## Fluid Temperature Rise Due to Net (Insolation + Radiation Loss + Convection Loss)

## Fluid Temperature Rise Due to Net (Insolation + Radiation Loss + Convection Loss)

(OP)

I have a problem which should be fairly simple, but which is beating me up pretty severely. Situation: A static water-filled insulated pipe sitting in the sun. I'm trying to determine the change in water temperature when subjected to a known cycle of air temperature and solar radiation. I have read thru several threads on similar topics here at Eng-Tips. The problem with the prior solutions is that all presume that the temperature of the water is a known value; very similar to most heat transfer problems that are concerned with calculating the heat flow required to maintain a given environmental condition.

This problem has two unknowns, water temperature (Tw) and temperature of the insulation outer surface (To), with Tair, the insolation, and the physical properties known. I can't figure out how to build another relation between Tw and To. Thoughts?

Alan

This problem has two unknowns, water temperature (Tw) and temperature of the insulation outer surface (To), with Tair, the insolation, and the physical properties known. I can't figure out how to build another relation between Tw and To. Thoughts?

Alan

## RE: Fluid Temperature Rise Due to Net (Insolation + Radiation Loss + Convection Loss)

I have created spreadsheets for similar problems (a box of unknown surface temperature but know dimensions and power output with only natural convective heat loss) in the past that cast a wide net on temperature guesses and then interpolate the results to find the correct value.

If you don't want to automate it so much just put all the formulas together in a spreadsheet and keep changing the input temperature until your heat out and heat in match.

Here is a screenshot of the example I talked about, I use this as a quick first order approximation to determine if power dissipation within a device is going to be an issue or not:

## RE: Fluid Temperature Rise Due to Net (Insolation + Radiation Loss + Convection Loss)

Alan

## RE: Fluid Temperature Rise Due to Net (Insolation + Radiation Loss + Convection Loss)

## RE: Fluid Temperature Rise Due to Net (Insolation + Radiation Loss + Convection Loss)

Good luck,

Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

## RE: Fluid Temperature Rise Due to Net (Insolation + Radiation Loss + Convection Loss)

One thing to do first is to calculate the Biot number and determine whether a simple lumped analysis will get you there. If not, the you'd need to do a finite element solution.

TTFN (ta ta for now)

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

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## RE: Fluid Temperature Rise Due to Net (Insolation + Radiation Loss + Convection Loss)

I found three papers on the subject:

"Transient analytical solution to heat conduction in composite circular cylinder", Lu, et al, Int'l J of Heat & Mass Transfer, 49, 2006, 341-348

"Analytical solution to transient heat conduction in polar coordinates with multiple layers in radial direction", Singh, et al, Int'l J of Thermal Sciences, 47, 2008, 261-273

"Heat conduction problem in a two-layered hollow cylinder by using the Green's function method", Kula and Siedlecka, J of Applied Mathematics and Computational Mechanics, 2013, 12(2), 45-50

In all three papers, the math looks like pretty hard slogging for a guy whose last calculus class was 35 years ago. Any suggestion on an FEA modeling tool instead?

## RE: Fluid Temperature Rise Due to Net (Insolation + Radiation Loss + Convection Loss)

It's possible you could fudge it into a 1D transient analysis and modify the few choices available in the file exchange:

http://www.mathworks.com/matlabcentral/fileexchang...

There appear to be a couple of possibilities in Excel:

https://www.google.com/url?sa=t&rct=j&q=&a...

http://homeenergypros.lbl.gov/group/buildingsimula...

The latter seems to be configurationally like your problem

TTFN (ta ta for now)

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

## RE: Fluid Temperature Rise Due to Net (Insolation + Radiation Loss + Convection Loss)

Thanks for the suggestions.

## RE: Fluid Temperature Rise Due to Net (Insolation + Radiation Loss + Convection Loss)

TTFN (ta ta for now)

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm