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I have a simulation model of a cylindrical hot water storage tank. The heat loss is determined by the surface area and the heat transfer coefficient.

A configuration of the storage tank with 900 liters was validated with a real scenario.

Now I would like to test how the scenario changes when the storage tank gets bigger. Thereby my surface becomes bigger, but I don't know if the heat transfer coefficient changes as well.

Does a larger storage tank usually improve the insulation so that the heat transfer coefficient changes?

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    $\begingroup$ A larger tank will cool more slowly due to having a lower surface area to volume ratio, with the same transfer coefficient, if nothing else has changed. $\endgroup$ – Jonathan R Swift Nov 13 '19 at 12:41
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    $\begingroup$ Yes, the HTC is a function of system geometry, fluid and flow properties and of course $\Delta T$, how to find it is actually lengthy. larger storage tank usually doesn't improve the insulation, there is a critical radius. $\endgroup$ – Sam Farjamirad Nov 13 '19 at 12:44
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    $\begingroup$ @JonathanRSwift I'm not agree with you, the larger the tank, the larger the area, so the larger heat loss duo to convection. As I mentioned before, there exist a critical radius. And the HTC doesn't remain the same. $\endgroup$ – Sam Farjamirad Nov 13 '19 at 12:45
  • $\begingroup$ @SamFarjamirad Thank you for your detailed answer. If I have understood it correctly, a larger heat storage tank with the same insulation will cause a changed HTC due to the changed system geometry. Would this change be significant if the ratio between radius and height remained the same? $\endgroup$ – MerklT Nov 13 '19 at 13:27
  • $\begingroup$ That's something that you have to calculate to know, I'm very busy these days, otherwise I would gladly do it for you, hope other users contribute. $\endgroup$ – Sam Farjamirad Nov 13 '19 at 13:47
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In a tank with no fluid movement and no heat source with steady ambient temperature, the temperature of fluid are layered strata roughly in onion layers but favoring the top of the tank, meaning the heat is gradually decreasing from the top in ellipsoid layers roughly following the geometry of the cylinder in you question, imagine inverte flames getting colder as they get near the tank walls and gently sliding up till they reach the top and flare open turn back down in a perpetuous circulation.

So if you increase the volume of your tank, it means you are providing new insulation for the hot core. So in the larger tank the surface temperature will be less than the smaller tank while keeping similar distribution topography.

So the ratio of heat loss will be smaller than jast smaller ratio of surface to volume of fluid.

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In solid-fluid interfaces the heat transfer coefficient (HTC) is dominated by the properties of the fluid and flow, geometry has no effect on the HTC other than promoting zones where flow changes velocity/pressure/turbulence.

In your case, for a simple geometry like a cylinder, the HTC will not change with the change in dimensions (if you keep the magnitude of the scaling within a reasonable range).

So yes, if you increase the surface area you will dissipate energy quicker.

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