Do the sums on solar heating and i think you will find its not so efficient compared to solar energy.
By "solar energy", do mean a solar photo-voltaic system, versus a solar thermal water heating system? I can't say I have "done the sums", as you put it - but I've always been under the impression that solar heating systems (water as well as other liquids) tended to be more efficient overall than a solar photo-voltaic system; according to this:
https://en.wikipedia.org/wiki/Solar_cell_efficiency
Solar-cells with currently "best available technology" (ie - in the lab, unfortunately) have a peak at about 43 percent efficiency; for most "home consumer available" technology, the actual efficiency you can purchase is around 30 percent.
My gut (not a reliable indicator, I know) says that after you add in the losses from storage (in a battery) and re-transmission/conversion to run an electric heater system - that in some manner it would have to be much less efficient than if you used panels to heat water up, stored it in an well-insulated tank, then used that water for heating and other needs. Strangely, though, I can't seem to find any "easy numbers" (like the chart at that wikipedia article for solar photo-voltaics) that would back this up, so I could very well be completely wrong in my gut assessment.
To heat water for household use its very efficient, as we use it daily, summer and winter, but for house heating the cost of solar heating is high for the period of time per year it would be used.
So - where do you see the extra costs, beyond thermal vs. photo-voltaic efficiency differences? I'd imagine that you'd need to add in water losses and such (hopefully, though, for an off-the-grid system you would be on a well, pumped by a photo-voltaic powered DC pump - or possibly even a wind-powered mechanical pump). Electricity to run the pumps for the water heating panels themselves would also likely come from a small dedicated panel and battery system (or perhaps even off the main house solar and battery storage). What other extra costs would there be?
Note that I am assuming good solar coverage, not high latitudes or altitudes where the winters can be cold and long...
I done the sums for use here in Australia some time back, and for 3-4 months of the year i use heating the cost of solar heating was not worth the return, it was more efficient to put the space and money into solar energy and pump it into the grid, then use it for heating and cooling when needed.
Once again, I haven't done the numbers; but I was thinking as far as space was concerned - I wasn't thinking a regular house in a subdivision, but rather a house situated on a larger tract of land (10 acres or more), where the extra space needed isn't really a concern. Furthermore - there wouldn't be a grid to pump anything back into; when I look at solar solutions, I am almost always, invariably thinking of "off-the-grid" living. That doesn't mean I don't consider the possibilities for my current living situation (very much a tract home - albeit an older one, with a larger yard and no HOA), which I where I was pointing at the idea of a "combined system". If such a system could be combined, with the photo-voltaics providing electric, and the heat-sink they are mounted on absorbing the excess heat being radiated by them (remember, they are only about 30 percent efficient, that excess sunlight is partially turning into heat) via a water-cooling system, that heated water could potentially be used for at least augmenting the hot water heating system, even if only partially (if not hot water heating of the house).
For a combined system, how can that work??? Sunlight needs to fall on a surface area to extract energy from it, so tell me how it can be in two places at the same time, or are shadows just a mith.
When sunlight strikes a solar cell, only a portion of the energy that strikes the cell is converted into electricity, with a rate approximately equal to 30 percent (for commercial readily-available cells). The remaining 70 percent of the energy has to go somewhere; much of it is likely reflected. However, a portion of it is converted into heat, just like with any silicon junction device. When a solar cell is in operation, its temperature rises, both from internal losses, as well as from thermal heating from being in the sun. There is an operational temperature band at which a solar cell operates most efficiently; go outside of this band at either extreme, and the efficiency rolls off. In addition to these losses, there is also the fact that the frame of the panel itself gets hot, merely from being in the sun, and the solar cells not completely covering the panel.
From what I understand about panel construction, the panels are designed to channel any excess heat away from the cells in a fairly passive manner; in other words, the cells are all mounted to a large heatsink. I know I have seen some panels where the frame is very apparent that it is a heatsink, with cooling fins and such molded/machined in place on the backside of the panel. Most simply rely on the size of the frame and ordinary convection to carry away the excess heat.
However, why not use it instead? Why not make that panel heatsink an active heatsink, and machine channels or tubing into the frame through which water can be circulated to pick up the excess heat? You could even potentially place the cells under glass with an air-gap (perhaps a dual-pane insulated system) to concentrate the solar heat more, and then use the circulating water to funnel the excess heat away, into a hot-water storage system, for general use or home heating.
There is no shadows involved - you're simply changing a passive system into an active one, and capturing the heat from the panels that's going to be there whichever system is used. Now I do understand that this complicates the system somewhat, and could introduce problems should a leak or other similar issue develop; I am also fairly certain that this idea has been tried out, and that there may be issues (beyond efficiency reasons) which may have ruled it out.
As Nigel quoted it only makes for a bigger system, 1+1 = 2 as the surface area needed for each system will remain the same.
I don't think the above system would necessarily be anywhere near as efficient as a "separated" system, where you have two individual banks of panels; one bank for hot water, and another for solar photo-voltaics. In that kind of system, though, you are still throwing away heat energy from the photo-voltaic panels; why not capture it if you can?