Authors: Neil Dominic D. Careo, Glanelle Ivy S. Cea
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Laboratory 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 tranfer 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 inulated and #oundar% condition.
Theory: The heat tranfer from a heated urface to the am#ient i given #% the relation &'hA(T. In thi relation h i the heat tranfer coefficient ) (T i the temperature difference and A i area of heat tranfer. To increae &) h ma% #e increaed or urface area ma% #e increaed. In ome cae it i not poi#le to increae the value of heat tranfer coefficient and the temperature difference (T and thu the onl% alternative i to increae the urface area of heat tranfer. The urface area i increaed #% attaching e*tra material in the form of rod + circular or rectangular" on the urface ,here ,e have to increae the tranfer 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 ditri#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% ditance * from the fin T0' Temperature Temperature at *'0 T/' Am#ient Temperature ' ength of the fin m'
√
hp KA
hc' onvective heat tranfer coefficient p' perimeter of the fin A' area of the fin
' thermal conductivit% of the fin 3eat flo, &' θ √ hPKA tanh mL
EFFETI!ENESS OF FINS : $ffectivene of a fin i defined a the ratio of the heat tranfer ,ith fin to the heat tranfer from the urface ,ithout fin. For end inulated 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 tranferred #% the fin to the ma*imum heat tranferred #% the fin area ,ere at #ae temperature.
5'
θ 0 √ hPKA tanh mL hPLθ 0 tanh mL
5'
mL
E"PERIMENTAL PROEDURE: 01. onnect the e&uipment to electric po,er uppl%. 02. eep the thermocouple elector ,itch to 6ero poition. 07. Turn the dimmertat 8no# cloc8,ie and ad9ut the po,er input to the heater to the deired value. 0:. S,itch on the #lo,er. 0;. Set the air flo, rate to an% deired value #% ad9uting the difference in mercur% level in the manometer. 0<. Allo, the unit to ta#ili6e. 0=. Turn the thermocouple elector ,itch cloc8,ie 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
' Benit% of manometric fluid' 17<00 gCm 7
m
a
' Benit% of air ' 11=0 gCm7
ALULATIONS: 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 atmopheric preure 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 eGnP 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 ditri#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 ditance at different poition. K'K1) K2) K7) K:) K;) K< here T'Temperature at a#ove point T'T1) T2) T7) T:) T;) T< Liven thermocouple ditance 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 )