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 CEE518_B3: Heat Transfer_Reddy

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 CEE518_B3: Heat Transfer_Reddy

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. 0.1714 x 10-8 Btu/(h.ft2.0R4) CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy Plank’s Law The graph of power versus wavelength for a perfect blackbody is called the blackbody spectrum. Solar spectrum CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy Wien’s Law Predicts wavelength at which emissive power is maximum Eq. (2.62) CEE518_B3: Heat Transfer_Reddy

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 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). CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy Emissivities of Some Common Building Materials Most building materials have emissivity values in infra-red ~ 0.9 CEE518_B3: Heat Transfer_Reddy

Radiative Properties of Materials Fig. 2.18 CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy Selective Surfaces Selective surfaces- emissivity changes with wavelength: = for an ideal solar collector: -High for solar spectrum - Low for infrared radiation CEE518_B3: Heat Transfer_Reddy

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) CEE518_B3: Heat Transfer_Reddy

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 CEE518_B3: Heat Transfer_Reddy

Figure 2.20 Shape factor for two adjacent orthogonal planes CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy Example 2.15 2.21 Fig. 2.21 CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy 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 CEE518_B3: Heat Transfer_Reddy

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 CEE518_B3: Heat Transfer_Reddy

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. CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy Important Equation (2.69) An effective emittance term is often used for convenience which is defined as: (2.70) CEE518_B3: Heat Transfer_Reddy

Linearized Radiative HT Coefficient + (2.72) CEE518_B3: Heat Transfer_Reddy

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? CEE518_B3: Heat Transfer_Reddy

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 CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy TABLE 2.9 Surface Unit Conductances and Unit Resistances of Air CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy 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. CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy Example 2.17 CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy Fig.2.22 hc= 0.30 Btu/h.ft2.0F CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy Solution: Both series and parallel resistances have to be considered (a) Standard cavity- without radiant barrier CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy (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) CEE518_B3: Heat Transfer_Reddy

CEE518_B3: Heat Transfer_Reddy 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. CEE518_B3: Heat Transfer_Reddy

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 16-42 % which translates to 2-10% of the air-conditioning costs. CEE518_B3: Heat Transfer_Reddy

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 CEE518_B3: Heat Transfer_Reddy

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 CEE518_B3: Heat Transfer_Reddy

Cool roofs have same visible color, but higher thermal reflectance Reflectivity R for solar spectrum Emissivity in infrared can be as high as 90% CEE518_B3: Heat Transfer_Reddy

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 CEE518_B3: Heat Transfer_Reddy