A heat balance is the primary tool for indicating the thermal efficiency of a process. Many Industrial Heating articles over the past several years have pointed out the benefits of decreasing the heat loss, controlling the combustion air to get closer to stoichiometric, enriching the air with oxygen and preheating the combustion air. Here, we show how to account for the heat flow into and out of a process, the amount of heat generated by fuel combustion and (by difference) the heat loss. Once you have a heat balance, you can calculate the effect of changing process variables on thermal efficiency. Our example is the same one used in last month’s article – the heating of aluminum ingots – where we demonstrated how to make a material balance. We’ll also need data from previous “Combustion Concepts” articles.

Figure 1 shows the flow sheet. The material balance gave us the flow and composition of all streams. We’ve converted the volume flow rates for gas streams to kg-mole to simplify the calculations. The first heat-balance step is to calculate the heat content of each stream; next, to calculate the amount of heat generated by the combustion of 1.31 kg-mole/minute of natural gas; and last, to use this data to calculate the heat loss from each device (the burner and the furnace).

## Heat-Balance Procedure

The reference temperature for heat-balance calculations is 25˚C, so we need to collect heat-content data for all substances whose temperature at any point is not 25˚C. These are: solid aluminum, N2, O2, CO2 and H2O(g). Next, we need a value for the heat of combustion of the natural gas at the reference temperature. The heat balance is calculated around each process device (burner and furnace) as follows:

1. Change all instream temperatures to 25˚C. (All instreams are at 25˚C, so this heat term is zero.)

2. Carry out all chemical reactions at 25˚C (the only reaction is the combustion of natural gas).

3. Change all outstream temperatures to their respective values. [The hot combustion gas to 1800˚C (3272˚F), the stack gas to 800˚C (1472˚F) and the aluminum to 550˚C (1022˚F)].

4. Include the heat loss as an unknown variable.

5. Sum all of the heat-effect terms, and set the sum to equal zero. Solve for the unknowns (here, the heat loss).

## Heat Content of Streams

Tabular values of enthalpy are available from various sources as noted in the downloadable Excel workbook HeatBalCalc.xlsx. Some handbooks contain enthalpy data in the form of polynomial equations, which are handy for spreadsheet use. Figure 2 from the workbook shows a chart of the molar heat content of aluminum, and it shows equations for the solid and liquid as derived from Excel’s trendline tool.

Similar charts and equations are presented for CO2, H2O, N2 and O2 in workbook HeatBalCalc.xlsx as well as instructions for calculating the heat content of streams 3, 4 and 7. The heat loss for the burner and furnace was calculated by difference from zero. The overall results are summarized in Table 1. IH

## References available online

References

1. Arthur Morris, “Making a Material Balance,” Industrial Heating, October 2012.

2. Wikipedia contributors, “Enthalpy”and “Thermodynamic Databases for Pure Substances.” Wikipedia, the Free Encyclopedia, July 2012. http://en.wikipedia.org/wiki/Main_Page.