Heat transfer with changing boundary conditions

[Alex K]

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.

 

[timthereaper]

Okay, so the plates are semi-infinite in the vertical direction, but they have a finite thickness in the horizontal (vertical and horizontal wrt the sketch)? I would think you could do a kind of 1D nodal analysis with the wall temperature fluctuating over time. You would have to set all the boundary and initial conditions and determine the proper time step. It might take a bit of doing, but I believe it would work.