A pipe is used for transporting boiling water in which the inner surface is at 100°C. The pipe is situated in surroundings where the ambient temperature is 10°C and the convection heat transfer coefficient is 70 W/m²∙K. The wall thickness of the pipe is 3 mm and its inner diameter is 30 mm. The pipe wall has a variable thermal conductivity given as k(T) = k₀ (1 + βT), where k₀ = 1.23 W/m ∙ K, β = 0.002 K⁻¹, and T is in K. For safety reasons and to prevent thermal burn to workers, the outer surface temperature of the pipe should be kept below 50°C. Determine whether the outer surface temperature of the pipe is at a safe temperature so as to avoid thermal burn.