Hi again - reply to #24. I recognise your theory of flame temperature versus heat flow into a liquid through walls of a container.
My understanding - not the text book or any other "known" theory, just what I have picked up along the way....
We know that in the combustion of hydrocarbons (is that politically correct nowadays?) the gases change from Hydrocarbons to ions of hydrogen and carbon: The hydrogen burns very quickly with O2 from the air to make water molecules (the light blue cone of the bunsen burner). The carbon ions combine with O2 to make CO - similarly quickly in the earlier stages of the flame. Actually, in your flame, there are free carbons that are glowing yellow with the heat of surrounding combustion, as there is a shortage of O2 (air) to get this to "blue flame". The CO, and free C ions then combine with any remaining O ions, in the dark blue flame of the bunsen burner, so there is no free C in the exhaust. (I think you will have some residual C smoke?). IF this mixture of water molecules, nitrogen (from the air), CO2 (from completed combustion of C/CO) and CO and C cools below around 300~350C, (Local temperature around the ions - pressure also affects this I think?), then the gas mixture ceases combustion. And we are left with unburnt CO and C (soot). Not smelly (BUT CO kills!). I have avoided any inclusion of NOx formation as we are talking of combustion around atmospheric pressure. (NOx form in the high pressure of ICE engines at over 900C.).
So we have "hot gas" below 300C.
To have a flame impinge upon a "cool" surface, the heat is transferred to the surface by conduction form the gas, plus radiant heat from anywhere in the flame (e.g. the yellow glowing particles of C smoke, even the infra-red from the combusting gas being hot!). The radiant heat is taken up by the cooler surface according to Stefan's law of the t-4th power - of the difference of temperatures and the reflectivity of the surface. The conduction of heat from the "hot-zone" of the flame to the cooler surface relies upon the temperature difference and the thermal conductivity of the gas mixture. (very poor). Then there is a temperature difference across the thickness of the surface, so the outside is hotter than the inside (at fluid temperature) to force the heat flow through the surface. Effectively, the non-combusting gas mixture at the surface is insulating the material surface from "flame" temperatures, so the surface cannot get above around 300C anyway. Actually, in a boiler that has some significant scale, there may only be 10~30C temperature difference across the surface, so "in extremis" we can use a surface temperature of (say) 20C higher than the "cooling fluid" temperature as the surface temperature of the metal tubes. - This means that in the paper cup experiment, the paper remains below char temperature. 3 thicknesses of paper may however not work, as the outer layer chars and weakens the container. - Did you do that one? I remember a "trainee teacher" trying it and wetting the bench when the outer paper went up in flames and the whole thing collapsed. We (Kids) collapsed laughing as well!
But practically, you can calculate the heat flow into the pipes, and therefore the rise of temperature of the liquid within, to determine the flow required to keep it from boiling. (Pretty standard calculations for all heat exchangers - I'm sure you'll find the calcs on the web). For water-tube boilers, fired like yours, we should expect to be able to generate steam of 5 ~ 6.5cu.in per 100 sq.in of surface are - according to the old text book. Considering the arrangement of tubes around the flame from your burner, some part of the surfaces will get radiant heat from the flames, but other parts of tubes will be in shadow, so only get "gas conducted" heating. Again there are some tubes that will see more turbulent gases on the surface, and at higher temperatures than other areas that are further along the cooling path of exhaust gases. So perhaps you need to consider the "extreme" tube surface temperature of around 300C where flames are licking, down to the exhaust pipe temperature of gases which will be only as cool as the pipes with cooling fluid at the exhaust exit point. It is worth noting, (for model steam) that one cannot get the exhaust cooler than the boiler temperature, unless you have a cold water boiler feed pre-heater. (Very few do so). People are often amazed how inefficient their boilers are, due to the "hottest" pipes being at (only!) 300C (or less!) and the coolest at the same temperature as the steam! They "want" to calculate based on "flame temperature" as the hottest, and below steam temperature as the lowest! Thermodynamics won't do that. - An example: Someone suggested to me that his tall, heavy copper tube exhaust chimney on a vertical boiler conducted heat from the exhaust gases (as the gases were cooled by the heat flowing into the walls of the chimney - below steam temperature) back into the boiler.... not realising the chimney was a great big conductive cooler for the boiler! Heat MUST flow from the boiler (hotter than the chimney) to the cooler (chimney!). I engineer a break between these parts so to stop heat being dragged out of the boiler by the chimney tube. It also means that transport is easier with a removable chimney!
Keep up the good work,
K2