Q=mCdT vs UdT

[RomanKatz]

Hello friends,
I am trying to calculate the required Q for a double jacket 10m3 vessel heated by a small boiler. If I do the Q=mcdt equation it turns out 500 kg,60 degC difference about 30+Kw.
How ever If I calculate the resistance of heating the water,convection to and throught the copper jacket, then the vessel and into material it turns about 10Kw wich is much closer to the real value because there was a heating boiler of about 7Kw that operated for 2 hr to heat the material that was latter taken appart(I dont know the final temp, only that was good enought).

So what am I missing?

Thanks

Best Regards
Roman Katz

 

[Snickster]

Q = m c dT is an equation that gives total heat energy such as kilowatt-hr or BTU, where m is mass in vessel, c is specific heat of that mass, and dT is initial minus final temperatures.

UAdT is a calculation of the heat transfer rate across a boundary in energy per unit time (kilowatts or BTU/hr) such as your tank wall given U the overall heat transfer coefficient, A area of heat transfer surface and dT the difference in temperature between the inside and outside of the tank wall. So when you heat the tank using jacketed water the heat from the boiler of 7 to 10 kilowatts (energy per unit time)is input into the vessel over about two or three hours to add up to the total energy calculated in the first equation of 30 killowatt-hours (energy per unit time x time). So you can heat up the vessel with a smaller boiler but it will just take more time.

 

[IRstuff]

The difference between power (energy rate) and energy.

Note that the calculated energy does not account for thermal losses, such as convection into the air from the object being heated; these losses can sometimes be quite significant.

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[pierreick]

Hi,
Consider this set of calculators to support your work.

https://checalc.com/heat.html

BTW I don't understand the replies above.
Get a copy of "Process Heat transfer" 1st edition by D.Kern
Good luck
Pierre

 

[pierreick]

Hi,
Probably good to review this document.
Pierre

 

[Snickster]

Pierre

Q = m c dT is total heat energy needed to be added to the liquid in tank to raise the temperature to the given amount in BTU.

U A dT is the actual heat transfer rate through the tank wall from the boiler/jacketed system in BTU/hr.

 

[pierreick]

Hi Snickster,
Thanks.
Pierre

 

[TiCl4]

RomanKatz,

The difference is well explained by others above. Note that in heat transfer equations, Q = Q, meaning that the two equations must equal each other. You are getting two different values because you are not acknowledging the physical reality that the heat gained by the vessel's contents must the heat transferred through the heating surface.

M*Cp*dT = U*A*dT

(ignoring heat losses to surroundings)

The rate of energy transferred to the vessel's contents (measured by M*Cp*dT) will be equal to the heat transfer capability of the vessel's heating system (U*A*dT). Note that this calculation is a snapshot in time at a given dT. To calculate heating time, you could calculate the heating rate at different delta T values and calculate heating over short time intervals, adding all time intervals up until the final T is reached.

 

[RomanKatz]

Thank you all.

Best Regards
Roman Katz

 

[Snickster]

M*Cp*dT = SUM (U*A*dT) dt