How to predict what inside surface of ceiling will be.

[tipsrfine]

I don't know enough math to even know if this is the right forum, so I apologize if it is not.

I have a known formula that allows me to calculate how much R-value a wall or ceiling has in it. The simple procedure requires me to know what the outside surface temp is, the inside surface temp, and what temp the inside air is; after that I just use a chart to find what the r-value is inside the wall/ceiling. My problem is, I am wanting to calculate what my inside surface temperature would be when all I know is what the inside air temp is, the ouside surface temp, and the r-value in the wall/ceiling.
Here is a link to the procedure. I am trying to determine if putting in a radiant barrier would be worth the effort. I have a 1000 sq.ft. cathedralized roof that will be at 190 degrees F without the radiant barrier, and only 90 with a radiant barrier and the r-value in the assembly will be R-26. What I need to know is what will the inside surface temp be with both. Thanks for any help.
http://pages.uoregon.edu/hof/W09HOF/SM20RValue_poster.pdf

 

[DrPhil]

I don't know enough math to even know if this is the right forum, so I apologize if it is not.

I have a known formula that allows me to calculate how much R-value a wall or ceiling has in it. The simple procedure requires me to know what the outside surface temp is, the inside surface temp, and what temp the inside air is; after that I just use a chart to find what the r-value is inside the wall/ceiling. My problem is, I am wanting to calculate what my inside surface temperature would be when all I know is what the inside air temp is, the ouside surface temp, and the r-value in the wall/ceiling.
Here is a link to the procedure. I am trying to determine if putting in a radiant barrier would be worth the effort. I have a 1000 sq.ft. cathedralized roof that will be at 190 degrees F without the radiant barrier, and only 90 with a radiant barrier and the r-value in the assembly will be R-26. What I need to know is what will the inside surface temp be with both. Thanks for any help.
http://pages.uoregon.edu/hof/W09HOF/SM20RValue_poster.pdf

The rate of heat flow through a surface is proportional to the temperature difference. In construction, the constant of proportionality is called 1/R, where R represents "Resistance" to heat flow. The simple differential equation is
dQ/dt = (Tout - Tin) A / R
where dQ is the amount of heat lost in a time dt, and A is the total area. As a physicist, I insist on putting units on all the numbers, as a guide to what arithmetic I can do. In this case, the units of R might be
R ~ F BTU/hr ft^2 [i.e., degrees Farenheit * BTU per hour per square foot]

You don't have to solve the equation - but these properties of R may be useful to you:

1) If there are two barriers in series, then the R-values add. That includes the "barrier" between the internal air and the ceiling, which seems to be a major point of interest for the author of the poster.

2) If there are parallel paths (e.g. studs and cavities), the R-values add as reciprocals. That is, if area A1 has value R1 and area A2 has value R2, then the combined R is found by
(A1+A2)/R_avg = A1/R1 + A2/R2
R_avg = (A1+A2) / [A1/R1 + A2/R2]

I hope that doesn't confuse you too much!