A pipe is used for transporting boiling water in which the inner surface is at 100°C. The pipe is situated in a surrounding where the ambient temperature is 20°C and the convection heat transfer coefficient is 50 W/m² · K. The pipe has a wall thickness of 3 mm and an inner diameter of 25 mm, and it has a variable thermal conductivity given as k(T) = k₀(1 +  βT), where k₀ = 1.5 W/m ∙ K, β = 0.003 K⁻¹, and T is in K. Determine the outer surface temperature of the pipe.