Consider a steam injection well in a heavy oil formation. The well is insulated to reduce heat loss. The inner radius of insulation is d. The heat transfer coefficient at the outer surface of insulation h and thermal conductivity k are known. The temperature of the steam and the environment surrounding the outer surface of insulation is Ta and To, respectively. a- Determine the heat transfer rate per unit well length as a function of well insulation radius and the thermal properties of the system. Determine the insulation radius (called critical insulation thickness) at which the heat loss is maximum. b- Plot heat transfer rate per unit length versus thickness of insulation using the following properties d=4 cm; h = 4 W/m2 and k= 0.181 w/m-C; Ta = 275 C, To = 10 °C