1. Chapter 2C: BASIC THERMAL SCIENCES: RADIATION HEAT TRANSFER
Agami Reddy (July 2016)
Radiation and thermal radiation: Basics
Stefan-Boltzmann Equation
Plank’s Law and Wien’s Law
Black body, grey body and selective surfaces
Radiative properties of materials
Radiation heat transfer: basic equation
Closed form solutions for special cases
Lookup figures for shape factors
Linearized radiation coefficient
Combined convection-radiation
Thermal bridges
HCB-3 Chap 2C: Radiation

2. Electromagnetic Radiation
Radiation is heat transfer emitted by substances in the form of electromagnetic waves (photons of energy) at the speed of light
(3 x10^8 m/s)
Thermal radiation is electromagnetic waves (including light) produced by objects because of their temperature.
HCB-3 Chap 2C: Radiation

3. Stefan-Boltzmann Equation predicts total power emitted by black-body
A perfect blackbody is a surface that reflects nothing and emits pure thermal radiation.
Surface area (m2)
Total Power
(watts)
Q = AT4
Absolute temperature
(K)
Stefan-Boltzmann constant
5.67 x 10-8 Watts/m2K4
The higher the temperature of an object, the more radiation it gives off.
x 10-8 Btu/hft2R4
HCB-3 Chap 2C: Radiation

4. Plank’s Law
The graph of power versus wavelength for a perfect blackbody is called the blackbody spectrum.
HCB-3 Chap 2C: Radiation

5. Model of Solar Wavelength Spectrum
Visible portion: light, color
Infrared portion: provides heat
UV portion: high energy, dangerous, filtered by ozone
HCB-3 Chap 2C: Radiation

6. Wien’s Law Predicts wavelength at which emissive power is maximum
HCB-3 Chap 2C: Radiation

7. Radiant Energy and Visibility
Objects glow different colors at different temperatures.
As the temperature rises, thermal radiation produces shorter-wavelength, higher energy light.
At 1,000°C the color is yellow-orange, turning to white at 1,500°C.
If you carefully watch a bulb on a dimmer switch, you see its color change as the filament gets hotter.
The bright white light from a bulb is thermal radiation from an extremely hot filament, near 2,600°C.
We do not see the thermal radiation because it occurs at infrared wavelengths invisible to the human eye.
HCB-3 Chap 2C: Radiation

8. Total Power Emitted by Real Surfaces
The total power emitted as thermal radiation by a blackbody depends on temperature (T) in K or oR and surface area (A).
Real surfaces usually emit less than the blackbody power, typically between % . A property used to characterize this is the emissivity . Then the Stephan-Boltzmann eqn:
Radiant heat exchange between one very small surface 1 enclosed in a large cavity 2 with temperatures
HCB-3 Chap 2C: Radiation

9. Emissivities of Some Common Building Materials
Most building
Materials have
Emissivity
~ 0.9
HCB-3 Chap 2C: Radiation

10. Radiative Properties of Materials
HCB-3 Chap 2C: Radiation

11. HCB-3 Chap 2C: Radiation

12. Selective surface: emissivity changes with wavelength
Selective body
The absorptivity (and hence
emissivity) characteristics of
such surfaces changes with
wavelength:
- High for solar spectrum
- Low for infrared radiation
From Goswami et al., 2004
HCB-3 Chap 2C: Radiation

13. Radiative Heat Transfer Equations
HT between two OPAQUE surfaces (general):
An effective emittance term is often used for convenience which is defined as:
HCB-3 Chap 2C: Radiation

14. Heat transfer between two grey surfaces
that form an enclosure
Example 2.16
2.15
2.15
A1= 16 x 8 ft
A2= 896 ft2
HCB-3 Chap 2C: Radiation

15. Solution
2.68
2.73
The –ve sign indicates that heat transfer is from surface 2 to surface 1.
HCB-3 Chap 2C: Radiation

16. Figure 2.19 Shape factor for two parallel planes
HCB-3 Chap 2C: Radiation

17. Figure 2.20 Shape factor for two adjacent orthogonal planes
HCB-3 Chap 2C: Radiation

18. 2.21
HCB-3 Chap 2C: Radiation

19. Figs 2.19 & 2.20,
2.19
HCB-3 Chap 2C: Radiation

20. Linearized Radiative HT Coefficient+
HCB-3 Chap 2C: Radiation

21. Combined Convection and Radiation
When comparing heat transfer for a pot 10 cm above a heating element on a stove, radiant heat accounts for 74%
How is heat transferred when the pot sits on the element?
HCB-3 Chap 2C: Radiation

22. Combined Convection/Radiation HT
Convection and radiation heat transfer coexist in building heat flows. A common example is the heat transfer from the interior and exterior surfaces of a wall. In such instances it is more convenient to use tables of combined or effective unit conductances or unit resistances (ASHRAE Fundamentals, 2013). Such tables have been developed based on calculations and experimental tests and include various effects: - wall position - direction of heat flow - surface emittance - still or moving air
HCB-3 Chap 2C: Radiation

23. HCB-3 Chap 2C: Radiation

24. For a brick wall with emittance of 0.93, from table on previous slide:
for a vertical interior wall in summer with horizontal flow direction, the average film coefficient is 8.29 W/(m2. oC) which increases to 34.0 under a wind velocity of 6.7 m/s for an external surface.
For a highly reflective inner surface (emissivity of 0.05)
the film coefficient is only 3.4 W/(m2. oC) illustrating the large contribution due to radiation under natural convection conditions.
HCB-3 Chap 2C: Radiation

25. Example 2.17 Convective coeff hc = 0.30 Btu/h.ft2.0F
HCB-3 Chap 2C: Radiation

26. hc=
0.30 Btu/h.ft2.0F
HCB-3 Chap 2C: Radiation

27. = (1/0.3) = 3.33
1/3.33 =1.21
0.83
Thermal resistance of gap 3.7 times that of standard wall gap.
Resistance of radiant barrier 13 times convective HT
Practical problems
(dust accumulation)
0.323
3.33
3.09
HCB-3 Chap 2C: Radiation

28. Effective emittance
For mean temperature difference 50oF and the temperature difference between both surfaces 10oF and for a 3.5” air gap with orientation of air space of vertical and horizontal heat flow, effective combined thermal resistance is 2.32
Note three fold decrease in the resistance as the emissivity increases from 0.03 to 0.82.
HCB-3 Chap 2C: Radiation

29. Radiant Barriers in Attics
The radiant barrier can be placed in different locations as shown .
Placing it on the attic floor insulation has been found to have the most benefit.
Because most attics are ventilated, the convective heat gain is relatively small provided the ventilation is adequate.
Typically radiant barriers can reduce summer ceiling heat gains by % which translates to 2-10% of the air-conditioning costs.
HCB-3 Chap 2C: Radiation

30. Thermal Bridges
A thermal bridge is a local area of a building's envelope with relatively lower thermal resistance than exists in its surroundings. The wood stud considered is an example of a thermal bridge. The presence of the stud caused the wall heat flow to increase by 18 percent.
Similar or greater increases are caused by structural members that penetrate walls (e.g., balcony supports in a high-rise building) or that support walls (e.g., the steel structure in a high rise)
Thermal bridges are unavoidable in conventional building practice and cause at least two significant difficulties:
- Heat losses and gains are increased.
- Lower temperature can cause condensation, leading to moisture problems in winter (material degradation, paint peeling, mold)
HCB-3 Chap 2C: Radiation

31. Outcomes
Familiarity with the solar wavelength spectrum with its different bands
Familiarity with Plank’s law and Wien’s law
Be able to solve problems involving Stefan‐Boltzmann equation
Familiarity with the various optical properties of materials
Familiarity with the radiative properties of building materials
Be able to solve problems involving radiation HT in enclosures and between different surfaces
Understand the concept of linearized radiative HT coefficient
Familiarity with the use of radiation shape factor concept and how to estimate it from charts for parallel and orthogonal planes
Familiarity with tables listing combined convection and radiation coefficients
Be able to solve problems involving combined convection and radiation HT
Familiarity with effectiveness of radiant barriers in attics
Familiarity with the concept of thermal bridges and its relevance to heat flows through building envelopes
HCB-3 Chap 2C: Radiation