Hi, I am new to iMechanica. I am also not sure whether this post is appropriate here or not.

I was doing some instability analysis of heat transfer between two rods
having a narrow gap in between them (they might have contacts and
separation with time, the gap is a function of temperature T, and
T=T(x,t)). I know about the matrix analysis used for stability of a
system of ODEs. I am not able to frame my problem (a 1-D transient heat
equation with non-linear boundary conditions) properly so that it
becomes amenable to the standard matrix method of stability analysis.
Does anyone have some references/examples where I can get some help
about this (like existence of limit cycles, under which conditions a
critical point becomes unstable, etc)? I have complete numerical
solution of the problem and I have seen that for certain input/initial
conditions (and parameter values) the solution becomes oscillatory or a
steady state solution cannot be obtained.

 Also, any comments on whether this kind of analysis can be done in Ansys (using gap elements, the gap contact conductance is a function of gap or the contact pressure in case of contact) will be highly apreciated.

 Thanks.