I know how to use thermal resistance circuits to calculate heat transfer in Cartesian and cylindrical coordinates, but I don't know how to deal with real-world insulation values, and I was not able to find much about this online.
For example, I have this hot water tank that has an insulation jacket with 2" R-12.5 insulation. For simplicity, let's assume the insulation is the only thing that separates the hot water from cold outside air (no heat transfer from bottom of tank, top of tank, etc. Just through the insulation jacket). Assume water tank thickness aside from the 2" insulation jacket is negligible.
So it goes hot water -> insulation -> cold air outside. I can look up a free convection coefficient for the tank's hot water and can look up a convection coefficient for air as well. That allows me to use the formula $$ R=1/(h*2*pi*r*heightofinsulationjacket) $$ twice (once for water and once for air).
So the problem is how to deal with the insulation jacket. How do I interpret 2" R-12.5 insulation? How do I factor in the thickness of the insulation? The surface area is taken care of in the heat transfer equation.
$$ Q''=(Tf-Ti)/R $$ or $$ Q=(Tf-Ti)/R*A $$
Updated: How do I use an R-value in cylindrical coordinates?
e.g. $$ R/A=1/(hW*2*pi*r1)+Rins/(whatAreaHere)+1/(hA*2*pi*r2) $$
I am missing the area for my R-value insulation