thermal insulation calculation
thermal insulation calculation
(OP)
Hi, I am trying to figure out what to use to insulate a telescope. the operating conditions are between 40 and 100 Farenheit. The telescope is built of approximately half an inch thick Carbon fiber material. I want to make the time constant as long as possible so when I take the telescope from a 65 degree building to a 95 degree parking lot I can minimize the effect. Air is inside the telescope. I am looking for the formulas to find out what type of k value I need and how to find inuslation for this application. I know the equations are pretty simple, just can't find them.
Thanks
Thanks





RE: thermal insulation calculation
That would be instationary heat conduction.
For a solid rod you can use some diagrams.
Maybe in your case a number of assumptions would make it possible though.
1) Conduction to inside gas is by free convection
2) conduction from outside is by forced convection
Then assume that the gas all have the same temp.
-Make a heat ballance in a spreadsheet
-Do a time sttep calculation solving the system timestep by timestep
The general expression is
t_1-t_2=Q/(pi*A)*(1/h_i+len/((D_m/D_i)*k)+1/(D_o/D_i*h_o))
where
h=heat transfer coefficient
D=Diameter
k=Heat transfer coefficeint
Q=Heat flux
A=Area
len=thickness of layer
and indicies:
i=Inside
o=ouside
2=Ambient outside
1=Ambient inside
You can get k from a book but h_i/o must be estimated. I dont have any good correlation for inside of a pipe..
For a horizontal pipe outside h=4.7*(dT/D)^0.25 ( metric units W/m2*C diameter i meters)
Maybe you could use this for both inside and outside.
(Here is assumed only 1 layer. If you add insulation then you should add an extra "len/((D_m/D_i)*k)"
1 Guess a layer thickness
2 Since you know 1 and 2 (65 and 95 deg F initial conditions)
solve first for finding Q
3 calculate heat "entered" scope and calculate a new eq. temperature by solving the energy balance:
Q=(t_new_1-t_old_1)*(Cp_gas*mass_gas)+ 0.5*Cp_scope*mass_scope)
where
Cp: Heat capacity of gas in scope
mass=mass
Here i assume that the temperature change inside the scope wall is linear. This is not true (conservative i believe) but if i dont then it becomes rather complex
I have not checked this - but i belive it would work. Beaware of the units though
Best Regards
Morten
RE: thermal insulation calculation
The simple equations you might be thinking of are
Q = UA dT and U = 1/R
Q is rate of heat transfer (e.g., in BTU/hr)
U is heat transfer coefficient (BTU/Hr*ft2*°F), inverse of
R value (Hr*ft2*°F/BTU)
A is exposed heat x-fer surface area (ft2)
dT is difference in temp from inner wall to outer wall
but there is more to the problem as Morten says. Keeping things simple, you wanted to "make the time constant as long as possible" - just maximize the insulating R-value.