## 1 Introduction
The mechanical method monitors the torque required to rotate a disc or a paddle in molten aluminum [8; 9] until the shear strength value starts to increase its value at the DCP point at a constant rotation speed. The two thermocouples technique, or the TA method [10; 11], determines the temperature in the center (T\({}_{\rm C}\)) of a test crucible and at a nearby inner wall (T\({}_{\rm W}\)) using two thermocouples. The DCP temperature is determined by the local minimum on the \(\Delta\)T versus time curve (\(\Delta\)T = T\({}_{\rm W}-T_{\rm C}\)) and its projection on the T\({}_{\rm C}\) cooling curve. Heat removal from the solid phase is faster than from the liquid phase and occurs at the minimum of the \(\Delta\)T versus time curve because there is a higher thermal conductivity in the solid dendrites than in the surrounding liquid metal. Other similar methods based on one thermocouple have been developed to decrease costs and increase productivity in the data analysis by reducing the total amount of processed data. The first method to define the DCP with one thermocouple located in the center of the TA cup is based on the determination of the first minimum point on the plotted second derivative vs. time graph [12; 13; 14], as shown in Figure 1.  
The second method with one thermocouple is based on the detection of the first minimum of the first derivative curve plotted vs. time graph [15; 16] as shown in Figure 2 with the determination of the maximum liquidus temperature in the first negative crossing of the first derivative curve with the zero line (T\({}_{\rm liq\,max}\)) and the determination of the DCP temperature in the first minimum of the dT/dt curve immediately after the maximum liquidus point. Figure 1: Method 1: the first minimum of the d\({}^{2}\)T/dt\({}^{2}\) curve. Figure 2: Method 2: the first minimum of the dT/dt curve after T\({}_{\rm liq\,max}\). Some works indicate that sometimes the thermal signal is so weak that it is difficult to define the minimum point on the second derivative curve [17]. The third method using only one thermocouple is based on the first derivative curve plotted versus the temperature analysis with the determination of the point at which the first derivative curve starts to change its slope [1], as shown in Figure 3.  
However, it is sometimes difficult to define the exact point of deviation because there are no loops in the first derivative curve, so it is not possible to define the exact position of the elbow point on the dT/dt versus temperature curve. The solid fraction at the DCP can be determined by using different experimental and/or arithmetic methods [8]. Among them, the Newtonian and Fourier [20; 21; 22] methods are mostly applied in the case when the cooling curve data are known. For the Newtonian analysis, first, the solid fraction at each point or temperature must be calculated, determining the integration or cumulative area between the cooling rate (first derivative (dT/dt) of the cooling curve) and the baseline dT\({}_{\text{BL}}\)/dt (BL). The base line corresponds to a cooling rate curve if there is no phase transformation. Applying this method, it is possible to determine the amount of solid fraction at the dendritic coherence point, identifying the temperature at which this event occurs. This temperature is determined in the elbow of the first derivative of the cooling curve when it starts to be constant. This method is applied as the following Figure 4 exhibits. Figure 3: Method 3: dT/dt curve vs. T, with the DCP point in the elbow.