Thermal Conductivity Lab-report

Abstract:The objective of this experiment is: To evaluate evaluate the thermal conductivity of copper experimentally using “Thermal “ Thermal Conduction System-Model 9!"# $xperimental results %ere compared %ith the theoretical results& There %as difference in theoretical and experimental results& Theoretical value of thermal conductivity %as ' ()m * and experimental value %as '+"&9' ()m *& This difference is due to experimental errors&

Introduction: Conduction ,

convection and radiation are basic modes of heat transfer& (hen a temperature difference exists in a stationary medium, %hich may be in solid, heat transfer occurs due to conduction across the medium& y conduction conduction heat spontaneously spontaneously flo%s from a body at a higher higher temperature to a body at a lo%er lo%er temper temperatu ature& re& .n the absenc absencee of extern external al drivin driving g fluxes fluxes,, temperat temperature ure differ difference encess disappear over time and the body approaches thermal e/uilibrium& e/uilibrium& Convection Convection is the major mode of heat transfer in the fluids& .n our experiments experiments %e had both convective and conduction heat transfer,

Apparatus:-

Experimental procedure:The follo%ing experimental procedure should be follo%ed %hile conducting this experiment:  $stablish constant and steady cooling %ater flo%&  Turn on heater of unit ' in given arrangement and set to 0 (& 1llo% the



system to reach steady-state conditions& Start recording temperatures using a digital thermometer& 2ote that selector

 

s%itch on the apparatus allo% you to select %hatever thermocouple you %ish to read& Measure cooling %ater flo% rate& 3ecord data at least once every " minutes, and continue until steady conditions have reached& 4ou may have to %ait for about an hour and nearly + min after setting up the apparatus to allo% the unit to reach the desired state conditions&

  (hen the readings do not change in t%o consecutive readings then record the data&

Observations and Calculations

Observations: 5iameter of Copper ar 6 !&7cm 8ength of Copper ar 6 8 6 0cm .nlet temperature of %ater 6 +!C  utlet temperature of %ater 6 0'C  .nlet eat;olume ?lo% 3ate 6 >@ 6 +&++ ml)sec

Calculations:Cross-Sectional Area:-

 A =

 A =

πd

2

4

−2 2

(

3.1416  x 5.08  x 10 4

)

−3

 A = 2.0268 x 10 m

2

Calculations of Mass Flow Ratem!" b# $olume Flow Rate$!":' 

V  =

' 

V  =

V  t 

2.2 ml

s

100 ml

' 

V  =

' 

V  =

=1 x 10− m 4

1 x 10

−4

3

3

m

45 s

−6 m 2.22  x 10

3

s

' 

m = ρ w x V ' 

m

' 

=

0.9956502 x 10

−3

' 

m =2.210 x 10

3

 kg m

3

3

 x 2.22 x 10

6

−

 m s

kg sec

Where density of water is calculated at average value of temperature of inlet and outlet water. T avg=

¿

25

T 1 + T 2 2

+ 34 2

¿ 29.5 c  ρ = 0.9956502

g cm

0

at 29.5 c 3

0

Calculations of %eat Ener&# 'ransferred (":-

( ) 2

 π d  ∆ T  m c p ∆ t = k  ∆ X  4 ' 

q ¿ m c p ∆ t =( 2.213 x 10

−3

' 

q =0.0832

) x ( 4.1814 ) x (9 )

kJ  sec

Calculation of rate of c)an&e of temperature w*r*t distance ∆ T  ∆ X 

: −¿

∆ T  =−97.288 ∆ X 

Calculations of

0.0832

Distance(m)

Temperature('C)

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!!

+:-

( ) 2

q=

 π d  ∆ T  k  4 ∆ X 

= k x 2.0268 x 10−  x 97.288

k =421.94

3

W  m K 

Result and discussion:There are fe% problems that may cause problems and had caused problem in our results& The t%o main reasons are given belo%&

 ?irst problem is in our assumption that %hen there is a steady state, then all the heat



generated %ill be taAen up by the %ater coolant& 1s there is a lot of heat loss through the copper bar in the surrounding atmosphere& 1lthough %e have applied a lot of insulation around the insulating bar but still some heat %as being %asted a%ay in the surrounding environment& There might be the calibration problem in the thermocouples %hich are installed on



the on the copper rod& 1ll the thermocouples may not respond uniformly& So the graph  bet%een temperature and distance %ill change and the accordingly slope %ill also change, affecting the thermal conductivity& There is human error in calculation of volume flo% as there %as no proper



measurement device %as not installed& .nlet %ater temperature %as too high to conduct significant heat through copper bar&