Calculating output temperature of a solar concentrator

[Rocketman8]

Hello all!

I am designing a roof-mounted 2kW Fresnel-reflector solar collector to replace my propane pool heater. I'm a bit new to solar power and unfortunately, I haven't been able to find a good explanation for how to calculate the steady-state temperature of the receiver that carries the working fluid (a normal garden hose). I feel like there is a differential equation for this hiding under my nose and laughing at me, but I'm more of a structural/aerodynamics guy than a thermal guy. As this thing is going on my roof (the only part of my property that gets any sun), I really would like to make sure it isn't going to melt or catch fire! I want to at least try to be accurate about it, account for convective cooling of the ambient air as well as the heat absorbed by the water, etc., if the math isn't too hideous. I'd really appreciate some help!

What I know:

• The heat flux (Watts) into the receiver
• The temperature of the water flowing into the receiver and its flow rate
• The surface area of the receiver
• Material properties of the receiver, air, water, etc.

What I want to know:

• The steady-state temperature of the hose and the water flowing out of it.

[J.P.M.]

Hello all!

I am designing a roof-mounted 2kW Fresnel-reflector solar collector to replace my propane pool heater. I'm a bit new to solar power and unfortunately, I haven't been able to find a good explanation for how to calculate the steady-state temperature of the receiver that carries the working fluid (a normal garden hose). I feel like there is a differential equation for this hiding under my nose and laughing at me, but I'm more of a structural/aerodynamics guy than a thermal guy. As this thing is going on my roof (the only part of my property that gets any sun), I really would like to make sure it isn't going to melt or catch fire! I want to at least try to be accurate about it, account for convective cooling of the ambient air as well as the heat absorbed by the water, etc., if the math isn't too hideous. I'd really appreciate some help!

What I know:

• The heat flux (Watts) into the receiver
• The temperature of the water flowing into the receiver and its flow rate
• The surface area of the receiver
• Material properties of the receiver, air, water, etc.

What I want to know:

• The steady-state temperature of the hose and the water flowing out of it.

Depending on the concentration ratio and the construction, you may melt the hose.
Usually, pool heating applications are most efficient when the heat loss to the environment is minimized. The best way to minimize heat loss to the environment is to keep the temp. rise of the working fluid as low as possible - idea being quantity of heat (1st law) being more important than quality (2d law).
Unless you're doing this for the fun of it, I'd get a pool cover. After that, a couple of common pool collectors will be cheaper and more efficient than a Fresnel device.

[inetdog]

Agreed.

There are two reasons for keeping the outlet temperature as low a possible, and one reason that you can get away with that.

1. The efficiency of the collector itself will be higher the lower the outlet temperature is. This can allow lower tech collectors to do "well enough" in a pool scenario.
2. The losses in the piping and other parts of the system will be lower the lower the outlet temperature is.

The reason you can get away with this for a pool is that you do not need a secondary heat exchanger when the pool water circulates through the collector. A secondary heat exchanger would be smaller in size and cost (but lower in efficiency) with a larger temperature differential across it.

[Rocketman8]

Part of my problem is that I live deep in the woods, on the northern face of a hill. Between the trees, clouds, and location, I don't get enough sunlight on average for conventional solar thermal panels to have much effect (tried in the past). I went with a Fresnel reflector design to make the most of what little sun I have available. (I do have an insulated pool cover, but the pool receives direct sun for less than an hour a day.) So far, my estimates put the up-front cost of this collector about on par with a standard propane heater; with the fuel savings, it will pay for itself in less than three years

My design incorporates active flow control to keep the temperature rise across the system reasonable and prevent heat loss when the collector isn't making any power, so I'm not really concerned about losing efficiency. My family also likes to have the pool pretty warm (80F or so), so efficiency is less a concern than output capacity anyway. I just want to be certain that the receiver won't catch fire if it sits for a couple hours in full sun, or if the system controller malfunctions. Being an engineer, I'm fond of numbers, and I'd rather figure that out with math than trial and error. I'm just not sure how to account for convective cooling and other factors.

[J.P.M.]

Part of my problem is that I live deep in the woods, on the northern face of a hill. Between the trees, clouds, and location, I don't get enough sunlight on average for conventional solar thermal panels to have much effect (tried in the past). I went with a Fresnel reflector design to make the most of what little sun I have available. (I do have an insulated pool cover, but the pool receives direct sun for less than an hour a day.) So far, my estimates put the up-front cost of this collector about on par with a standard propane heater; with the fuel savings, it will pay for itself in less than three years

My design incorporates active flow control to keep the temperature rise across the system reasonable and prevent heat loss when the collector isn't making any power, so I'm not really concerned about losing efficiency. My family also likes to have the pool pretty warm (80F or so), so efficiency is less a concern than output capacity anyway. I just want to be certain that the receiver won't catch fire if it sits for a couple hours in full sun, or if the system controller malfunctions. Being an engineer, I'm fond of numbers, and I'd rather figure that out with math than trial and error. I'm just not sure how to account for convective cooling and other factors.

Consult the text: Duffie & Beckman, Solar Engineering of Thermal Processes. The information you need is more extensive than can fit into a forum.

[trainpilot]

I'm interested in what you come up with. I would certainly consider a backup pump as temperatures can rise really quickly when flow stops--my evac tube collectors start making steam within a couple of minutes without flow. So I would go even further to consider a t&p relief that discharges in a safe place. I am looking at using an automotive thermostat for a low-cost thermal relief. In any event, it would be great if you could give us a more detailed description of your project and results.