Exhaust Gas Heat Loss Calculation (Electric Arc Furnace)

Detailed Description

The following formulas describe the calculation of heat loss from exhaust gases, including chemical heat, total heat value per unit volume, corrected volume flow rate, and total heat loss. Each step is documented with its own formula and symbol table.

The calculation follows a top-down approach:

1. Total Heat Loss - Calculate total heat carried away by exhaust gases
2. Corrected Volume Flow Rate - Adjust measured flow rate to standard conditions
3. Total Heat Value per Unit Volume - Sum of chemical heat and sensible heat content
4. Chemical Heat - Heat content from unburned combustibles in exhaust

Total Heat Loss

---

Total heat loss from exhaust gases.

The total heat loss is calculated by multiplying the corrected volume flow rate, heat content per unit volume, and conversion factor from minutes to hours.

\begin{equation}\label{eq:exhaust-gas-total-heat-loss-cpp} Q_{total} = VFR_{total} \cdot Q_{flue} \cdot 60\end{equation}

Symbols

\(Q_{total}\)	Total heat loss \([\unit{ \btu\per\hour}]\)
\(VFR_{total}\)	Corrected volume flow rate \([\unit{ \cubicFoot\per\minute}]\)
\(Q_{flue}\)	Total heat value per unit volume \([\unit{ \btu\per\cubicFoot}]\)
\(60\)	Minutes per hour - see physics::conversions::kMinutesPerHour \([\unit{ \minute\per\hour}]\)

Corrected Volume Flow Rate

---

Conversion of measured flow rate to standard conditions.

The measured volume flow rate is corrected to standard temperature (520°R = 60°F) using the ideal gas law temperature correction.

\begin{equation}\label{eq:exhaust-gas-total-vfr-cpp} VFR_{total} = VFR_{measured} \cdot \frac{T_{std}}{460 + T_{gas}}\end{equation}

Symbols

\(VFR_{total}\)	Corrected volume flow rate \([\unit{ \cubicFoot\per\minute}]\)
\(VFR_{measured}\)	Measured volume flow rate \([\unit{ \cubicFoot\per\minute}]\)
\(T_{std}\)	Standard gas temperature - see physics::us::kStandardGasTemperatureR \([\unit{ \degreeRankine}]\)
\(460\)	Fahrenheit to Rankine offset - see physics::conversions::kFahrenheitToRankineOffset \([\unit{ \degreeRankine}]\)
\(T_{gas}\)	Exhaust gas temperature \([\unit{ \degreeFahrenheit}]\)

Total Heat Value per Unit Volume

---

Heat content per unit volume of exhaust gas.

The total heat value includes chemical heat from unburned combustibles plus sensible heat from the temperature of the gas and entrained dust.

\begin{equation}\label{eq:exhaust-gas-total-heat-value-cpp} Q_{flue} = Q_{chem} + 0.0225 \cdot (T_{gas} - T_{ambient}) + Dust_{loading} \cdot 0.25 \cdot (T_{gas} - T_{ambient})\end{equation}

Symbols

\(Q_{flue}\)	Total heat value per unit volume \([\unit{ \btu\per\cubicFoot}]\)
\(Q_{chem}\)	Chemical heat per unit volume \([\unit{ \btu\per\cubicFoot}]\)
\(0.0225\)	Sensible heat factor for gas \([\unit{ \btu\per\cubicFoot\degreeFahrenheit}]\)
\(T_{gas}\)	Exhaust gas temperature \([\unit{ \degreeFahrenheit}]\)
\(T_{ambient}\)	Ambient/reference temperature \([\unit{ \degreeFahrenheit}]\)
\(Dust_{loading}\)	Dust loading in exhaust gas \([\unit{ \pound\per\cubicFoot}]\)
\(0.25\)	Dust heat factor \([\unit{ \btu\per\pound\degreeFahrenheit}]\)

Chemical Heat

---

Chemical heat from unburned combustibles.

The chemical heat represents the heating value of unburned combustibles (CO, H₂, and other combustibles) in the exhaust gas. Each component is multiplied by its heating value and summed.

\begin{equation}\label{eq:exhaust-gas-chemical-heat-cpp} Q_{chem} = \frac{CO \cdot 321 + H_{2} \cdot 325 + Combustibles \cdot 1020}{100}\end{equation}

Symbols

\(Q_{chem}\)	Chemical heat per unit volume \([\unit{ \btu\per\cubicFoot}]\)
\(CO\)	Percent CO in exhaust gas \([\unit{ \percent}]\)
\(H_{2}\)	Percent \(H_2\) in exhaust gas \([\unit{ \percent}]\)
\(Combustibles\)	Percent other combustibles in exhaust gas \([\unit{ \percent}]\)
\(321\)	Heating value for CO \([\unit{ \btu\per\cubicFoot\per\percent}]\)
\(325\)	Heating value for \(H_2\) \([\unit{ \btu\per\cubicFoot\per\percent}]\)
\(1020\)	Heating value for other combustibles \([\unit{ \btu\per\cubicFoot\per\percent}]\)
\(100\)	Percentage conversion factor \([\unit{ \unitless}]\)

See also

physics::us::kStandardGasTemperatureR for standard gas temperature

physics::conversions::kFahrenheitToRankineOffset for temperature conversion

physics::conversions::kMinutesPerHour for time conversion

Modules
	Total Heat Loss Formula
	Total heat loss from exhaust gases.
	Corrected Volume Flow Rate Formula
	Conversion of measured flow rate to standard conditions.
	Total Heat Value per Unit Volume Formula
	Heat content per unit volume of exhaust gas.
	Chemical Heat Formula
	Chemical heat from unburned combustibles.

Files
file	exhaust_gas_heat_loss_electric_arc_furnace.h

Namespaces
namespace	exhaust_gas_heat_loss_electric_arc_furnace
	Calculates total heat loss from exhaust gas in electric arc furnaces (EAF).

Functions
double	exhaust_gas_heat_loss_electric_arc_furnace::totalHeatLoss (double off_gas_temp, double co_percent, double h2_percent, double combustible_gases_percent, double volume_flow_rate, double dust_loading)
	Calculates the total heat loss due to exhaust gases in an Electric Arc Furnace (EAF).

Function Documentation

totalHeatLoss()

double exhaust_gas_heat_loss_electric_arc_furnace::totalHeatLoss	(	double	off_gas_temp,
		double	co_percent,
		double	h2_percent,
		double	combustible_gases_percent,
		double	volume_flow_rate,
		double	dust_loading
	)

This function computes the heat loss caused by exhaust gases leaving the EAF, based on gas temperature, composition, flow rate, and dust loading.

Parameters

[in]	off_gas_temp	Temperature of exhaust gases before mixing with outside air \([\unit{\degreeFahrenheit}]\)
[in]	co_percent	Percent of CO in exhaust gas \([\unit{\percent}]\)
[in]	h2_percent	Percent of H2 in exhaust gas \([\unit{\percent}]\)
[in]	combustible_gases_percent	Average percent of combustible gases in exhaust \([\unit{\percent}]\)
[in]	volume_flow_rate	Total volume of exhaust gases \([\unit{\cubic\foot\per\minute}]\)
[in]	dust_loading	Dust loading for exhaust gases \([\unit{\pound\per\cubic\foot}]\)

Returns

Total heat loss \([\unit{\btu\per\hour}]\)

See also

• exhaust_gas_heat_loss_electric_arc_furnace_formula