Water – Should hot water heater pipes in the basement be insulated

You are correct that having a hot radiator on what's effectively a cold space - the porch - is very inefficient and, presuming nobody's on the porch most of the time, wastes a lot of energy.

And you are correct that the hot water going into that radiator is being cooled in the process.

However, it is unlikely that the water is going to any other radiators, but rather it's going back to the boiler to be reheated. Nevertheless, you are right that stopping water flow to this radiator will save you on your heating bills.

But - if you stop the flow of water through the radiator, no amount of insulation will keep the pipe from freezing, because with no place for the cold water to go, the hot water in the rest of the system WILL NEVER reach the pipe you insulated. It's just like turning on the hot water in a cold bathroom - the water runs cold for a while even though the hot water is available elsewhere in the house.

On a cold enough day, the stopped pipe with water in it will freeze, no matter how hot the rest of the system.

The best solution to this is to remove the radiator completely. To accomplish this, you need to trace both the input and output pipes for the radiator in question back to an interior space that doesn't ever drop below freezing. The entire system will then need to be drained, and the input and output pipes cut off and capped so that the useless radiator can be removed.

EDIT:

Since you're looking for a short-term, this winter solution, here's what you can do for now to minimize the waste.

1. DO NOT TURN OFF THE RADIATOR
2. DO turn down the radiator to as low as you can get it without shutting it off. You don't want it to have a chance of freezing.
3. Wrap the radiator in blankets to keep in the heat it does generate and conserve energy as much as possible.

Disclaimer: I'm not a scientist or an engineer, so it's entirely possible that all of this is wrong.

For the last part of your question regarding whether the insulation you used was too thin -- extruded polystyrene typically has an R-value of 5 per inch.

Here's the part where it would be great if someone who knew "the maths" could help me out. I've calculated out at 60 lb/ft^2, 6" thick, and specific heat of 0.21 BTU/ft^2*F, the heat capacity should be 11.55 BTU/ft^2*F, or ~65.6 W/m^2*K

Anyway, if my understanding and math is correct, which it frequently isn't, it should require about 65 watts per square meter to change the temperature of your concrete by 1C. Your insulation of 1 inch has an R-value usually of 5, which means that:

((Concrete Temperature C - Ground Temperature C) / 5) will be the amount of watts per square meter of heat lost. So -- 10C temperature diff = 2 W per square meter of heat loss, or 32.5 hours to lose 1 degree C per square meter. Without that 1 inch of insulation, you would be generating 10W per meter square of heat loss, and it would only take 6.5 hours to drop 1C -- so yes, that 1" extruded polystyrene can make a significant difference. (I assumed it was extruded and not expanded... I hope!)

This obviously doesn't account for other types of heat loss, and is theoretical, but is to really say -- that 1" is a whole lot better than nothing. However -- this also means that to heat your concrete evenly, it will require applying 65 W per square meter of heat per degree (plus 0.5W per degree for each hour it takes to apply that), which means it is going to take a long time to warm that puppy up unless you start it off in the summer.