Modeling the Heat Gain of a Window With an Interior Shade ... - inive

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Proceedings of Clima 2007 WellBeing Indoors Solar Transmittance, Absorptance, Reflectance vs Theta 120 Transmittance, Reflectance, Absorptance, percent 100 80 60 40 20 Transmittance Reflectance Absorptance 0 0 10 20 30 40 50 60 70 80 90 100 θ degrees Figure 2. Optical properties of heat absorbing glass. 2.5 2 Ktransmittance Kreflectance Kabsorptance Linear (Ktransmittance) Poly. (Kreflectance) y = 0.1825x 2 + 0.2728x + 0.9845 R 2 = 0.9986 Incidence Angle Modifier 1.5 1 0.5 y = -0.2054x + 0.9945 R 2 = 0.9918 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 (1/cos(θ)) - 1 Figure 3. Incidence angle modifiers versus (1/cos(θ)) – 1)
Proceedings of Clima 2007 WellBeing Indoors Long Wave Radiation Exchange The long wave radiation exchange between the glass and the shade can be characterized by treating the problem as one of gray body radiation exchange with essentially the same geometric interpretation as for short wave radiation. The interior is assumed to behave like a cavity and hence a black body. The long wave radiation heat exchange between the glass and shade can then be written as: ε ( ) 4 4 ssl 1− P εglσ(T g − T s ) Q& W / m 2 glsl = into the mesh 1− (1 − εgl )(1 − P)(1 − εssl ) Eq[10] where σ =Boltzman constant = 5.670E-08 W/m 2 -K 4 and T g and T s are the glass and shade temperatures in degrees Kelvin. Note that the conductivity of the glass and shade are sufficiently high that their temperatures can be assumed to be locally uniform. Similarly, Q & s lg l = − & W / m 2 Qglsl into the glass Eq[11] The long wave radiation from the interior to the glass is: Pσ(T 4 4 i − T g ) Q& W / m 2 igl = into the glass 1− (1 − εgl )(1 − P)(1 − εsl ) Eq[12] The glass also exchanges long wave radiation with the outdoors. Assuming that all the surroundings are at the outdoor temperature, the long wave radiation received by the glass from the outdoor environment is: Q & (T 4 T 4 ogl = εglσ o − g ) Eq[13] Similarly, the radiation from the interior to the shade can be written as: P(1 − ε 4 4 gl )(1 − P) εslσ(T i − T g ) Q& (1 P) (T 4 T 4 isl = sl i s ) 1 (1 gl )(1 P)(1 sl ) + − ε σ − Eq[14] − − ε − − ε Hence the total incoming long wave radiation for the glass is: Q & gl = Q& ogl + Q& s lg l + Q& igl Eq[15] and for the shade: Q & sl = & & Qglsl + Qisl Eq[16] Convection Heat is transferred from or to the glass and shade by convection to the interior air and outdoor air. For the glass, heat flow in by convection is: Q & gc = hi *(Ti - Tg) + ho *(To -Tg) Eq[17]
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Modeling the Heat Gain of a Window With an Interior Shade ... - inive

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