I have a simple maple syrup evaporator. Fuel is burned in a firebox located under 1mm stainless steel pans containing maple sap--which becomes syrup once enough water is evaporated. After passing under the pans, exhaust gasses flow up through a chimney. (Some evaporators use flue gasses to preheat sap, but that is not the case for this evaporator.)
A high fuel consumption rate will cause evaporation to be faster, but a greater amount of heat will escape the system in the flue gas, causing energy efficiency to be lower. A lower fuel consumption rate will cause energy efficiency to be higher (lower flue gas temperatures), but the evaporation process will be slower.
If I know the cost of energy =X/kcal and I know the cost of one hour of evaporation in terms of labor, overhead, etc =Y/hour, it seems like it would be possible to calculate the optimal flue gas temperature--which we could then use to control our rate of fuel consumption.
For simplicity, I think we can assume that heat loss through means other than steam production and flue gasses are minimal enough to be ignored.
My intuition tells me that it's possible to calculate the optimal flue gas temperature for this scenario based on the cost of energy and time, but I'm not quite sure how to get there. Any help you can provide is much appreciated!