I need to compute the equivalent thermal resistance and thermal capacitance of a structure used for heat transfer. For illustration purpose let’s say it’s the 2D problem of the following figure. In the top surface (nodes 1 to 4) I have a constant heat generation boundary condition (BC) and in the bottom surface (nodes 15 to 20) I have a convection BC. I am interested in the equivalent resistance and capacitance between the top and bottom surfaces given the Finite element matrices.
I found in this answer the hint that I need to use static condensation to compute the reduced matrix $K_{cc} - K_{ci}K_{ii}^{-1}K_{ic}$. My first question is: how to transform that matrix into a scalar quantity (resistance and capacitance)?
My second question is regarding the following approach: I would intuitively just impose at $t_0$ the constant heat generation $Q_V$ in the top surface and make a transient simulation. For the equivalent resistance I would take $R_{th}$ = ( average temp top surface - average temp bottom surface) / Average power flowing from top surface downwards. For the equivalent capacitance I guess I would fit an exponential function to the transient temperature, get the time constant $\tau$ and compte $C_{th}$ as $\tau/R_{th}$. My question is: how does this intuitive solution relate to the formal method using static condensation?
Many thanks in advance!