HI Sansub, You don't say what type furnace, but for direct fired heaters and furnaces used in refineries and chemical plants, the formulas for thermal design and rating may be found at
Hi Sansub, not sure what you mean by saying you would like to calculate furnace heat duty. Duty is usually a term associated with the heat absorbed by the process stream that the furnace is providing heat to. In this case, difficult to find a general formula except to say that Qabs = mass flow * (Enthalpy out - Enthalpy in). Determining the Enthalpy can be easy or tricky depending on what you know about the process fluid, temperature and pressure.
You could also approach the heat absorbed from the flue gas side, which means looking at the efficiency of the heater from the stack temperature, excess oxygen and air preheat temperature (if provided.) Simple equations exist for this. Once you have the efficiency, look at the measured fuel flow rates (need to know if these are accurate!) and heat values for the fuels. Calculate the heat fired from fuel flow and heat value of fuel. Multiply this by efficiency and you have heat absorbed or duty.