Choosing the optimum number of solar panels for my roof- Any advice?

Well as black absorbs heat better they will become quite warm/hot I would think. There will be shading to the roof of course but black also radiates more heat. Theoretically that heat should rise but no doubt it will have an effect on the roof. 
I’m sure someone can do the calculations .. the panels don’t have a silver underside do they ?

Oh heck, I’d not considered the heat rising aspect !! So much for A level physics… oh hang on, i only got an E grade 🙄 

So it’s absorption, radiation and convection: which one wins? And I hear they don’t work so well when they’re hot!!!

I’m out of my depth now but from what I read, the panels will ‘protect’ the roof giving a cooler effect. The fact that they will themselves be hotter is said to be compensated by the structures used in modern panels 

That’s good news !! I’ll go with that 👍🏻😎

With 24 panels, on a good day you will probably get around 50 kWh. That will obviously easily supply your house, plus heat pump. If you can estimate the kWh for those, the surplus will be available to charge the EV. The big question is how much will the EV take? Even though there will be days when all surplus is used charging it, you say it is low mileage, so there will also be days when it is nearly full, needing little to charge it. On these days the surplus will be exported ... but when the sun goes down you will be importing to power lights, kettle, cooker etc.

It is this import that you can avoid by having a battery. However, the savings depend on a large number of variables, including power requirements for the heat pump, your house; and charging the EV. These vary over time and season, and the weather affects the PV output.

If you want to avoid exporting (at low rate) and importing (at high rate), a battery must help. But cost savings also depend on these rates ... over several years!

You should also check if VAT is still reduced if PV and battery are bought together, but not if battery is added later?
 

Thanks @mavison I know that I can order the battery now with 0% vat but only take delivery (and pay) at a later date (though not stretch that for too long I imagine), or cancel if I find it’s not required. It’s the battery cost that’s putting me off, if I max out on panels ! That gives me time to see how our actual generation v usage matches up.

However, I’m liking @jason.lewis ‘s idea of getting the full 15p SEG from Octopus and look at investing in Ripple rather than spend on a battery. It’s a shame OVO aren’t involved with Ripple, and I don’t think they’re ever going to match the 15p. Looks like I may well switch...

Octopus SEG looks attractive, I agree, and we may switch to them after our Ovo fixed rate ends. And we have been happily with Ovo for many years. They must be losing customers.

Careful with those hidden links @juliamc 

@juliamc We're with Octopus, benefitting from 15p kWh SEG payments. We're also on their Cosy Octopus tariff which works really well in combination with a battery. We can mostly avoid using grid electricity in the expensive evening period, even on winter days.

There's also Octopus Flux that varies the export payments by time of day. Some people are making a fair amount of money by actively managing the charging and discharging of their battery.

I’ve just got a quote from Octopus for their standard variable tariff and it would cost me £138 more per annum than OVO. That’s quite a lot of 15p SEGs!!