Heating with water

[Jezovuk]

Hello everyone!

I would appreciate if someone could help me with the calculation of pressure vessel heating.
We have a pressure vessel V1= 31,1 Liter and our task is to heat the Working fluid with water.
PV is insulated and we don´t take losses into consideration.

We need to know how long does it take for this medium (31.1 lit. and 2,1 kJ/kg*K) to be heated by 1 °C when heated with water (19.9 lit. at 50 ° C). (Pic. attached)
I first calculated the energy stored in water with this formula:
E =𝑐𝑝 ∗ Δ𝑇 ∗𝑚= 4,157 * 30 * 19,9 = 2482 kJ

Than i calculated the power absorbed by material with this formula: P =(𝐺 ∗𝑆𝐻 ∗ Δ𝑇 )/3600= 31,1 * 2,1 * 1 = 65,1 kJ/s
In order to calculate the needed time i divided: E/ P= 38 sec.
I am not shore if i got the calculation right or not?

Thank you!

 

[LittleInch]

Very little of this makes sense I'm afraid.

The heat energy in the water is mass x heat capacity x deg C rise. This normally needs some sort of datum point ( you seem to have chosen 20 Deg C based on the 30 in your equation?)

However heat transfer between fluids in your case is subject to many inputs such as transmission across the metal, conduction into the fluid ( paint), convection within the paint or mixing.

A 1C rise might be fairly small compared to the temperature of the water, but you don't say what the start temperature of the paint is? This will affect the heat transfer rate ( or power as you put it).

If its 20C then the amount of energy transfer is not going to change much but if the start temperature is 45 then the heat transfer rate will be much lower.

So no, I don't believe you've got the calculation right.

Is this a real problem or a test question?


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[Jezovuk]

Thank you LittleInch,

Yes, i presumed that the start temperature of the paint (31.1 lit. and 2,1 kJ/kg*K) is equal to the ambient temperature = 20 °C.
Water (19,9 lit.) is constantly kept at 50 °C by means of external heat exchanger.
I also presumed that the p.vessel is 100 % insulated (heat losses are 0) and that losses from other inputs (transmission across the metal, conduction into the fluid) are negligible.

My company is in the process of building this vessel but now, after few weeks the customer asks such a question...

 

[LittleInch]

The transmission of heat into the fluid isn't a loss, it is vital to actually calculate the time but its value is not a simple one to obtain.

"Paint" is a fairly viscous substance. It won't circulate heat transferred on the skin boundary very well unless you mix it. How well the pain absorbs heat from the metal surface is not clear.

Also how much are you trying to raise the temperature of the paint?

Seems a little late for someone to be asking these questions.....

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.