LAWS OF RADIANT HEAT TRANSFER AND RADIANT HEAT EXCHANGE

Jorge Sepulveda Maldonado #50437January 31, 2017

CHE 3321- 22 Prof. Pablo Traverso

Polytechnic University of Puerto RicoChemical Engineering Department

Winter 2016

AGENDA

• Objectives

• Theory

• Equipment

• Procedure

• Data

• Calculations

• Security

• References

OBJECTIVES

• Demonstrate the Stefan-Boltzmann Law in the experiment

• Determine the View Factor

• The Lambert Cosine Law

• Corroborate the Lamberts Law of Absorption

• Determine the Inverse Square Law for thermal radiation and

light

THEORY

• Electromagnetic SpectrumThermal Radiation

THEORY

• Electromagnetic Radiation:• The emission of energy as electromagnetic waves or as moving subatomic

particles, especially high-energy particles that cause ionization.

• Thermal Radiation• The electromagnetic radiation emitted by a body as a result of its

temperature. Its propagated at the speed of light.

𝛎where,= speed of light = wavelength

𝛎 = frequency

THEORY

• Blackbody• A blackbody absorbs all incident radiation,

regardless of wavelength and direction.• No surface can emit more energy than a

blackbody. • Although the radiation emitted by a

blackbody is a function of wavelength and temperature, it is independent of direction.

• The blackbody is a diffuse emitter.

THEORY

• Emissivity

• Stefan-Boltzmann Law

where, = Energy emitted by unit area of a black body surface = Stefan-Boltzmann constant ( ) = Surface temperature of heated plate (K) = Temperature of surroundings including radiometer (K)

𝜺=𝑬𝑬𝒃

THEORY

• View Factor

The portion of energy which leaves surface A that strikes surface B.

THEORY

• Radiation Intensity• The rate of emitted energy from unit surface area through unit solid angle.• The radiation from a surface has different intensities in different directions. • The intensity of radiation along a normal to the surface is known as intensity of

normal radiation, In. By using Lambert’s cosine law and Stefan-Boltzmann law for a surface at absolute temperature, T and emissivity, , we obtained:𝜀

𝐼𝑛=𝜀 𝜎 𝑇4

π

THEORY

• Lambert’s Cosine Law

where,= intensity of radiation (Lux)= intensity of radiation in normal direction (Lux) = cosine of the angle of incident

THEORY

• Inverse Square Law

THEORY

• Lambert’s Law of Absorption

where, = Luminous intensity after filter (Lux) = original luminous intensity (Lux)= absorptivity of the filter material (dimensionless)= thickness of the filter material (m)

∝

𝑡

𝐼 𝑓𝐼 0

Absorbance: measure of the capacity of a substance to absorb light of a specified wavelength.

THEORY

• Luminous Intensity

where,= luminous intensity (cd= candela) = luminous flux = solid angle

𝐼= 𝜙𝝮

EQUIPMENT

• Rigid aluminum frame (1)

• Right hand carriage (2)

• Thumb screw (3)• Carrier (4) • Scale (5) • Thumb screw (6)• Plug connection (7) • Thermocouple plug (8)• Protective cage (9) • Circular copper plate

(10)• Flat metal plates (11)• Radiometer (12)• Thumb screw (13)• Connecting lead (14)

EQUIPMENT• Light source power

lead (15)• Housing (16)• Glass diffuser (17)• Integral scale (18)• Carrier (19)• Plastic filter plates

(20)• Cork-coated metal

plates (21)• Carrier (22)• Integral connecting

lead (23)• Lightmeter (24)

PROCEDURE: Inverse Square Law

1. Switch on the front Mains switch.2. Remote operation, check connection PC - HT10X/HT10XC console. Set selector switch to REMOTE.

Check that the USB indicator lights on the console are both lit, run the HT13 software. 3. Set the Heater Voltage to 20 Volts. 4. Allow the HT13 accessory to stabilize. Monitor the temperature T10 and the radiometer output on

the mimic diagram screen. 5. When T10 and R are stable, select the icon on the software toolbar to record the following in the

software results table: Temperature of heated plate T10 (°C) Temperature of surroundings T9 (°C) Distance from heated plate to radiometer x (m) Radiometer reading R (m)

6. Move the Radiometer 100 mm towards the heated plate. (move the carriage, do not hold the radiometer body).

7. Wait for the reading from the radiometer to stabilize, record x and R. 8. Repeat the procedure in steps of 100 mm until the radiometer is 300 mm away from the heated

plate.

PROCEDURE: Stefan-Boltzmann Law

Equipment Setup:1. Attach the heated plate to the left-hand end of the track. 2. Attach the radiometer to the right-hand carriage.3. Position the carriage with the radiometer at a distance of 900 mm from the heated plate. 4. Connect the lead from the radiometer to the socket R. Allow it to stabilize at STP, then

adjust the zero potentiometer until the reading is zero. 5. Connect the thermocouple on the heated plate to the socket T10, the thermocouple on

the polished plate to the socket T9 and place the plate adjacent to the equipment, not be subjected to sources of radiation.

6. Set the voltage control potentiometer to minimum, switch manual/remote selector to manual, connect the power lead from the heated plate to the socket OUTPUT 3 (HT10X) or OUTPUT 2 (HT10XC) at the rear of the service unit.

PROCEDURE: Stefan-Boltzman Law

1. Repeat steps 1 & 2 from previous procedure.2. Set the Heater Voltage to 4 Volts. 3. Adjust the voltage control potentiometer to 4 Volts, selector switch set to position V. 4. Allow HT13 to stabilize. Move the radiometer to a position 300 mm away from the plate. Allow

the radiometer to stabilize. Monitor temperature T10 and radiometer R. 5. When T10 and R are stable select the icon on the software toolbar to record the following: • Temperature of heated plate T10 (°C) • Temperature of surroundings T9 (°C) • Radiometer reading R (m) 6. Move the radiometer to the far end of the track. Set the Heater to 8 Volts. Wait for the

temperature of the plate T10 to stabilize then move the radiometer back to the 300-mm position.

7. Allow the reading from the radiometer to stabilize then record T10 and R. 8. Repeat the procedure, increasing the voltage to the heated plate in steps of 4 Volts until voltage

is set to 24 Volts.

PROCEDURE: View Factor

• Repeat steps 1 through 5 from previous procedure adjusting the voltage potentiometer to 20 Volts.

1. Move the Radiometer 100 mm towards the heated plate.

2. Wait for the reading from the radiometer to stabilize then record x and R.

3. Repeat the procedure in steps of 100 mm until the radiometer is 300 mm away from the heated plate.

4. After taking the last reading move the radiometer to the far end of the track and set the Heater Voltage to zero.

PROCEDURE: Lambert’s Cosine Law

Equipment Setup:

1. Attach the light source to the left hand end of the track. Front of the light source is square to the track with the angle indicator set to 0 degrees.

2. Attach the radiometer to the right-hand carriage.

3. Position the carriage with the light meter at a distance of 200 mm from the light source

4. Connect the lead from the radiometer to the socket L.

5. Set the voltage control potentiometer to minimum, switch manual/remote selector to manual, connect the power lead from the heated plate to the socket OUTPUT 3 (HT10X) or OUTPUT 2 (HT10XC) at the rear of the service unit.

PROCEDURE: Lambert’s Cosine Law

1. Monitor the light meter output, L. 2. Adjust the voltage supply to the light source until the light meter output indicates 230 Lux. 3. When the reading L is stable select the icon on the software toolbar to record the following:

• Angular position of light source ∅ = 0 (degrees) • Light meter reading L (Lux)

4. Rotate the body clockwise by 10 degrees. 5. Enter the new angular position of the light source in the data entry box on the software

mimic diagram screen. 6. Wait for the reading from the light meter to stabilize then record ∅ and L. 7. Repeat the procedure rotating the light source clockwise in steps of 10° until the light

source is at 90° to the light meter. 8. Return the light source to the 0° position then repeat the readings rotating the body of the

light source counter-clockwise.

PROCEDURE: Lambert’s Law of Absorption1. Monitor the light meter output, L. 2. Adjust the voltage supply to the light source until the light meter output indicates 230 Lux. 3. When the reading L is stable select the icon on the software toolbar to record the following: • Light meter reading (no filter installed) L (= I0).

4. Obtain readings for filters with the same optical density but increasing thickness as follows:• Record the light meter reading L (= If) with:• one of the medium filters: (t = 3 mm)• two of the medium density filters: (t = 6 mm)• three of the medium density filters: (t = 9 mm)

5. Obtain readings for filters with increasing optical density but constant thickness as follows:• Record the light meter reading L (= If) with the lightest filter only: (t = 3 mm).• Repeat the reading (= If) with one of the medium filters only: (t = 3 mm).• Repeat the reading (= If)with the darkest filter only: (t = 3 mm).

DATA

Heater Voltage

Heater Current

Surrounding

Temperature

(constant)

Plate Temperatu

re

Distance from

heated plat

Radiometer reading

Symbol V I T9 x RUnits Volts Amps (°C) (°C) (m) ()

Width of aperture W

Thickness of filter material

Absorptivity of the

filter material

Angular position of

light source

Light meter

reading Luminous intensity

Symbol W t L

Units (m) (m) Dimensionless (˚) Lux Lux

CALCULATIONS

• General Data & Formulas• Temperature of heated plate

• Temperature of surroundings

• Energy emitted by unit area of

a black body surface (W/m²)= σ ()• Corrected R (W/m²)

1. Inverse Square Law

The inverse square law for lightLogarithm of light meter reading L (Lux)

Logarithm of distance from light meter x(m)

CALCULATIONS

2. Stefan-Boltzmann Law Constant Factor F

3. View Factor

View Factor F

Radiation received by the radiometer

4. Lambert’s Cosine Law Light meter reading L at angle ∅

(Lux)

CALCULATIONS

5. Lambert’s Law of Absorption

Luminous intensity after filter (Lux)

Linear equation

Plot vs t

SECURITY

REFERENCES

1) http://physics.bu.edu/~duffy/py105/Heattransfer.html2) J P Holman, S. B. (2011). HEAT TRANSFER (In SI Units). (10). (M.-

H. G. Holdings, Ed.) New York, United States3) Instruction Manual, Laws of Radiant Heat Transfer and Radiant

Heat Exchange HT13-Issue 1, November 20044) Bergman, T. L., Dewitt, D. P., Incropera, F. P., Lavine, A. S. (2008)

Fundamentals of Heat and Mass Transfer. 7th ed. Hoboken, NJ, United States: John Wiley & Sons