Tank energy loss to surrounding 3

[deOx]

I am looking for a way to calculate the heat loss of a tank to ambient temperature.
The tank is filled with a fluid:
Density = 910 Kg/m³
Specific Heat (cp) = 1,95 kJ/kg K
Ambient Temperature = 8 °C (46 °F)
Temperature Hold = 50 °C (122 °F)

The goal is to keep the temperature inside the tank at 50 °C. I don’t have any flows for the calculation.
The thickness (2 cm) of the wall is much much smaller than the diameter (60 m) of the tank. The tank is made of steel and is not insulated.

For the area I was thinking just to calculate A=pi*D²*H and not including the roof because the tank is filled only half way up and the air should be a good insulation. How about losing energy to the ground?

I know it should be easy using Q = k A (dT), but because the k-value is based on the ratio wall thickness and diameter I am rather sceptical concerning the calculated value.

I found a formula Q=h A dT
h = convection factor, which probably includes the heat capacity in an approximation

Anyway I tried a few ways and did not get results which do make sense.
I would be happy if anyone could help me.

 

[pmover]

my apology's for being direct, but this matter is a textbook example in most heat transfer books.

another consideration for determining heat loss is wind speed.

the website containing the 3eplus insulation calculation software should be adequate for this application. suggest conducting a search using google . . .

with that much of a temperature difference, it may be difficult to maintain the fluid temp without insulation or some heat addition.

the formulas you listed are appropriate for this application.

good luck!
-pmover

 

[25362]

If you are interested in unsteady-state heat losses from the tank to the surroundings,

the heat lost in time t is Q = mCp_o(T-T_o)

And the time/temperature relation:

t = [-mCp_o/(U_oA_o)]* ln[(T-Ta)/(T_o-Ta)]​

Ta = outside air temperature
T_o = Tank fluid temp. at time 0,
T = tank fluid temperature at time t
U_o = OHTC based on T_o
A_o = Tank surface area upon which U_o is based
m = mass of fluid in thee tank
Cp_o = Heat capacity of the fluid at T_o

Be careful in using consistent units.

 

[deOx]

Thank you guys!
I didn’t want to use programs to understand what’s behind the calculations.

"The only statistics you can trust are those you falsified yourself." Winston Churchill

So I tried a lot of equations and finally it was clear just to use the one given by “25362”. It was probably too obvious. The slope of t vs. ln(dT/dT) leads you to Uo which was the missing part all the time.
I wasted some time on some convection equations I found in Perry's Chemical Engineers' Handbook. The result was double as high as it is now.
Now I have nice diagrams which even show me the influence of the wind direction. In general I might say for non-insulated tanks, like the one above, you can use u0 or k-values from 5-7 W/m²K and you are on the safe side. I used roof and fluid level for area calculations.

 

[TD2K]

Little late but this is a copy of a paper on calculating tank heat transfer coefficients. For the external surface to air, Kern has some much simplier ones than the ones presented in this paper.

http://s17.yousendit.com/d.aspx?id=3V7OEZGNPCLK823CU2LS5A58UB

 

[quark]

I hope this excellent paper didn't go unnoticed.

 

[deOx]

No, it is really interesting. So far I had no time to check the equations for my case.
All that BTU/ft²H aso kills me.
Another think is you need much more details like viscosity and this beta value which I do not have at hand.
I am going to check this paper please give me more time.
Thank you anyway for the paper.
Have a nice day folks.

 

[biofueler]

is there anyway somebody cand send this to YSI again? The link is expired. Thanks!

 

[1969grad]

Please post the paper again so that those of us who missed out previously can obtain a copy. Thanks.

 

[TD2K]

http://s32.yousendit.com/d.aspx?id=2ZEATIYD1AS3K1S2PMB75VJALF

Good for the next 7 days.

 

[TangoCleveland]

Track down a copy of ASTM C680, "Standard Practice for
Estimate of the Heat Gain or Loss and the Surface
Temperatures of Insulated Flat, Cylindrical, and Spherical
Systems by Use of Computer Programs". It has good, consistent formulas for heat transfer and properties of air.

Larry