I am currently working on Thermal Energy Storage and interested in knowing that if we can use a Lumped Thermal Analysis to evaluate the discharge time for Latent Thermal Energy System.
Dear Ahmed,
In general, if the storage material has poor thermal conductivity, the heat entrapped at the centre core of PCM cannot easily dissipate out to the exterior during discharging. There it has a inherent resistance to heat flow. In these cases, i dont agree with the use of Lumped analysis.
Lumped Analysis is applicable in the cases in which Bi number is less than 0.1. Bi is the convective heat transfer resistivity to conduction heat transfer Resistivity. in PCMs, phase change occurs which has a high convective heat transfer coefficient, and to use lumped analysis the thermal conductivity of the material must be very high.
I think LCM is not applicable for TES system since it has large thermal conduction resistance, Bi>>0.1.
Yes BUT the errors will be more important and you MUST fragment the storage mass in a row of masses connected by conductive resistances. In this way you approach the problem of heat diffusibility in the storage.You cannot assume the whole mass as a lump in your simulation.
lumped parameter cannot be applied as the thermal conduction resistance is very high and biot number is more than 0.1
To Hemish Vaidya:
You are right as long as you consider the mass as a whole, but if you fragment the mass in several "lumps" with conductive connections in between you can do it.
The only question is which is the error level you could accept.
In fact the solution is to build up a model between the single "lump" model and the FEA which in fact is also a "lumped" model but with very small "lumps".
Let us consider a series of "lumps" of mass M[kg] and specific heat cp [J/kg*°K] connected by thermal resistances R [K/W], this leads to a series of first degree filters with the time constant T=R*M*cp [s].
If the last "lump" is connected to the heat in/off source you can obtain an approximation of the accumulator behavior.
The number "n" of "sub-lumps" and the values for R can be adapted to the level of error assumed. If the number increases then the time constant decreases since as well M as R will be smaller. If dimensions are a x b x c and for instance the transfer surface is a x b and we part it in "n" slices each element is in length c/n then the R can be estimated as R= (c/n)/(a*b*k) with k [W/m*°K] and
M= a*b*c*Rho/n [kg] with Rho [kg/m^3].
In research creativity is a must.
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