I am grateful there is a forum like this for my physics/engineering questions , hello everyone! I hope some kind engineer out there can help me. I don't know exactly where to begin, so I'll just describe the general process I am trying to understand. When dealing with transient heat transfer with finite elements (explicit forward difference) how exactly are boundaries defined? I mean the system has its bounds applied before entering the defined time loop - correct? The capacity matrix is divided by the time-step size, but will not be modified again in the program (remains constant)? Upon entering the defined time-loop, the nodal heat and heat-rate vectors from the previous time iteration are saved. The heat-rate vector is altered to reflect the time-step and the result is then solved for the current time by multiplying the new heat-rate vector by the inverted capacity matrix? The new solution/nodal temperatures are adjusted to reflect the boundaries of the system? I apologize for all the questions - making sure I understood the process properly. Kind regards.