A flat panel used on a spacecraft is fabricated from a single layer of composite material, 𝐿𝑐 = 0.02 m t

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A flat panel used on a spacecraft is fabricated from a
single layer of composite material, 𝐿𝑐 = 0.02 m
thick. The spacecraft has inside air temperature
𝑇i = 298 K. The panel’s outer surface is exposed to deep
space where 𝑇𝑆 = 0 K. Thermal conductivity of the
composite material of the panel is 𝜅𝑐 = 5.0 W
m-1K-1 and the outer surface has emissivity 𝜀=
0.8. The inner surface of the panel is exposed to airflow resulting
in a convection heat transfer coefficient ℎ𝑖= 70 W
m-2K-1. The Stefan Boltzmann constant 𝜎 = 5.67 x
10-8 W m-2K-4.
Regarding the outer surface of the panel as a greybody
(temperature 𝑇𝑐, area 𝐴,
emissivity 𝜀) the radiated heat 𝑄
transferred by radiation when the surroundings have
temperature 𝑇𝑠 is given by

A Flat Panel Used On A Spacecraft Is Fabricated From A Single Layer Of Composite Material Lc 0 02 M Thick The Spacec 1 (2.34 KiB) Viewed 62 times

A heat transfer coefficient, ℎrad, can
be used in calculating the heat lost by radiation from the
surface,

A Flat Panel Used On A Spacecraft Is Fabricated From A Single Layer Of Composite Material Lc 0 02 M Thick The Spacec 2 (3.17 KiB) Viewed 62 times

(i) Write an equation for the heat transfer per unit
area from the inside of the spacecraft to outer space in terms of
the radiation and convection heat transfer coefficients and the
thermal conductivity of the panel.
(ii) Show how to obtain the following quartic equation
for the temperature 𝑇𝑐 of the outer
surface.

A Flat Panel Used On A Spacecraft Is Fabricated From A Single Layer Of Composite Material Lc 0 02 M Thick The Spacec 3 (3.18 KiB) Viewed 62 times

(iii) The solution for the panel outer surface
temperature is 𝑇𝑐= 291.97 K. Find the heat transfer rate per unit
area from the panel to outer space.
Q = Αεσ (T. - T,4)
hrad = x (T.2 - T:2)(T. + Ts) o
8.296 x 10-107* +Tc -298 = 0