I am trying to find a way with which I can find out the temperature of a certain point inside a body undergoing thermal conduction. I understand that this might not be very simple to calculate since the temperature difference changes with time and so the rate of heat transfer changes too.
To make this clear, I am trying to find the temperature variation with time at the center of a steel sphere that is 10 centimeters in radius that starts at t=0 with surface temperature of 500 °K, knowing that the heat capacity of steel is 500 J/kg.K and its thermal conductivity is 55 W/(m.K). So is there a way that is simple enough to do this ? Or are there any simulators on the internet that can do the job ?