Conjugate gradient method for determining unknown contact conductance during metal casting

The air-gap formation between the casting and the metal mold during the casting of metals creates a thermal resistance that reduces the heat transfer and solidification rates. In this work, the inverse solution methodology based on the conjugate gradient method is developed for estimating the variation of air-gap resistance with time from the transient temperature measurements taken with thermocouples inside the casting region and at the outer mold surface. The advantage of the conjugate gradient method is that there is no need to assume a specific functional form for the unknown quantity beforehand, since the solution automatically determines the functional form over the domain specified. Furthermore the method is stable and converges over an order of magnitude faster than the least square method.