Energy loss in pipe/hose with hot water (how its affected by pipe/hose size, temperature)?

Question

I'm working on low budget small solar power project.

I want to transport heat (peak heat power about 1kW) over ~10 meter (~30ft) long pipe or hose.

I was thinking about thin hose (6-8mm / about 1/4 inch inner diameter ) to keep small surface area and make water flow faster (and loose less energy) - im right?

Im thinking about some kind of synthetic, transparent hose. I dont know how this material is called in english, it's similar to fuel hoses used in old motocycles.

I want to cover pipe/hose with some kind of thermal insulation (maybe mineral wool) and maybe aluminium foil to keep/reflect IR radiation inside - it's good idea?

1. I need help to decide what pipe/hose diameter shall I use.

2. Any suggestions about "im right" and "it's good idea" questions above?

I don't need exact formulas, just want to know what is proportional to what etc.

Answer 1

Don't take this as authoritative, but my back-of-the-envelope calculation suggests that the cube-square law applies in this case, meaning that a bigger pipe is better in terms of heat loss than a smaller pipe.

Consider a cylindrical volume of water that only loses heat through the sides of the cylinder, not through the two faces. The rate of heat loss will be proportional to the fraction of the total area that is the sides:

$$rate = \frac{1}{1 + \frac{{\pi}r^3}{Vol}}$$

which basically varies with 1/r³.

That volume of water will be subject to heat loss for the amount of time that it is in the pipe. Assuming you're pumping a constant volume per time, the velocity will vary with 1/r² and the time duration of the heat loss will be proportional to r².

Let's assume the rate of heat loss is constant along the pipe (i.e., it doesn't depend on the fact that the water temperature, and therefore the temperature differential, varies), so the total heat loss will be just rate×duration

This means that the total heat lost for a given volume of water will be proportional to 1/r.

If I've gone off the rails at any point in this, I'd appreciate it if someone would point out my error.