EXPERIMENT 14

RADIATION HEAT TRANSFER 14.1 OBJECTIVES

1) To verify the Inverse Square Law for Heat 2) To verify the Stefan-Boltzmann Law 3) To validate Kirchoff’s Law 4) To study Area Factors 5) To verify the Inverse Square Law for light 6) To verify the Lambert’s Cosine Law 7) To verify the Lambert’s Law of Absorption

14.2 DESCRIPTION OF THE EXPERIMENTAL RIG

The Radiation Heat Transfer Rig consists of a pair of electrically heated radiant heat and light sources, together with a comprehensive range of targets and measuring instrumentation.

The unit consists of a horizontal bench mounted track fitted with a heat radiation source end and a light source at the other. Between the two sources may be placed either a heat radiation detector or a light meter. In addition, a number of accessories can be fitted for experimental purposes. These include metal plates with thermocouples attached, two vertically oriented metal plates to form an aperture, and a number of acrylic filters. The radiation detectors and accessories are all clamped to stands which enable them to be positioned at different distances from the appropriate source. Distances are measured with a scale mounted on the front track. Electrical power for the two radiation sources is supplied from control panel and a variable transformer. Temperatures of the two metal plates used in conjunction with the heat radiation source are displayed on a digital read-out, either reading being selected by switching the connectors. Output from heat radiation detector and light meter are displayed on digital read out.

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EXPERIMENT 14

FIGURE 1 VIEW OF THE RADIATION HEAT TRANSFER UNIT

14.3 EXPERIMENT A: INVERSE SQUARE LAW FOR HEAT

Objective: To show that the tile intensity of radiation on a surface is inversely proportional to the square of the distance of the surface from the radiation source. Theory:

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FIGURE 2

The total energy dQ from an element dA can be imagined to flow through a hemisphere of radius r. A surface element on this hemisphere dA1 lies on a line making an angle φ with the normal and the solid angle subtended by dA1 at dA is dω1 = dA1/r2.

(Note: solid angle which is by definition the intercepted area on a sphere divided by r2.) If the rate of flow of energy through dA1 is dQ1 then dQ1 = i φdω1dA where iφ is the intensity of radiation in the φ direction i.e., dQ1 ∝ 1/ r2.

EXPERIMENT 14

Procedures:

FIGURE 3

1. Allow time for radiometer reading to stabilize (at steady heat source temperature) before noting radiometer reading.

2. Record the radiometer reading (R) and the distance from the heat source (X) for a

number of positions of the radiometer along the horizontal track. Distance X (mm) 100 200 300 400 500 600 Radiometer Reading R (Wm-2)

Results:

Plot radiometer reading against distance on a log-log graph.

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EXPERIMENT 14

14.4 EXPERIMENT B: STEFAN-BOLTZMAN LAW

Objective: To show that the intensity of radiation varies as the fourth power of the source temperature. Theory:

The Stefan-Boltzman law states that: qb = σ (TS

4 – TA4)

Where qb = energy emitted by unit area of a black body surface (Wm-2)

(Note: Energy emitted by surface = 3.04 x reading from radiometer) σ = Stefan-Boltzman constant (= 5.67 x 10 –8 Wm-2K4) TS = Source temperature (K) TA = Temperature of radiometer and surroundings (K)

Procedures:

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FIGURE 4

1. Set the power control on the panel to maximum. 2. Set the distance from radiometer to heat source (X) as 110 mm and the distance

from black plate to heat source (Y) as 50mm. 3. Record the temperature (T) and radiometer reading (R) at ambient conditions and

then for selected increments of increasing the temperature up to maximum within practical range. Both the readings should be noted simultaneously at ant given point.

Results:

EXPERIMENT 14

σ = 5.674 x 10-8 W m2 K-4

Temperature Reading (Ts), 0C

Radiometer Reading (R), W m-2

Ts, K

TA, K

qb = 3.04 x R W m-2

qb = σ (TS

4 - TA4)

W m-2

Compare calculate values for qb.

14.5 EXPERIMENT C: KIRCHOFF’S LAW Objective: To determine the validity of Kirchoff’s law which states that the emissivity of a grey surface is equal to its absorptivity of radiation received from another surface when in a condition of thermal equilibrium.

Theory:

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FIGURE 5

For a grey body having an area A1, temperature T1, emissivity E1 and absorptivity α1 surrounded by a black enclosure of area A2 at the same temperature T1, then for thermal equilibrium the grey body must absorb as much radiation as it emits.

i.e., α1 σ T24 A1 = E1 c T1

4 A1 from which α = E.

EXPERIMENT 14

Procedures:

FIGURE 6

1. Place the radiometer on a bench away from the heat source. 2. Set the power to heat source to maximum and allow the temperature of the metal

to stabilize. 3. Set the distance form radiometer stand to heat source (X) as 110 mm and the

distance from black metal plate to heat source as 50 mm.

4. Ensure that the equipment has fully stabilized i.e., temperature of metal plate is steady and radiometer reading is zero when pointed at the walls of the room.

5. Briefly return the radiometer to its stand and record the reading of plate

temperature and radiometer. 6. Remove the radiometer from its stand, disconnect cable and place the radiometer

in a cold location for several minutes, e.g., refrigerator.

7. Quickly return the radiometer to the equipment and record the radiometer readings for metal plate and walls of the room.

8. Remove the radiometer again and place it in a warm location for several minutes

(e.g., drying cabinet, DO NOT EXCEED 700C). Note: When the radiometer is returned to the equipment from the cold or warm location it will gradually return to room temperature causing readings to drift. This experiment is only a demonstration and accurate, steady readings are not required).

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EXPERIMENT 14

Results:

Temperature of metal plate, 0C = Radiometer Readings, W m-2

Condition of radiometer Metal Plate Walls of Room Radiometer at room temperature Cold radiometer Hot radiometer

14.6 EXPERIMENT D: AREA FACTORS Objective: To demonstrate that the exchange of radiant energy from one surface to another is dependent upon their interconnecting geometry i.e., a function of the amount that each surface can ‘see’ of the other.

Theory:

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FIGURE 7

The heat transfer rate from one radiating black surface to another is dependent on the amount that each surface can ‘see’ of the other surface. In order to solve radiant heat transfer problems an area factor F is introduced where F is the defined by the fraction of energy emitted per unit time by one surface that is intercepted by the other surface.

Thus the time rate of radiant heat transfer (Q12) between two black surfaces of area A1 and A2 at temperatures T1 and T2 respectively, is given by:

Q12 = A1 F12 σ (T14 – T2

4)

Area factors are found by analysis, numerical approximation and analogy, and results for common configurations have been published in graphical form.

EXPERIMENT 14

Procedures:

FIGURE 8

FIGURE 9

1. When using the aperture plate make sure the insulation faces the radiometer and

the silvered surface faces the heat source. 2. Set the power control on the control panel to maximum. 3. Set the distance form radiometer to heat source (X) as 300 mm and the distance

from aperture plate to heat source (Y) as 200 mm. Note: The black plate should be placed in the stand and moved close to the heat source, i.e., approximately 50 mm.

4. Once the temperature of the black plate (T) has reached a steady value, record the

radiometer readings (R) for a range of apertures from 60 mm down to zero in steps of 5 mm. Care should be taken when setting the apertures to ensure that the plates are equally disposed either side of the track center-line. Ensure the plates are both vertical and securely clamped before a radiometer reading.

Results:

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EXPERIMENT 14

Black plate temperature (T), 0C =

Aperture mm 60 55 50 45 40 35 30 Radiometer Reading (R)

Aperture mm 25 20 15 10 5 0 Radiometer Reading (R)

Plot radiometer reading versus aperture. 14.7 EXPERIMENT E: INVERSE SQUARE LAW FOR LIGHT Objective: To show that the illuminance of a surface is inversely proportional to the square of the distance of the surface from the light source. Theory:

FIGURE 10

The luminous flux φr from a point light source is considered to partially radiate and produce an illuminance Er on a spherical surface at radius r from the light source. Since the surface area of the sphere is given by 4πr2, the illuminance is inversely proportional to the square of the distance of the surface from the light source. Procedures:

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EXPERIMENT 14

FIGURE 11 It is necessary to set up the equipment in the darkened room in order to eliminate the influence of the ambient light conditions.

1. Record the light meter readings (E) and the distance from the light source (X) for a number of positions of the light meter along the horizontal track.

Results: Distance X, mm 100 200 250 300 350 400 Light Meter Reading E, lux

Plot light meter reading against distance on a log-log graph.

14.8 EXPERIMENT F. LAMBERT’S COSINE LAW Objective: To show that the energy radiated in any direction at an angle with a surface is equal to the normal radiation multiplied by the cosine of the angle between the direction of radiation and normal to the surface. Theory: Lambert’s law of diffuse radiation states that Iφ = IN Cosφ where IN = intensity of radiation in normal direction and Iφ is intensity of radiation in a direction at an angle φ to the normal.

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EXPERIMENT 14

Procedures:

FIGURE 12 It is necessary to set up the equipment in the darkened room in order to eliminate the influence of the ambient light conditions. The light source should be rotated to each desired angle relative to the track and clamped in position before taking measurements.

1. Set the distance from light source to light meter (X) as 150 mm.

2. Record the light meter readings at 150 intervals for each angle of the light source relative to the track between the limits of ± 900 either side of the track centre-line.

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EXPERIMENT 14

Results:

Angle above track centre-line (φ0)

Light Meter Reading (lux)

Angle below track centre-line (φ0)

Light Meter Reading (lux)

0 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90

Plot light meter reading against the angular position of the light source on the same graph. 14.9 EXPERIMENT G: LAMBERTS LAW OF ABSORPTION Objective: To show that light passing through non-paque matter is reduced in intensity in proportion to the thickness and absorptivity of the material. Theory:

FIGURE 13 The luminous intensity (I) after having penetrated the material to a distance (X) is given by as I = I0 e-αX where α = absorptivity of the material, X = thickness of material, I0 = original luminous intensity and I = luminous intensity after traverse.

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EXPERIMENT 14

Procedures:

FIGURE 14 It is necessary to set up the equipment in the darkened room in order to eliminate the influence of the ambient light conditions.

1. Set the distance from the light source to filter plate (X) as 100 mm and the distance from the light source to light meter (Y) as 200 mm.

2. Record the light meter readings first with no filters in position and then with each

of the filters of increasing optical density in succession. Repeat this procedure, but using instead increasing thickness of filters having the same optical density i.e., the medium density material.

(a) Variable optical density demonstration

Filter type No filter Pale Medium Dark Light Meter Reading (lux)

(b) Variable filter thickness test

Filter type 0 3 6 9 Light Meter Reading (lux)

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