I am trying to set up for an experiment, and I need to know the time dependence of the temperature of the front surface of an assembly of plates. The assembly has a heater on one side and is exposed to a gaseous environment (of constant known pressure and temperature) on the other. I am interested in the temperature of the plate where it meets the gas. My problem is that no equations or literature I have yet found describe the assembly when the heated side is changing temperature. I am simplifying it to 1 dimension for my calculations. The temperature of the heated side follows an arbitrary function that is only known after I run the experiment. Assumptions: homogeneous plates of constant thermal conductivity perfect thermal contact between plates Th = f(t) I am stuck here. What equations exist to describe this? Everything I have seen deals with materials at constant temperature exposed to a fluid and allowed to reach equilibrium, not a plate with one side forced to have a changing temperature. Note: This is not a homework problem, but a research experiment I am conducting in a lab at my university.