Determination of temperature gradient and spectrum in the mold’s core and wall by solving the differential equations using Wolfram Mathematica software ☆

Using of mathematical tools to calculate, simulate the technical problems was widely being used by many researchers. This study was developed based on the Wolfram Mathematica software to determine the temperature spectral and temperature gradient transmittance in the mold’s wall and core, in order to determine the influence of the material thermal conductivity to the mold temperature gradient, as well as evaluating the effect of changing the position of the mold surface to the thermal gradient in the mold. The calculations demonstrated that the increasing of the coefficient of thermal conductivity of the mold material would reduce the temperature gradient of the mold, and the mold walls were identified to have higher thermal gradient than in the mold’s core that were in similar working conditions. The experiments had also shown that TiN and CrN had the same temperature and temperature gradient spectrums as the SKD61, but the gradient values on their surfaces were higher than those of SKD61 and the slopes were higher, too.