thermal insulation calculation

[becma27]

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

 

[MortenA]

actually they are not simple for what you are looking at.

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

 

[ChasBean1]

becma, call me silly, but I've read your problem a couple times and don't understand what affect you're trying to minimize, the rate of heatup from 65 to 95? Condensation?

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.