Boilers, Furnaces & Combustion · Study · PE Mechanical: HVAC and Refrigeration · FE → PE Prep

Boilers, Furnaces & Combustion

6% of exam

Fuel heating values, air-fuel ratio and excess air, combustion and thermal efficiency, boiler/furnace fuel rate, and flue-gas losses.

4 concepts

B. Boilers and Furnaces

Heating Values, Combustion Efficiency and Fuel Rate

Higher vs lower heating value, combustion vs thermal efficiency, and how to back the fuel-input rate (and boiler horsepower) out of a required output.

Almost every boiler or furnace problem on the PE Mechanical HVAC exam is a single energy balance read in one of two directions. Forward: a fuel burns, releases its heating value, and some fraction reaches the water or the air stream. Backward: a building needs a known output, and you must size the burner, the gas meter, or the fuel bill that delivers it. The trap that quietly sinks candidates is not the algebra — it is the heating-value basis and the efficiency basis. Mix higher heating value with a lower-heating-value efficiency, or charge a furnace's output against its input on the wrong basis, and the answer is off by ten percent before the arithmetic even starts. This concept builds the bookkeeping so that never happens. The reference is the NCEES PE Mechanical Reference Handbook — §10 Combustion and Fuels, with the fuel-input-rate relation in §10.6 and the boiler-horsepower conversion in §1 unit tables.

Higher versus lower heating value

When a hydrocarbon burns, the hydrogen in the fuel becomes water. Whether you count the heat released when that water vapor condenses is the entire difference between the two heating values. The higher heating value (HHV, also gross or total heating value) is measured with the product water condensed to liquid, so it includes the latent heat of vaporization; the lower heating value (LHV, or net heating value) leaves the water as vapor and omits that latent term. For natural gas the gap is about

Key equations

Higher vs lower heating value

HHV = LHV + m_{w}\,h_{fg}

$m_w$ = mass of water formed per unit fuel (lb water / lb fuel), $h_{fg}\approx 1{,}060\,\text{Btu/lb}$ at the heating-value reference temperature (~60 °F, where the product water is condensed to liquid). HHV counts the latent heat of the product water; LHV does not.

Fuel-to-load (overall) efficiency

\eta_{f\text{-}l} = \dfrac{\dot{Q}_{out}}{HHV\cdot \dot{m}_{f}}

Combustion efficiency (= handbook §10.3 thermal efficiency)

\eta_{c} = 100\% - L_{stack} = \dfrac{Q_h - Q_{fl}}{Q_h}\times 100\%

Fuel-input rate from output

\dot{Q}_{in} = \dfrac{\dot{Q}_{out}}{\eta}

Fuel quantity (mass or volume)

\dot{m}_{f} = \dfrac{\dot{Q}_{in}}{HHV}\qquad \dot{V}_{f} = \dfrac{\dot{Q}_{in}}{HHV_{vol}}

Gas input rate with meter correction

\dot{Q} = HHV\cdot VFR\cdot \dfrac{T_s\,P}{T\,P_s}

Efficiency basis conversion

\eta_{HHV} = \eta_{LHV}\,\dfrac{LHV}{HHV}

Boiler horsepower

\text{BHP} = \dfrac{\dot{Q}_{out}}{33{,}470} = \dfrac{\dot{m}_{s}}{34.5}

Boiler steam output (real feedwater)

\dot{Q}_{out} = \dot{m}_{s}\,(h_{s} - h_{fw})

Hot-water output (standard coefficient)

\dot{Q} = 500\cdot \text{gpm}\cdot \Delta T

Sensible heat of water; $500 = 8.33\,\tfrac{\text{lb}}{\text{gal}}\times 60\,\tfrac{\text{min}}{\text{h}}\times 1\,\tfrac{\text{Btu}}{\text{lb}\,^\circ\text{F}}$

Worked examples

Natural-gas furnace fuel rate

Problem. A gas furnace must deliver $80{,}000\,\text{Btu/h}$ of heat to a house. The furnace AFUE (seasonal fuel-to-load efficiency, HHV basis) is $92\%$ and the supplied natural gas has a higher heating value of $1{,}020\,\text{Btu/ft}^3$ at standard conditions. Find the fuel input rate and the gas consumption in ft³/h.

Solution. Work the balance backward. Fuel energy input:

\dot{Q}_{in}=\frac{\dot{Q}_{out}}{\eta}=\frac{80{,}000}{0.92}=86{,}960\,\text{Btu/h}.

Gas volume (HHV basis matches the fuel data):

\dot{V}=\frac{\dot{Q}_{in}}{HHV_{vol}}=\frac{86{,}960}{1{,}020}=85.3\,\text{ft}^3/\text{h}.

Final answer: input

8.70\times 10^{4}\,\text{Btu/h}

, gas rate

85.3\,\text{ft}^3/\text{h}

. Sanity check: at

92\%

the input is just above the output, and

85.3\,\text{ft}^3/\text{h}\times 1{,}020\approx 87{,}000\,\text{Btu/h}

recovers the input — consistent.

\dot{V}=\dfrac{80{,}000/0.92}{1{,}020}\approx 85.3\ \text{ft}^3/\text{h}

Oil-fired boiler: fuel rate and boiler horsepower

Problem. A steam boiler delivers a gross output of $5.0\times 10^{6}\,\text{Btu/h}$ at a fuel-to-load efficiency of $82\%$ burning No. 2 fuel oil with a higher heating value of $138{,}000\,\text{Btu/gal}$ . Find the oil consumption (gal/h) and the boiler's output rating in boiler horsepower.

Metered gas with temperature and pressure correction

Problem. A gas meter reads $120\,\text{ft}^3/\text{h}$ of natural gas. The gas in the meter is at $90\,^\circ\text{F}$ and $15.5\,\text{psia}$ , and its higher heating value is

Boilers, Furnaces & Combustion

B. Boilers and Furnaces

Heating Values, Combustion Efficiency and Fuel Rate

Higher versus lower heating value

Combustion efficiency versus fuel-to-load efficiency

Backing out the fuel-input rate

Volumetric gas input and meter corrections

Boiler horsepower and output ratings

Exam strategy

Key equations

Worked examples

Common pitfalls

References

Air-Fuel Ratio, Excess Air and Flue-Gas Analysis

Boiler and Furnace Types, Ratings and Turndown

Flue-Gas Losses and Condensing-Boiler Efficiency