Posted By: James NortonHow to work out the heatloss over say 24 hours and the effect on temperature in tank vs room...

I guess it depends how accurate you want to be. If you just work out the U-value of the insulation as if it was all flat layers and then use the external surface area (i.e. area of cupboard walls) that should give you a worst case. There are formulae for calculating cylindrical insulation for pipes if you want to make a closer estimate.

Edit: To calculate effects on temperature: for the tank, you calculate energy stored in the tank (specific heat x volume x delta T) and subtract your heat loss to calculate the new temperature. For the room, you need to do a calculation of heat losses to the outside and to other parts of the house, which is more complicated. It's probably easier just to think of the tank's heat loss rate as an extra heater added to the room - if it was say 1 kW, you can guess what the room would feel like.

Can I do this as a steady state do you think?

I would think so. But if you do the calculation in a spreadsheet, it shouldn't be too hard to do multiple estimates at hourly intervals or whatever.

If you find that the bedroom is going to get too hot in the summer, you might consider leaving a one or two inch air gap around the insulation inside the cupboard. Then you could vent it outside in the summer, and keep it sealed in the winter.

Is this an academic exercise or is it a real one.
If real, then measure it, if not then spreadsheet it.
You could treat the tank as a heater, and the room as s semi infinite heat sink. So as the tank cools, the room warms, reducing the ⌂T.

The posh way is to use Newtons Law of Cooling (and heating) and subtract one from the other at either know time intervals or known temperature intervals. Then plot the results.

End up with something like this:

I'm not sure that Gödel had much to say about the incompleteness/inconsistency of solar heating systems, though heroic and very general were his oeuvres...

Rgds

Damon