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

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

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. 0.1714 x 10-8 Btu/hft2R4 HCB-3 Chap 2C: Radiation

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

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

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

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

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 10- 90 % . 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

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

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

HCB-3 Chap 2C: Radiation

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

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

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

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

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

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

2.21 HCB-3 Chap 2C: Radiation

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

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

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

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

HCB-3 Chap 2C: Radiation

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

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

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

= (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

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

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 16-42 % which translates to 2-10% of the air-conditioning costs. HCB-3 Chap 2C: Radiation

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

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