# Stagnant heated water jacket

I am currently working on heating a feed with a stagnant water jacket cylinder avoiding water flow by dipping the electrical immersion heater directly at the side of the cylinder jacket. With this scenario, I would like to know what equation should I use to determine the total heat requirements. Thank you.

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CWatters
Homework Helper
Gold Member
That could be too difficult for me to answer but there is scope to simply things if you have more information.

Is the whole tank well insulated

Is there water flowing in and out of the feed section while it's being heated? Constant flow rate?

Or is it heated then sometime later the now hot water is drawn?

Is there a requirement to heat the whole tank in a fixed time?

Do you have information about the thermal conductivity between the heater and feed section?

Thank you for the response,

The insulation of the cylinder is fiberglass which has a thermal conductivity of 0.045 W/ m.K.
The feed that is being heated can be assumed as fixed since the rate is feed addition and discharge is per day in small volume compare to total feed volume.
My aim is maintaining the temperature throughout the process with 60-degree Celsius, The specific heat of feed in the same with the water.
Stainless steel will be used between the feed and the water which is around 30W/m.K.

CWatters
Homework Helper
Gold Member
The insulation of the cylinder is fiberglass which has a thermal conductivity of 0.045 W/ m.K.
The feed that is being heated can be assumed as fixed since the rate is feed addition and discharge is per day in small volume compare to total feed volume.
My aim is maintaining the temperature throughout the process with 60-degree Celsius...

Ok If I understand correctly you may only need to calculate two things:

1) The power needed to maintain the tank at 60C (eg the heat loss through the outer fiberglass jacket). For that you need to know the outside air temperature, the surface area and thickness of the insulation. You already have the thermal conductivity.

2) The power needed to heat the tank from cold in a given time. For example if the tank allowed to cool for some reason, how fast must it heat up? For that I think we just need to know the likely cold starting temperature (5C? 10C? 20C?), the total mass of water in the tank (heater and feed sections), and how fast it must heat up.

If the tank is well insulated its likely that the power calculated in 2) will determine the power rating of the element.

Given the heated jacket are in between feed and the surface, Should I calculate the heat requirements for the feed and the heat losses to the atmosphere separately and add them for total heat requirements?

I am also looking for the equation for maintaining the temperature

CWatters
Homework Helper
Gold Member
I would do a simple calculation first...

Assume the whole tank is one mass of water and work out how much energy is needed to heat it from say 20C to 60C. Google specific heat capacity of water.

Then if the tank has to be heated in time t calculate the power = energy/time.

This would give you a reasonably accurate figure assuming the tank is stirred or has reasonably good convection.

CWatters
Homework Helper
Gold Member
The power required to maintain temperature is the same as the heat lost through the insulation...

P = thermal conductivity * (area/thickness) * temperature difference

Area = surface area of tank in square meters.
Thickness = thickness of insulation.
Temperature difference = inside temperature - outside temperature.