1. Chapter 2C: BASIC THERMAL SCIENCES: RADIATION HEAT TRANSFER
Agami Reddy (rev Dec 2018)
Electromagnetic 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
Lookup figures for shape factors
Closed form solutions for special cases
Linearized radiation coefficient
Combined convection-radiation
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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.
Electromagnetic
radiation spectrum
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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
(2.61)
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/(h.ft2.0R4)
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Plank’s Law
The graph of power versus wavelength for a perfect blackbody is called the blackbody spectrum.
Solar spectrum
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Wien’s Law
Predicts wavelength at
which emissive power is
maximum
Eq. (2.62)
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6. 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 is modified to:
Figure 2.17
Example of thermal radiation spectra for black and gray (ε = 0.6 in.) surfaces at room temperature, 70°F (530°R; 294 K).
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Emissivities of
Some Common
Building Materials
Most building
materials have
emissivity values
in infra-red ~ 0.9
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8. Radiative Properties of Materials
Fig. 2.18
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Selective Surfaces
Selective surfaces- emissivity changes with wavelength:
= for an ideal solar collector:
-High for solar spectrum - Low for infrared radiation
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10. Radiative Heat Transfer Equations
HT between two OPAQUE surfaces (general):
Some function of emissivities
of both surfaces
Two important relations exist among shape factors:
Reciprocity eqn:
Conservation eqn:
(2.66)
(2.67)
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11. Figure 2.19 Shape factor for two parallel planes
0.2
0.5
2.0
5.0
Figure 2.19 Shape factor for two parallel planes
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12. Figure 2.20 Shape factor for two adjacent orthogonal planes
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Example 2.15
2.21
Fig. 2.21
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Figs 2.19 & 2.20,
2.19
Since both areas 1 and 6
are equal, we can select
Y and X interchangeably
Note: Since area 2 is twice area 1
we have F21 = 0.3x(A1 / A2) = 0.15
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15. Heat Transfer between Two Grey Opaque Surfaces
that form an enclosure such that one encloses the other
(2.60)
General Eqn
A1= 16 x 8 ft = 128 ft2
A2= 896 ft2
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16. CEE518_B3: Heat Transfer_Reddy
Solution
For opaque surface
2.68
(2.73)
The –ve sign indicates that heat transfer is from surface 2 to surface 1.
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17. CEE518_B3: Heat Transfer_Reddy
Important Equation
(2.69)
An effective emittance term is often used for convenience which is defined as:
(2.70)
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18. Linearized Radiative HT Coefficient+
(2.72)
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19. 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?
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20. 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
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TABLE 2.9
Surface Unit Conductances and Unit Resistances of Air
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For a brick wall with emittance of 0.9, from Table 2.9:
For still air and for horizontal surface, the direction heat flow is important ( values of h change from 9.26 to 6.13)
for a vertical interior wall in summer with horizontal flow direction, the average film coefficient h 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)
h is only 3.4 W/(m2. oC) illustrating the large contribution due to radiation under natural convection conditions.
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Example 2.17
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Fig.2.22
hc=
0.30 Btu/h.ft2.0F
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Solution:
Both series and parallel resistances have to be considered
(a) Standard cavity- without radiant barrier
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(b) with radiant barrier
Thermal resistance of gap 3.7 times that of standard wall gap.
Resistance of radiant barrier 13 times convective HT
Practical problems (dust accumulation)
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Effective emittance
Table 2.10
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 3.63 (as against 3.09 from example above)
Note three fold decrease in the resistance as the emissivity increases from 0.03 to 0.82.
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28. Radiant Barriers in Attics
Fig.2.23
The radiant barrier or reflective foil can be placed in different locations as shown.
Placing it on the attic floor insulation has been found to have the most benefit (and is also practical).
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.
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29. CEE518_B3: Heat Transfer_Reddy
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
Familiarity with the use of radiation shape factor concept and how to estimate it from charts for parallel and orthogonal planes
Be able to solve problems involving radiation HT in enclosures and between different surfaces
Understand the concept of linearized radiative HT coefficient
Familiarity with tables listing combined convection and radiation coefficients
Be able to solve problems involving combined convection and radiation HT
Understanding benefit of using radiant barriers in attics
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30. Cool Roofs Summer Heat Gain through Roofs and
Another example where radiation heat transfer plays an important role
Summer Heat Gain through Roofs and
Effect of Roofing Reflectance
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31. Cool roofs have same visible color, but higher thermal reflectance
Reflectivity R for solar spectrum
Emissivity in infrared can be as high as 90%
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32. CEE518_B3: Heat Transfer_Reddy
Green Roofs
Saves on building cooling energy
Retains stormwater
Reducing urban heat island
Another strategy of reducing heat gains from roofs in summer while providing
psychological benefits and mental fatigue recovery
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