# How to calculate temperature rise rate for hydronic water tank

The engineering to figure this out is beyond me!

I have a freshwater hot water tank that holds 30 liters of water. It is heated by hot water (coolant) running through an internal pipe (the heat exchanger). The heat exchanger pipe is 304SS, 17mm diameter and is 850mm long.

Based in input temperature of 10°C and output temperature of 60°C and assuming that the 75°C coolant is flowing through the heat exchanger pipe at 24 liters per minute, how long will it take to heat the entire tank of water?

The tank is sort of like this cut-away image (the heat exchanger pipe is the lower pipe, ignore the electrical element protruding from the middle of the tank).

If someone can give me an idea of heat rise rate or where/how to figure it out, would be appreciated.

Actually this is in relation to an upgrade we are planning for our sailboat to figure out if upgrading our hot water heating system is a worthwhile investment.

• This sounds more like a "do my homework for me" than a practical home improvement question. If it's a practical home improvement question despite that appearance, use a thermometer and a stopwatch. If it's a homework question, you don't learn by having others do your homework. – Ecnerwal Oct 7 '20 at 14:44
• Actually it's a sailboat upgrade question - I finished school 30 years ago :) The trouble with getting the thermometer & stopwatch is the $1100 cost for the water tank and the hydronic heater is another$1400. I am trying to figure out how fast the tank will actually heat to full temperature. But I see where you are coming from :) – MadDogDean Oct 7 '20 at 14:52
• To calculate it, you would need a good deal more information than you have given - which the manufacturer may or may not provide to you. Specifically the thermal resistance of the coil to tank, for a start. Tank insulation will also play into it. It's a complicated function since the heat transfer rate is lower as the tank water heats and the differential reduces. Certainly "sailboat" pricing (i.e. that's an absurdly large upcharge for the hydronic add-on, but NOT getting "free" hot water from running your motor/generator is also wasteful.) – Ecnerwal Oct 7 '20 at 15:58
• Did you check the manufacturer's data for this unit? They almost certainly have a table or graph of just what you are asking for. As for solving this, if water is also flowing through the tank it's a differential equation which is not overly difficult except for the fact that you are missing some key pieces of data. If the water in the tank is status, it's a simple heat transfer equation but you are still missing the heat transfer rate from the coil to the tank. – jwh20 Oct 7 '20 at 16:11
• The tank manufacturer claims to have only data for their 1200w electrical element and NOTHING for the heat exchanger side. The most we know is that (I stand corrected) the exchanger pipe is AISI 316 Stainless Steel (Thermal conductivity is 16 W/m °C), the tank is 1.5mm AISA 316SS and is coated with 2" of high-density polyurethane foam. We are going mainly off the grid, using solar & wind generated power. The hydronic heater is fantastic! It uses 0.62 liter diesel per hour and 3.1 Amps to produce 17,100 BTU - hence wondering how long to heat the tank. Thanks – MadDogDean Oct 7 '20 at 16:32