A nonlinear unsteady state optimal control problem for a classical, constant diameter ethane thermal cracking reactor is formulated and solved. The process is represented by a pseudo steady state mathematical model, consisting of mass and heat balance, pressure drop, and coking equations. The performance index is of an economical nature, representing the global benefit of reactor operation over a constant operating time. As control variables, the space and time dependent skin tube temperature, the time dependent steam to hydrocarbon ratio, and the time dependent feed flow rate were considered. The results are in agreement with the process physicochemical and technological fundamentals.