Replacement bathroom towel rail

Indeed! Heated towel rails are designed for drying towels, not heating rooms. Consequently the colour is way less important than rust resistance. The heat transfer is going to be mostly by conduction, not radiation.

Tim

The emissivity you can find in tables for most materials, however the short version is that most non metal / polished surfaces will have higher values - closer to the perfect "black body" radiator that would score 1. So 0.9+ is common.

However there are going to be lots of approximations and assumptions. For example, one thing you will note is the "T^4" term, means that there is a very significant effect of temperature on the result - even a small change will make a noticeable difference in the radiated output. So the radiated output can vary quite a bit for different parts of the rad based on the local temperature - but that is much harder to model than making a blanket decree that the surface temperature is the same all over and the same as the flow temp.

Fins, extra panels etc serve to increase the surface area of the rad - which improves the amount of air contact and hence convected heat output. It does also give a larger area to radiate from - however there are more "internal" or obstructed radiation paths that will hit other bits of the rad. So you will get some reabsorption from those surfaces reducing the net radiated.

It will reduce the amount of radiated heat to be absorbed by the wall, and reflect most of it back at the rad, although some will "miss" and escape into the room.

For outside walls with poor insulation there will be more benefit than for well insulated walls. Once the wall is heated by radiation, it will become a source of convected heat loss to the room and that is not a "bad thing". However that is more advantageous when it is not also losing lots of heat via conduction to the outside.