Radiation Problems Solutions

Page 1

0.1 Radiative heat transfer: exercise 3 0.1.1 Description The components of an electronic package in an orbiting satellite are mounted in a compartment that is well insulated on all but one of its sides. The uninsulated side is inclined to the sun radiation (surface temperature: Ts 5800K, heat flux at the orbit of the earth: qs 1.35 103W m 2) and consists of an isothermal copper plate (squared, flat, opaque, di↵use, side: l 1.0m, plate temperature: Tp 500K, inclination to sun radiation: ✓ ⇡ 6rad, spectral emissivity: ✏ ,1 0.20 for 0.0; 2.0 µm, ✏ ,2 0.80 for 2.0; µm) whose outer surface is exposed to the vacuum of outer space and whose inner surface is attached to the components. Assuming steady-state operating conditions: 1. compute the power dissipated by the components. 0.1.2 Questions 1. compute the power dissipated by the components. 0.1.3 Data SUN surface temperature: Ts 5800.0 K 5527.0 C heat flux at the orbit of the earth: qs 1.35 103 W m 2 1.35 kW m 2 COPPER PLA TE squared flat opaque di↵use side: l 1.000 m plate temperature: Tp 500.0 K 227.0 C inclination to sun radiation: ✓ 0.5236 rad spectral emissivity: ✏ ✏ ,1 0.20 0.0; 2 .0 µm ✏ ,2 0.80 2.0; µm (1) CONST ANTS Stefan - Boltzmann constant: 5.67 10 8 W m 2 K 4 Wien’s displacement law constant: Cw 2.90 103 µmK 0.1.4 Solution QUESTION 1 The Wien’s law provides the wavelength corresponding to the peak emission of a blackbody at a given surface temperature. That value, which is not strictly required, is useful, selecting the right temperature, to estimate in advance, for a given spectral hemispherical emissivity distribution: • the total hemispherical absorptivity (the sun surface temperature is required), • the total hemispherical emissivity (the copper surface temperature is required), and check the outcome of the…