Experiment No 7 Pin Fin Apparatus

Experiment No.7 PIN FIN APPARATUS AIM: 01. To determine the variation of temperature along the length of the pin fin under forced convection. 02. To determine the value of heat tranfer co!efficient co! efficient under forced condition and to find a" Theoretical value of temperature along the length of the fin. #" $ffectivene $ffectivene and efficienc% of of the pin!fin for inulated and #oundar% condition.

Theory:  The heat tranfer from a heated urface to the am#ient i given #% the relation &'hA(T. In thi relation h i the heat tranfer coefficient ) (T i the temperature difference and A i area of heat tranfer. To increae &) h ma% #e increaed or urface area ma% #e increaed. In ome cae it i not poi#le to increae the value of heat tranfer coefficient and the temperature difference (T and thu the onl% alternative i to increae the urface area of heat tranfer. The urface area i increaed #% attaching e*tra material in the form of rod + circular or rectangular" on the urface ,here ,e have to increae the tranfer rate. -Thi e*tra material attached i called the e*tended urface or fin-. The fin ma% #e attached on a plane urface) then the% are called plane urface fin. If the fin are attached on the c%lindrical urface) the% are called a circumferential fin. the cro ection of fin ma% #e circular) rectangular or para#olic.

 TEMPERATURE DISTRIBUTION AND HEAT TRANSFER FROM FINS FROM END INSULATED ONDITION: Temperature Temperature ditri#ution along the length le ngth of the fin i

θ θ0

 '

T − T ∞ T  0−T ∞

'

cosh m ( L− x ) cosh mL

here T' Temperature Temperature at an% ditance * from the fin T0' Temperature Temperature at *'0 T/' Am#ient Temperature ' ength of the fin m'

√

hp  KA

hc' onvective heat tranfer coefficient  p' perimeter of the fin A' area of the fin

' thermal conductivit% of the fin 3eat flo, &' θ √ hPKA tanh mL

EFFETI!ENESS OF FINS : $ffectivene of a fin i defined a the ratio of the heat tranfer ,ith fin to the heat tranfer from the urface ,ithout fin. For end inulated condition4 ∈

'

'

√

θ

*

0

√

hPKA  tanh mL hAθ 0

 PK  hA  tanh m

The efficienc% of fin i defined a the ratio of the actual heat tranferred #% the fin to the ma*imum heat tranferred #% the fin area ,ere at #ae temperature.

5'

θ 0 √ hPKA tanh mL hPLθ 0 tanh mL

5'

mL

E"PERIMENTAL PROEDURE: 01. onnect the e&uipment to electric po,er uppl%. 02. eep the thermocouple elector ,itch to 6ero poition. 07. Turn the dimmertat 8no# cloc8,ie and ad9ut the po,er input to the heater to the deired value. 0:. S,itch on the #lo,er. 0;. Set the air flo, rate to an% deired value #% ad9uting the difference in mercur% level in the manometer. 0<. Allo, the unit to ta#ili6e. 0=. Turn the thermocouple elector ,itch cloc8,ie and note do,n the temperature T 1 to T<. 0>. Note do,n the difference in level of manometer. 0?. Repeat the e*periment for different po,er input to the heater.

OBESER!ATION TABLE:

Sr.No

@oltmeter in @olt

Ammeter in Amp

Po,er in att

anometer in mm of 3g

Temperature reading in deg. c

h1

T1

h2

3

T2

T7

T:

OBSER!ATION: here d0' Biameter of orifice'0.02 m or 10 mm d p' internal diameter of pipe' 7.>1 cm  ρ

 ρ

' Benit% of manometric fluid' 17<00 gCm 7

m

a

' Benit% of air ' 11=0 gCm7

ALULATIONS: 1. @elocit% of orifice ' @ 0'

√ 2 gh ( ρ m − ρ a )  ρ a∗1− β 4

do  β here ' dp

2. @a ' @elocit% of air in the duct'

Vo∗π  @a'

∗do

4

Velocity at orifice ∗cross −sectional area of orifice Cross sectional area of duct  Vo∗π 

2

idth of duct ∗!readth of duct 

'

4

 ∗"

7.Average Surface Temperature of Fin i given #%)

T  1 + T 2 + T 3 + T  4 + T  5 + T 6 T'

6

:. T/' Am#ient Temperature'

2

∗do

T;

Ts + T ∞ ;. Tm' ean Temperature'

2

1" From BRD AIR atmopheric preure ta#le!1 E'1.><10G!; gC m) P r ' 0.=2) '0.02< Cm 8 ) d f '0.012 m

Va di R e'  #

•

The relation for Nu i 2" Nu' R eGnP r G1C7 The value of ) P r  and n from tandard ta#le For R e'0.: to :.0) '0.?>?) n'0.77 R e': to :0) '0.?11) n'0.7>; R e':0 to :000) '0.<>7) n'0.:<< R e':000 to :0000) '0.2?7) n'0.<1> R e':0000 to :00000) '0.2=) n'0.>0;

 $u K  7" hc' df  here +Tm" of air at ::.1
√

hp  KA

,here P' perimeter' df 

π  A' Area' Temperature ditri#ution i given #%

T −T ∞ T  0 − T ∞

'

cosh m ( L− x ) cosh mL

T' T/J+ T 0 −T ∞ "

cosh m ( L− x ) cosh mL

4

2

∗d 0

here K i the thermocouple ditance at different poition. K'K1) K2) K7) K:) K;) K< here T'Temperature at a#ove point T'T1) T2) T7) T:) T;) T< Liven thermocouple ditance K1'20 mm' 0.02 m K2' ;0 mm' 0.0; m K7'>0 mm' 0.0> m K:'110 mm' 0.11 m K;'1:0 mm ' 0.1: m K<' 1=0 mm' 0.1= m cosh m ( L− x )

T1' T/J+ T 0 −T ∞ " Bitance K in mt

$ffectivene of fin'

cosh mL

Temperature e*periment in deg. c

√

hPKA  tanh mL hAθ 0

tanh mL

$fficienc% of fin '

mL

from Temperature from calculation in deg. c