How do I convert $W/(mK)$, $W/m^2$ and $W/(m^2K)$ to the same "dimensionality" and unit?
$W/(mK)$ is thermal conductivity. $W/m^2$ is heat flow density related to one unit. $W/(m^2K)$ is the heat transfer value.
By performing arithmetic on them?
I have a sum of integrals where each term is multiplied by a constant in one of the given units. And I need to be able to compute the sum so that the units "agree".
So as an example consider some heat system governed by:
$$\int a \space f \space ds, \int b \space g \space ds, \int c\space h \space ds$$
And particularly I want to make these satisfy equilibrium so that e.g.
$$-\int a \space f \space ds -\int b \space g \space ds +\int c\space h \space ds=0$$
where $a,b,c$ have the given different units respectively and $f,g,h$ are some functions. The integrals can be computed, but how to make the units agree?