Estimating tank's internal surface temperature based on external surface temperature

[visum]

Hello,

I need help to estimate tank's internal surface temperature based on the measurements on the outside surface. The tank made of carbon steel, 1/2" thick.
What would be the algorithm for determining the temperature differential on the tank's shell? The tank is being heated internally to about 100F-200F for couple of days. Outside temperature is 70F-80F.

Thanks in advance

 

[racookpe1978]

1/2 thick steel wall, heated to "about" 100 - 200 F and held for a couple of days, right?

The heat transfer will be from the fluid (at the starting time), across the fluid-to-tank-wall boundary, across the 1/2" steel wall (essentially zero! under these conditions), and then across the outside wall-to-atmosphere boundary. Since the fluid will be constantly losing heat energy to the outside, but the loss will be at a slowing decreasing rate as the tank cools down, your greatest heat loss will be at the beginning of the process. Are you worried about heat transfer rate at the start, or the end, of your "couple of days" period?

Compared to the tank-to-outside-atmosphere boundary losses, the tank wall temperature difference will be vary, very small.

(wind will affect your outside boundary heat rate significantly)
(Real world outside temperature (at night) will NOT be the 70 - 80 degrees you seem to be assuming for the daytime temperature!)
(Sun's energy could be significant as it tries to heat the south wall of the tank every day - if you are actually trying to calculate 1/2 degree increments.)

 

[IRstuff]

You know the internal heat, right, since you're the one doing the heating? This establishes the heat flow into the ambient, through convection and radiation. This establishes the surface temperature. Conservation of energy provides that the heat lost to the ambient is equal to the heat transferred through the skin, which is only by conduction. This allows you to determine the internal wall temp.

TTFN
faq731-376

 

[Terminus0]

What ever you measure to be the outside temp of the tank, as the wall is only made of 1/2" steel, is very likely to be very close to the temp inside the tank.

Steel has a fairly high Thermal Conductivity(k), and thus the heat has little trouble making it through the wall of the tank.

 

[corus]

This depends on the heat transfer coefficient to the air. Typically, for natural convection and radiation it's about 10 W/m^2 K, but this can depend on the surface temperature, and if there's any forced convection from wind, say. The heat flow through the steel is k/x(To - Ti) = h(To - 20 ^oC). You know what To (the outer surface temperature is), k is about 50 W/m K, x is 12.7mm, so you can work out Ti, the inner temperature. After that you have to convert it back to fahrenheit.

 

[Terminus0]

Does the tank experience any significant wind? because as 'corus' said that could substantially increase the amount of convection from the outer surface of the tank to the air cooling it off. Whcih would increase the delta T between the inside and outside surfaces.

 

[visum]

The tank is in doors, no wind, as I mentioned in the original post, 70F-80F inside the tank room.

 

[IRstuff]

Still, it's something you can estimate, given the known heat input and the ambient temperature.

TTFN
faq731-376

 

[racookpe1978]

Your problem still isn't clear - probably because I can't understand your initial conditions, your (desired ?) end conditions, and what you are having problems trying to solve.

For an indoor condition, 1/2 steel tank walls, and input water flowing into a tank, the temp difference (water-to-tank wall) with circulating or pumped (flowing) liquid will be only 2-4 degrees F. Across the (uninsultaed) tank wall, for 150 some-odd degree water and 70-80 degree, assume 1/2 difference. Your thermometer is (I think) mounted on the tank wall, so there is no tank wall-to-outside air heat loss - ===> if and only if you are measuring outside tank wall temperature.

Once the water stops flowing into the tank, the temp difference of water to tank wall through tank wall to room air quickly approaches zero, but will never actually reach zero until the room air equals the water temperature.

If you have some sort of continuous heat flow problem - like something is heating the tank internally, then you (we!) have to know how much energy that heat is, and how it decays/stays the same/increases over time.