the rectangular and cylindrical fins.

2 INTRODUCTION Convection is the transfer of energy in a moving liquid or gas flowing through a duct or over an object. The transfer of that energy is due to conduction (the interactions between micro-scale energy carries) and the enthalpy (sum of the internal energy of the fluid and the product of its pressure and volume) carried by the macro-scale flow.[1] The combination of both fluid motion and heat conduction makes convection heat transfer complex. The motion of the fluid enhances the heat transfer by initiating higher rates of conduction at a greater number of sites in a fluid, making it a more effective method of cooling than conduction alone.[2]

There are generally two types of convection, force or natural (free). If the movement of the fluid is assisted by external devices such as a pump, fan or compressor it can be classified as forced convection. However, if the motion of the fluid is a result of inequalities in the density due to temperature differences, it is classified as natural or free convection. Both Figure 21: Convection and conduction heat transfer mechanism form of convective heat transfer strongly depends on the fluid properties such as dynamic viscosity, thermal conductivity, density, and specific heat as well as the fluid velocity. The dependence of convection on so many variables makes it a very complex mechanism of heat transfer. However, for this experiment the fluid we are dealing with will be air and as such most of these values such as density and thermal conductivity are a given constant and the variables that we will be investigating is the fluid flow (laminar or turbulent) via Reynolds number and the Nusselt number.[2, 3]

3 THEORY Regardless of the complexity of convection, the rate of convection heat transfer is observed to be proportional to the temperature difference and is conveniently expressed by Newton’s law of cooling as[4, 5] (3.1 ´ Q=h A s ( T s −T ∞ ) )

where h=convection heat transfer coefficient, W/m2 ∙ ˚K A s =heat transfer surface area, m

2

T s=temperature of the surface,˚ C T ∞=temperature of the fluid sufficiently far from the surface,˚ C Because the convection heat transfer coefficient h depends on the several of the mentioned variables and is thus difficult to determine, a simpler equation will be used in determining the heat transfer

´ m (3.2 ´ C p ( T out −T ¿ ) where Q= ) T out =outlet temperatures T ¿ =inlet temperature C p =heat capacity And the mass flow rate for the system can be found using the following formula (3.3 m=ρ ´ ∙ A ∙ U avg )

where ρ= air density A=cross section areaof the inlet

U avg =average velocity The close connection between convection heat transfer and fluid mechanics mean that the fluid flow plays a key role in heat convection. Some flows are smooth and orderly while others are rather chaotic. The highly ordered fluid motion characterized by smooth streamlines is called laminar. The flow of high-viscosity fluids such as oils at low velocities is typically laminar. The highly disordered fluid motion that typically occurs at high velocities characterized by velocity fluctuations is called turbulent. The flow of low-viscosity fluids such as air at high velocities is typically turbulent. To determine the flow type the Reynolds number of the flow is determined[2]

U ×L (3.4 R e flat plate = ¿ v ) (3.5 U ¿ × Dh ) R e cylinder =

v

where L=width of the flat plate D h=hydraulic diameter of the cylinder ν =kinematic viscosity

In convection studies, it is common practice to non-dimensionalize the governing equations and combine the variables, which group together into dimensionless numbers in order to reduce the number of total variables. It is also common practice to non-dimensionalize the heat transfer coefficient h with the Nusselt number, defined as (3.6 ) Nu=

´ Dh Q∙ A s λ ( T o−T m )

where λ=thermal conductivity

T m=

T ¿ +T out 2

Finally, to determine the efficiency of the heat transfer rate, the ratio of power of the heat dissipated by the fins and plate and the electrical power supply is obtained (3.7 )

η=

´ Q ´ power Q

4 EXPERIMENTAL INVESTIGATION

Figure 41: G.U.N.T WL-350 Heat Convection Apparatus; 1) Temperature sensor, 2) Air duct, 3) Thermocoup

4.1 EXPERIMENTAL APPARATUS a) b) c) d)

GUNT WL-352 Heat Convection Apparatus Digital Anemometer Thermocouple thermometer Vernier Caliper

4.2 PROCEDURE Experiment #1 a) Free convection 1) The air duct is set up with the fan switched off. The flat plate is carefully mounted from the back and connected to the power supply. The power is switched on and turned to maximum. 2) As the flat plate receives power, it gets heated up. The cut-off point for the voltage needs to be achieved before any readings can be taken. 3) Once the condition in (2) is met, temperature readings of the flat plate surface, the inlet and the outlet are recorded using the thermocouple. 4) The air velocity at the inlet and the outlet are measured using the anemometer. 5) Steps 1-4 were repeated for the rectangular and the cylindrical fins. b) Forced convection 6) The fan switched on rig was switched on.

7) The flat plate is inserted and the same measurements as for free convection were taken after an appropriate amount of time. 8) Steps 2 to 5 were repeated. Experiment #2 1) The cylindrical fin plate was mounted in the rig as seen in Figure 4-1 with the fan and power set to max. 2) The plate is allowed to heat up and the cut-off point of the voltage was achieved before any readings were taken. 3) The inlet and outlet temperature, the air flow rate was measured using the anemometer and the power input to the heater was noted. 4) The temperature distribution along the fin (T2, T3, T4 and T5) was measured using the thermocouple. 5) Steps 1 to 4 were repeated using the rectangular fin plate. 6) The temperature distribution along the length of each of the fins was plotted.

5 RESULTS 5.1 SAMPLE CALCULATIONS Hydraulic Diameter of Air Duct D h=

4 × 0.01495 =0.1223 m 0.4891

Average Temperature

T m=

Tin+Tout 26.1+ 29 = =27.55° C 2 2

Density

(

1.1881+ ρ=

(

20−T m 1.1120 T m−40

)

20−T m +1 T m −40

)

1.1120 ( 20−27.55 27.55−40 ) +1 ( 20−27.55 27.55−40 )

1.1881+ ρ=

ρ=1.1594 kg/m

3

Specific Heat Capacity 1.007+ Cp=

(

(

)

20−T m +1 T m −40

)

1.008 ( 20−27.55 27.55−40 ) +1 ( 20−27.55 27.55−40 )

1.1007+ Cp=

20−T m 1.008 T m−40

C p =1.0074 kJ /kg ∙ K

Thermal Conductivity 0.02603+ λ=

(

(

20−T m 0.02749 T m −40

)

20−T m +1 T m −40

)

0.02749 ( 20−27.55 27.55−40 ) +1 ( 20−27.55 27.55−40 )

0.02603+ λ=

λ=0.0266 W / K ∙m

Velocity (15.13× 10−6 )+ ν=

(

(

20−T m (16.92× 10−6) T m −40

)

20−T m +1 T m −40

)

(16.92 ×10 ( 20−27.55 27.55−40 ) 20−27.55 ( 27.55−40 )+1

(15.13× 10−6 )+ ν=

−6

)

ν =1.5806× 10−5 m2 / s

Mass Flow rate m=1.1594 ´ × 0.01495× 0.1=0.00173 kg /s

Output Power ´ Q=0.00173 ×1.0074 × ( 29−26.1 ) =0.00506 W

Efficiency η=

0.00506 ×100=0.00298 170

Reynolds Number ℜ=

0.1 ×0.1223 2 =7.7349 ×10 −5 1.5806 ×10

Nusselts Number Nu=

0.00506 ×0.1223 =0.039 0.01407 ×0.02667 × 42.45

Heat Transfer Coefficient ´ 0.039 × 0.0266 =0.0085 W /( m2 . K ) h= 0.1223

5.2 CALCULATED RESULTS

AND

GRAPH

5.2.1 Experiment 1 Table 5-1: Experimental results for heat convection of flat plate.

Flat Plate Free

Forced

0.01407

0.01407

0.00506

0.06139

η (%)

0.00298

0.03654

Re

773.49

24886

h (W/m^2.K)

0.0085

0.1406

Aeff (m^2) ´ Q

power

(W)

Table 5-2: Experimental results for heat convection of cylindrical fins.

Cylindrical Fins Free

Free

0.10012

0.10012

0.04025

0.29497

η (%)

0.02354

0.17250

Re

1507.7

1507.7

h (W/m^2.K)

0.0078

0.0078

Aeff (m^2) ´ Q

power

(W)

Table 5-3: Experimental results for heat convection of rectangular fins

Rectangular Fins Free

Free

0.1539

0.1539

0.02625

0.27549

η (%)

0.01572

0.16496

Re

1378.6

23497

h (W/m^2.K)

0.0046

0.1059

Aeff (m^2) ´ Q

power

(W)

5.2.2 Experiment 2

Temperature vs. Distance 45.0 40.0 35.0 30.0 25.0 Temperature (°C)

20.0 15.0 10.0 5.0 0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 Distance (m)

Figure 5-1: Temperature profile for cylindrical fins from outlet T2-T5

Temperature vs. Distance 12.0 10.0 8.0

Temperature (°C)

6.0 4.0 2.0 0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 Distance (m)

Figure 5-2: Temperature profile for rectangular fins from outlet T2-T5

6 DISCUSSION OF RESULTS For the first half of experiment 1, that is natural or free convection, the results indicates that the cylindrical pins fins has the best performance among the 3 plates tested. The cylindrical pin fin had an efficiency of 0.023 % with an effective surface area of 0.10012 m2 which is lower than the rectangular fin at 0.1539 m2. The flat plate was the least efficient at 0.003 % while the rectangular fins came in second at 0.016%. The results for the second half of experiment 1, forced convection, shows a significant increase in the efficiency of the plates. The cylindrical pin fin still holds the best performance with an efficiency of 0.17% followed closely by the rectangular fins at 0.16% and finally the flat plate at 0.04%.

Figure 61: (a) Heat transfer results for fin-baseplate assemblies with a 68-fin array; (b) heat transfer per unit area for

The low performance of the flat plate can be attributed to its small surface area, 0.01407m2. In accordance to research done by Sparrow and Vemuri [6] on the free convection on different populous of pin fin arrays, the results showed a proportional increase in the heat transfer rate as surface area increase. Figure 6-1 shows the results from said research as a graph of Nusselts number against Rayleigh number. The Nusselts number defined in the graph was intended to be a direct reflection of the rate of heat transfer from the fin-baseplate assembly per unit baseplate-toambient temperature difference while the Rayleigh number is a dimensionless version of the temperature difference. From the graph the higher the pin-fin array with the higher length over diameter ratio (L/D) yielded the best heat transfer performance. However, this doesn’t not explain the performance difference of the cylindrical pin versus the rectangular fins. The surface area of the rectangular fins is significantly higher (>50%) than that of the cylindrical pins but has a lower performance in heat transfer rate.

7 CONCLUSION

8 REFERENCES [1]

[2] [3]

[4] [5] [6]

G. Nellis, S. A. Klein, and Ebooks Corporation. (2009). Heat transfer. Available: http://ezproxy.lib.monash.edu.au/login? url=http://www.MONASH.eblib.com.au/EBLWeb/patron/? target=patron&extendedid=P_424535_0 Full text available (with Read Aloud feature) from Ebook Library Y. A. Çengel, Heat transfer : a practical approach, 2nd ed. Boston: McGrawHill, 2003. B. Sunde**n and Ebooks Corporation. (2012). Introduction to heat transfer. Available: http://ezproxy.lib.monash.edu.au/login? url=http://www.monash.eblib.com.AU/EBLWeb/patron/? target=patron&extendedid=P_876771_0 Full text available (with Read Aloud feature) from Ebook Library F. P. Incropera, Fundamentals of heat and mass transfer, 7th ed. Hoboken, NJ: John Wiley, 2011. L. M. Jiji and L. M. Jiji, Heat convection: Springer, 2006. E. Sparrow and S. Vemuri, "Natural convection/radiation heat transfer from highly populated pin fin arrays," Journal of heat transfer, vol. 107, pp. 190197, 1985.