There are probably hundreds of ways to make a solar powered hot tub, but today I'll be just referring to my specific situation. For example, I know that if the hot tub were raised on a platform, then I could make a thermosiphon that would require no pump at all. But it would also mean that I would need to make an expensive platform and also I would need some way to shut down the thermosiphon when the temp gets too hot or too cold.
But, right now, I have the hot tub pump that shuts itself off when the thermostat says so. And hooking it up will be super simple. I will just separate the pump from the hot tub and tap into the pump output section and just run that through 50 feet of black garden hose.
The hose would be wrapped and secured on a 2 foot by 2 foot piece of plywood painted black. The plywood will be the back of a solar hot box and a piece of glass or other glazing on the front. It should raise the water in the hose up to 180 or a little more during the heat of the day. The hose wouldn't be under any pressure, so it won't burst. But I live in the pacific northwest. Living in the desert of the south west, things would be different. But even if it started to boil, then it would just expand back into the hot tub.
So, 4 square feet at about 50% efficiency is about 240 watts or about 800 BTUs per hour. The hose would have 1.1 gallons or 9.1 pounds of water inside. And 800 BTUs divided by 9.1 pounds = 88 degrees F. And 88 plus 105 F (starting temp of the water) would be 193. The solar box won't be that well made, because I will make it quickly and cheaply, so it may only peak at about 170F or so. If I get 5 hours of effective full power sun for the whole day, then that means 4000 BTUs per day. The hot tub holds 220 gallons or 1826 pounds of water. So, I could use the sun to recover 2.2 F per day. I could double that number by using a 3 foot by 3 foot solar box, but I would have to use 100 feet of hose, otherwise the water would be boiling in the hose. That 5 hours is based on solar photovoltaic panels. The early morning and late afternoon sun doesn't make much power and may not make enough to reach battery voltages, therefore can't charge. But in solar thermal applications, any heat is good. You just have to make up enough heat to overcome any losses in heat from you heat collector. So, 6 or 7 hours may be closer to a good estimate here.
So, let's say that the hot tub is at 105F and the thermostat shuts the pump down at 11am. From 11am to 12pm the temp drops to 104F and the pump kicks on again. At that point there is a 20 to 30 second insurge of 170F or so of water. That could scald if you are sitting up against a jet. So it is better to either turn on the jets 30 seconds before you get in and leave them on. Or, just turn the hot tub off when you get in.
I may make 2 or 3 of these hot boxes and just use one in the summer. When the weather starts getting cooler, I will add the second and then third boxes to the mix. Then, during the winter, just disconnect them and put them away until April or so.
My hot tub is already pretty energy efficient. It is a "softtub" and it has no heaters. The waste heat from the pump motor is captured and put into the water to heat the water up. Adding heat with solar will mean that I could easily run the hot tub from my small PV array and still have plenty of power left over.
Also, I'll have it on a timer so that it turns off at 6pm and comes back on in the morning at 9am. That way I don't hear the motor at night and also if it ran at night with this setup then the heat would escape through the hose.