Gut feel is an accepted design tool but has its limitations and all solutions are possible given infinite time and resources. We have neither of those and a few days to decide. My theoretical engineering skills are 40 years in arrears, so it is probably best to rely on empirical data and the work of others. However, before we started, it was necessary to consider a worst-case scenario as the basis of calculation.
How to Simplify the Cooling Requirements?
We have a glycol water mixture in contact with a 12 mm aluminum skin. The hull is coated in a thin coat of antifouling, then in contact with seawater. Given that turbulent flow is more efficient at heat transfer than static conditions, we can assume the vessel is at anchor in still water. So any heat transfer we achieve will be convective for the liquid phases and conductive for the aluminum hull. The Heat Transfer Coefficient for Ethylene Glycol is 5/10% less than freshwater. For this review, they can be considered equal in our 50/50% mixture.
Limiting Operating Conditions
The coolant temperature is limited to 35oC before systems begin to de-rate. This limitation applies to batteries and inverters only. So the maximum coolant temperature is now anchored at 35oC.
410 liters of tank capacity port and starboard plus 1.6 m2 of seawater surface area per tank.
Water temperature can be all over the place from just below zero upwards. The average worldwide surface temperature is 16oC, so we assumed 25oC as the worst case. That then gives us a temperature gradient of 10oC. The best case is 0oC seawater giving a 35oC delta. Also, although the thickness of the hull is significantly over code requirements, at 12 mm, it is still considered a thin plate for heat flow purposes.
Approximating the Expected Performance
Enter an excellent resource – The Engineers Toolbox. A great collection of worked examples for typical engineering problems. We looked at a few different scenarios:
Scenario 1 – liquid or steam heating of a liquid tank. Forced heat flow across the metal heating coil surfaces with convective heat flow in the tank.
28oC delta produces a heat flux of minimum 570 w/(m2.oC)
Scenarios 2 – Liquid-Liquid tank heat loss with a metal interface at tank sides.
Water/Mild Steel/Water 340/400 w/m2.k (k=Kelvin, same as oC)
Water/Copper/Water 340/455 w/m2.k
We know the thermal conductivity of aluminum is somewhere between Mild Steel and Copper. It is reasonable to assume this set-up’s heat flux will be upwards of 340 watts per square meter, per degree of temperature rise.
Scenario 3 – this time, we looked elsewhere and, in our example, found an empirical vertical skin tank (keel cooler) calculation table for a Beta diesel engine installation.
They recommend the tank side area exposed to seawater is: engine kW/40 = square area in M2. It’s also reasonable to assume that 30% of fuel energy is lost to cooling loads. Thermal efficiency is about 40%. So energy to power is about 4/3 energy lost to the coolant.
So for our JD 4045 engine, 120/40 = 3m2 will cool water from 90 to 60oC, dissipating 90 kW of heat energy in the process across a 30oC temp drop.
Final Estimated Results
So, taking our worst-case scenario. 10oC temperature delta across the hull should result in:
Dimensional equivalent transposition: W/(m2.k) x k/1000 = kW/m2
Scenario 1 – 570×10 = 5.7 kW/m2 heat dissipation (per 10oC delta)
Scenario 2 – (340 to 400)x10 = 3.4-4.0 kW/m2 heat dissipation …….
Scenario 3 – 90x((10/30)/3) = 10.0 kW/m2 heat dissipation ……..
These three results are pretty close, especially given all the different assumptions we have made to arrive at this point. I think it would be conservative to assume that every 1 m2 of hull bottom exposed to fluid in this tank will dissipate >4 kW of heat for a fluid difference of 10oC. The situation improves under less demanding temperature conditions.