Heat transfer calculation for immersion tube heat exchanger in solar tank

[ZANL]

Hi all,

Im new to this forum and would greatly appreciate any help i can get.

I work for a solar hot water company and we have taken on an unhappy client who has been sold a custom thermal storage tank (by another firm), with a corrugated stainless steel tube immersion heater. The hot solar water, flows through this tube HEX and then warms the tank, or so the theory goes!

In reality this is not happening and we can see that the system is not able to transfer enough energy into the tank, because the solar panel temp rises way to quickly and remains high. The tank also takes way to long to heat, based on what we normally expect from a solar system.

I am desperately looking for a way to calculate the heat transfer from the tube HEX to the surrounding water in the tank.
We may choose to lengthen the tube HEX, if viable, or supply a brazed plate HEX to perform the duty required.

Basic data is as follows:

Total collectors: 20 panels
Desired flow per panel: 100l/m/panel
Solar flow rate: 33l/m
Solar temp : 70C
HEX Dia: 25mm
Total developed HEX length: 3M (ignoring corrugations)
HEX Tube Material: Stainless Steel
Tank volume: 2500L
Peak energy from all solar collectors: 36kWh

I need to know that in peak conditions i can transfer 36kWh to the tank and return much cooler water back to the panel, so that my overall efficiency is higher.

Thanks!
Nick

 

[edgepflow]

The most accurate way to do this would be to solve this differential equation:

m cp dT / dt = QHX = UA (Tsolar - T)

for T which is the tank fluid temperature.

And approximate way to find the total heatup time would be:

t = m cp (Tf - Ti) / [ U A (Tsolar - Ttank-average) ]

where Tf and Ti are your tank fluid initial and final temperatures and T-tank-average is a suitable average temperature of the tank.

If you are not familar with these kind of calculations, let me know!

 

[ZANL]

Thanks so much! I figured those heat balance equations would be used... This is quite a challenge for me. I assume we are after the U value for the tube hex? Also on the left side of the first equation...what exactly are dT and dt respectively and are they logarithmic temp differentials?

 

[SteamKing]

dT/dt is the rate of change of tank temp. with respect to time.

 

[ZANL]

Thanks SteamKing and edgepflow!
I think i have all the puzzle pieces now...
I will post my calc once done...