heat transfer with conduction and radiation heat transfer problem

[ottomated]

hello

I am designing a cryogenic tank that stores liquid hydrogen. we are trying to estimate the heat transfer with our insulation approach. I will attach a picture of our model. can anyone be so kind to help us come up with a heat transfer equation based on our model? thank you.

 

[IRstuff]

You set up the heat balance for radiation in the vacuum section, and conduction through the two walls, and solve the 3 simultaneous equations for t1, t2, and tshield. You can refer to:

http://web.mit.edu/lienhard/

http://www/ahtt.html

if you don't have a HT textbook.

TTFN

FAQ731-376

 

[corus]

This isn't a simple problem to solve by simultaneous equations as the radiation term makes the problem non-linear. You'd have to iterate in order to solve it.
The problem is 1D of course and so the equation through each region will be T=ax+b. At the boundary points the heat flow will be by radation to the opposing surface. You'd need 6 equations for the 3 regions to find a and b, and each equation would involve T^4 for the radiation. Better to use finite elements or finite difference methods to solve for T everywhere.

Tata

 

[IRstuff]

This problem is quite simple to set up in Mathcad's solver block.

TTFN

FAQ731-376

 

[cloa]

He needs to have true properties of internals like how close to perfect vacuum(which is impossible) and how good is this radiation shield (which can't stop all radiation). If they were all perfect, no heat could flow out of the internal system.

 

[ottomated]

I have yet to determine the actual values of the material. I could however derive equations for the system. that is why i was asking the question. but since it sounds like I need a finite element analysis program to do this, I simplified the model.

This is just an estimate so I assumed t1 to be 296k and t2 to be 24k. Our heat transfer was around 1.9watts which is extremely good considering before the insulation our heat transfer rate was around 500,000 watts.

 

[ottomated]

How do you find the enthalpy of vaporization at 6 bars for liquid hydrogen? there are values readily available for pressures of 1atm. I am having trouble finding the enthalpy of vaporization at different pressures.

 

[cloa]

http://www.hydropole.ch/hydropole/hydrogen/about.htm#4

should help

 

[ione]

You could try this for enthalpy of vaporization

http://webbook.nist.gov/cgi/fluid.c...STUnit=N/m&Type=SatT&RefState=DEF&Action=Page

 

[ione]

It seems the link I have provided doesn't work.
Let's try again

http://webbook.nist.gov/cgi/fluid.c...STUnit=N/m&Type=SatP&RefState=DEF&Action=Page

 

[IRstuff]

Same result. You might using the TGML approach for these types of links: NIST Hydrogen Properties


TTFN

FAQ731-376

 

[ione]

Thanks IRstuff, this is exactly the page I wanted to be displayed