Cj. Chen et Mn. Ozisik, OPTIMAL CONVECTIVE HEATING OF A HOLLOW CYLINDER WITH TEMPERATURE-DEPENDENT THERMAL-CONDUCTIVITY, Applied scientific research, 52(1), 1994, pp. 67-79
An infinitely long hollow cylinder with temperature dependent thermal
conductivity is heated optimally by controlling the ambient temperatur
e, T(a)(t), such that at the final specified time t(f), the final temp
erature distribution T(f)(r) of the hollow cylinder approximates a des
ired uniform temperature T(d) as closely as possible with a minimum am
ount of energy spent for the heating.