Consider a large plane wall of thickness L 0 3 ft and thermal conductivity k 1 2 Btu hftF in space The wall is covered with a material having an emissivity of 0 80 and a solar absorptivity of as 5 0 60 The inner surface of the wall is maintained at 520 R at all times, while the outer surface is exp...

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Consider a large plane wall of thickness L = 0.3 ft and thermal conductivity k = 1.2

Question:

Consider a large plane wall of thickness L = 0.3 ft and thermal conductivity k = 1.2 Btu/h·ft·°F in space. The wall is covered with a material having an emissivity of ε = 0.80 and a solar absorptivity of as 5 0.60. The inner surface of the wall is maintained at 520 R at all times, while the outer surface is exposed to solar radiation that is incident at a rate of q̇_s = 350 Btu/h·ft². The outer surface is also losing heat by radiation to deep space at 0 R. Using a uniform nodal spacing of Δx = 0.1 ft,

(a) Obtain the finite difference formulation for steady one-dimensional heat conduction

(b) Determine the nodal temperatures by solving those equations.