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# Temperature rise of pipe in the sun

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## Temperature rise of pipe in the sun

(OP)
thread391-264134: Temperature rise of object in the sun

I'm sorry if this has been covered already, but I want to calculate the expected temperature rise of a length of pipe in the sun, and following the above linked thread instructions gave me a temperature rise much smaller than I was expecting.

So I have used the formula Q = a * G + epsilon * sigma * (Ta^4 - Ts^4)
Where: "a" is coefficient of absorption; "G" = Gp * cos(theta)+ Gdiff; "Gp" is Solar Radiation; "theta" is the Angle between the radiation beam and the line perpendicular to the surface; Gdiff is Diffused Thermal Radiation; "Epsilon" is the Coefficient of Emissivity; "Sigma" is the Stephan-Boltzmann constant; "Ta" was assumed to be 285K; "Ti" was initial object surface temperature assumed to be kept constant.

However I combined the terms "a" and "G", and instead used the Global tilted irradiation at optimum angle figure from Global Atlas (1355.2 kWh/m^2) (perhaps this is why I don't get realistic values!).

I then rearranged Q = m * C * dT to find the temperature rise as a result, but my temperature rise was only ~2degC.

Can anyone help me with this?
Replies continue below

### RE: Temperature rise of pipe in the sun

Usually a temperature of 120 F is used for pipe exposed to sun with fluid at ambient temperature inside when doing a piping stress analysis/thermal expansion calculation. Never did a calculation like that in 40 years of doing stress analysis. Would not trust it anyway since too many variables.

Now if you had a flat plate that was in sun then it would be more predictable calculation. The energy in is known if all the plate is exposed to the sun, and the energy out can be calculated as the sum of radiated and convected, and maybe conduction too if the plate was in contact with another object. So equillibrium temperature will occur when energy in equals energy out.

### RE: Temperature rise of pipe in the sun

(OP)
Thanks for the reply.

My scenario is a little more complicated than that unfortunately; I am looking at designing a Concentrating Solar Collector, and need to know what the theoretical Energy transfer to an internal fluid would be.

### RE: Temperature rise of pipe in the sun

OK

So you know the energy in based on tables such as ASHRAE for sun radiation.

So the surface will heat up until the energy in equals the energy out. Energy out to the atmosphere would be by radiation and convection. Energy out to the internal fluid will be by convecttion across small liquid film resistance on inside surface. Also may be conduction if fluid is not in motion to keep it at a constant temperature. Find equations that cover this type of heat transfer.

### RE: Temperature rise of pipe in the sun

(OP)
I hadn't heard of ASHRAE before, so that is useful to know about.

Okay, so I am assuming a steady-state is achieved as I am considering average values over the course of a year, I have worked out net thermal power transmitted by radiation, and I have worked out heat gain by convection, however the radiative value seems low to me, and the convective value seems high.

Also, I don't know whether I am able to simplify the radiative equation as I had done; I do not know whether my assumption that "a" and "G" can be combined and replaced with data from Global Solar Atlas is valid.

### RE: Temperature rise of pipe in the sun

#### Quote:

My scenario is a little more complicated than that unfortunately; I am looking at designing a Concentrating Solar Collector, and need to know what the theoretical Energy transfer to an internal fluid would be.

You've given nowhere near enough information about the design. A solar concentrator implies much more collection area than the aera of the pipe, so you could to the point where the pipe is red hot, as is the case with the solar farm in the Mojave Desert.

The simplest case would be where the you have X area of collector radiating onto Y area of pipe, which is radiating and convecting to the ambient.

TTFN (ta ta for now)
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### RE: Temperature rise of pipe in the sun

Those units for Gp you state (kWh/m2) dont seem right to me. It should be just kW/m2.
Agreed, since this solar radiation is concentrated by the collector, there must be a multiplier to the solar radiation value ( which is approx 900w/m2 peak in non desert areas) to get to the actual flux emanating from the collector to the pipe.

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