Numerical solutions of transient temperature and thermally induced stress distributions in a solid disk heated with radially periodic expanding and contracting ring heat flux

Thermal stresses are taken into consideration as important phenomena in many manufacturing processes and design applications. Moreover, moving heat source is frequently encountered in these processes. The aim of this study is to analyze the numerical solutions of transient temperature and thermally induced stress distributions in a solid steel disk heated with radially periodic expanding and contracting ring heat flux under stagnant ambient conditions. It was assumed that the ring heat flux per unit area at the each ring surface was uniform. The applied heat transfer rate, Q, regularly increases from 3.14 to 311 W and then decreases to 3.14 W in one period depending on the area of heated ring. The FLUENT 5.3 program was chosen as computer code to calculate these numerical solutions. Furthermore, a computer program, applying the SIMPSON integration method to the obtained temperature distributions from the heat transfer calculations, has been developed to calculate numerically the governing thermal stress distributions. The calculations were performed individually for a wide range of thermal conductivity, from 20 to 60 W/m K stepped by 5 W/m K and in addition 43 W/m K, and for the various ring heat flux expansion and contraction speeds, from 0.0005 to 0.001 m/s stepped by 0.0001 m/s, under transient conditions. The temperature and thermal stress distributions were obtained as per the moving ring heat flux per unit area, q0. Due to the fact that the maximum temperatures distribution profiles peak at the first and last rings while they increase linearly with the process time, the maximum thermal stress ratio profiles also vary quasi-periodically by peaking at that rings. Furthermore, the thermal stress ratio profiles at the processed surface peak at the heated ring except the first ring and they are repeated with a time interval of one period by almost not changing the peaked shapes of themselves. These obtained results would be useful for similar process using the steels considered in this study.