On the left side, a steel plate is subjected to a uniform heat flux of 50 kW/m² and maintained at a constant temperature of 800 K. On the right side, the temperature is maintained at 600 K. The steel plate has a variable thermal conductivity given as k(T) = k₀ (1 + βT), where k₀ = 9.14 W/m∙K, b = 0.0023 K^-1, and T is in K. Determine the thickness of the steel plate (in m).