A pipe is used for transporting hot fluid in which the inner surface is at 150°C. The pipe has a wall thickness of 5 mm and an inner diameter of 15 cm. The pipe wall has a variable thermal conductivity given as k(T) = k₀ (1 + βT ), where k₀ = 8.5 W/m ∙ K, β = 0.001 K⁻¹, and T is in K. The pipe is situated in surroundings of freezing air at 0°C with a convection heat transfer coefficient of 60 W/m²∙K on the pipe’s outer surface. Solar radiation is incident on the pipe’s outer surface at a rate of 100 W/m², and both the emissivity and solar absorptivity of the outer surface are 0.9. Determine the outer surface temperature of the pipe.

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T₂ T₁ Hot fluid E, α Pipe wall K(T) = ko(1+BT) 12 qsolar h, T لله