The lumped capacitance works well when the conductivity of the medium is high and dimensions small - as represented by a small value of Biot number. In this case, N2 is a poor conductor and I assume the accumulator dimensions to be large, hence Bi will normally be > 0.1, and the lumped system approximation will not hold good.

A better approach will be to look for a 1D transient solution. This is available in all standard heat transfer textbooks. The analytical solution is difficult, normally we use tabulated data or a graphical solution (Heisler charts) for obtaining the spatio-temporal variation of temperature. Assuming the accumulator to be cylindrical (a similar approach can be followed for planar and spherical shapes also), the solution will give temperature at any radius at any instant of time.

Without dimensions, materials, times, and temperatures, it's hard to get any feel for the problem. That said, it's interesting that you suspect your calculated heat transfer rate is too fast rather than too slow. With a layer of insulation and a layer of viton, I would expect those to be dominating the heat transfer rate and temperature drop, so that's something to check. That's the purpose of insulation, after all. Adding in the other resistances (metal and film coefficients) would only slow the heat transfer down more. You could try modeling the energy of the N2 simply with du = Cv dT, using a tabulated value of Cv at the approximate pressure and temperature, for a rough estimate.

Thanks for your comments. I have tried to formulate it and attached is the methodology used. Can you have a check and put your comments to understand if this approximation is fine or not. If I am seriously missing something, then I will be need to correct it. Thanks for your support in advance. If there any additional info required, please advise.

I haven't worked through the math, but 2 things that I noticed. First, there is no "convective heat transfer of stagnant air". You should find an appropriate natural convection coefficient for the geometry, which may be difficult to find. There will be one for the air to the cylinder, and then both internal fluids will have a heat transfer coefficient at the membrate that will be geometry dependent. And if the temperatures are rising and falling, then the heat transfer may be going both ways. Second, are you considering heat transfer from the barrier fluid to the N2 as important to the N2 heat content but not to the barrier fluid heat content? It looks like you are only considering it in one of the steps. That may be adding artificial heat to the barrier fluid.

Lawrence Matta

First of all thanks for your reply. I have used convective heat transfer for stagnant N2 and air in the formulation. This would be the first term with "h". For the calculation purpose, I just assumed it as 10 W/m2K. Is this what you are referring to? But you are correct that I did not take the convective heat transfer coefficients when calculating the heat transfer from barrier to N2.

For your second question, yes I am considering heat transfer happening from barrier fluid to N2. I do get your point. In the heat transfer for the barrier fluid, I am only considered the heat from the ambient and not the loss that is happening to the N2. As an approximation, I assumed the heat loss in the barrier fluid to the minimal else it would be a complex vicious problem. Do you have a good suggestion on how to deal this?

Also in my calculations, what I have done is for each time step, I calculate the ambient temperature, then calculate the barrier fluid temperature and this two are used to calculate the N2 temperature.

I would normally approach a problem like this by writing the equations for each of the temperatures in terms of the time derivatives and then time march the equations simultaneously.