Thermal Conductivity of Metal BarC B A

mw at Ti

ro ri

mw at To

C B AFig - 1 Schematic Diagram of Experimental Set-up

T1 T2 T3 T4 T5

T6 T7 T8T9

AC

EXP :1

EXPERIMENT NO: 1

Objective: - To find out the thermal conductivity of a given metallic rod.

Apparatus Used: - Voltmeter Ammeter Stop watch Copper – constantan thermocouple Power supply Heating element Digital temperature indicator Voltage regulator(Variac)

Theory: -

Thermal conductivity is an important thermo - physical property of conducting materials, by virtue of which the material conducts the heat energy through it. From Fourier’s law of conduction the thermal conductivity is defined as

Q dT dTk = - ---- ----------- = q ------------ (W/m.K)

A dx dxWhere,

Q = heat transfer rate, watts,q = heat flux, W /m2 A = area normal to heat transfer, m2, and

dT / dx = temperature gradient in the direction of heat flow.The thermal conductivity for a given material depends on its state and it varies with direction, structure, humidity, pressure and temperature change. Thermal energy can be transported in solids by two means.

1. Lattice vibration,2. Transport of free electrons.

In good conducting materials, a large number of free electrons move about their lattice structure of metal. These electrons move from higher temperature region to lower

temperature region, thus transport heat energy. Further, the increased temperature increases vibration energy of atoms in the lattice structure. Thus in hotter portion of the solid, the atoms which have larger vibration energy, transfer a part of its energy to the neighboring low energy molecules and so on throughout the whole length of the body.

In this experiment we have considered heat transfer in only in one direction and losses in radial directions. The tube has an inner radius and an outer radius . This nomenclature, shown in the part of the figure, is enhanced by the control volume outlined in red. The inner and outer radii of the control volume are, respectively, and .

Let the temperature at the surface of the bore of the tube beT1, and the temperature at the outside surface of the tube be T2 . These temperatures create a radially-outward heat flow . In the steady state, is independent of the radial position. If were to vary with , the temperature would necessarily vary with time. At any moment of time, let the magnitude of the heat flow that is entering the control volume at the radius . By the same token, let represent the heat flow that is

leaving the control volume at a radius

From fourier’s low

Q=KA dTdx and so Q=KA

dTdr

Where L=length of the rod

Qdrr =k 2π LdT

Q∫ drr =k 2π L∫ dT

Q ln(R2R1

¿ = k 2π L(T2-T1)

Q = k 2π L(T 2−T 1)

ln (R2R1

)

This is the heat loss due to conduction in insulating material. Heat is carried away by the cooling water at the end of the rod Heat carried away by cooling water = Heat transfer at section AA = Qw =QAA Thermal conductivity at section AA

W/mK W

dTdx

is found out by as a slope of the graph temperature v/s distance

Heat transfer at section BB

W/mK W

W/mK

at

Qw=mwc pw(T i−T o )

Thermal conductivity is changed with change in temperature. Below some metals behavior of thermal conductivity is changed due to change in temperature describes

Thermal conductivity of the pure copper is varies as below

Experimental set up with neat Diagram

The apparatus consist the heating elements fitted on a table stand. One hole is made in it to accommodate the metal rod whose thermal conductivity has to be measured. The metal rod of copper is inserted into hole of an insulating material so that when power supplied to heater coil, heat transfer will take place from the base to another end. The temperature of the metal rod is measured at five positions on rod and four positions in insulating materials by using copper constantan thermocouples and digital temperature indicator. The power supply to heat may be adjusted to desire quantity by means of electronic controlled circuit for that one rheostat is provided on the control panel. Electric power input can be measured by using digital voltmeter and ammeter multiplier. Constant water supply is given at the end in which water is supplied at atmospheric temperature and by conduction & convection heat is supplied to water from rod.

Assumptions

Heat loss after thermocouple section is negligible. Steady state condition:-The time rate between any two parallel points is constant.

This means that the temperature of the fixed points with in a heat conducting body doesn’t change with time.

Consider heat flow in one direction. Boundary surface are also in thermal steady state condition i.e. constant & uniform

temperature is maintained at the faces. Material is homogeneous & isotropic. No internal heat generation.

Procedure: -

Switch on the power supply and adjust voltage and current so as to allow some 500 watts input to heater coil.

Wait for steady state. Steady state can be observed by the temperature reading at one or all points on the surface of the metal rod. Steady state is reached when these temperatures stop changing with time.

Under steady state conditions note the temperature of each point on the surface of the rod as well as temperature of surrounding.

Measure the amount of water flow by measuring time for some fix amount of water and from that measure the mass of collected water.

Measure the temperature of water at inlet and outlet with the help of thermometer. Repeat above procedure for several power input.

Specifications:

(1) Length of Metal bar 430 mm

(2) Size of the metal bar (d) 37.5 mm

(3) Test length of bar 200 mm

(4) No. of thermocouple on bar 5 -

(5) No. of thermocouple on insulation shell 4 -

(6) Length between plane AA, BB & CC 100 mm

(7) Temperature at insulation at distance from centre 46 mm

(8) Temperature at insulation at distance from centre 26 mm

Constants:

Thermal conductivity of asbestos powder Kcal/hr-m-k 0.2

(Note: 1.16306 Kcal/hr-m-k = 1 W/mk) 0.172 W/mk

Specific heat of water 4.187 kJ/kg-k Thermal conductivity of some of the metal at room

temperature Pure copper 330 Kcal/hr-m2oC

Brass 95 Kcal/hr-m2oC

Observations during test:

1 Inlet water temperature oC 2 Outlet water temperature oC 3 Mass flow rate of water (250 CC/min) CC/min 4 Heat input at voltage (80,120,160,200,240) V 5 Temperature at different locations of thermocouple

T1 = ____ oC T4 = ____ oC T7 = ____ oCT2 = ____ oC T5 = ____ oC T8 = ____ oC

T3 = ____ oC T6 = ____ oC T9 = ____ oCTo_water = ____ oC Ti_water = ____ oC

1 Lit = 1000 CC

61 sec for 250 CC i.e 244 sec for 1000 CC or 1lit or 1 Kg or (1/244 sec) is mass flow rate in Kg/sec

Observations table

Points on which Temp is measured

Temp of points

T1T2T3T4T5T6T7T8

Volume lit :

time sec :

mass water :

dT water :

Cp water :

Qwater = QAA :

dt/dx :

Area of rod :

KAA :

dt at AB :

Log(ro/ri) :

QAB :

QBB :

KBB :

dt at BC :

QBC :

QCC :

KCC :

Kmean - AA :

Kmean - BB :

Kmean - CC :

Tmean :

K Mean :

Results and Discussions:

1) Temperature of the bar decreases along the length of the bar. 2) Thermal conductivity at three sections can be studies at different temperature level 3) Change in thermal conductivity observed with the change of temperature for the bar

4) Deviation in the value of 'K' is because of:(i) Steady state condition was not attained

(ii) Rod material may not be pure(iii) Improper insuation

(iv) Human error of conducting experiment

(v)Error in measurement of water due to high temperature, time measuring device, ect..