Leakage Heat Loss Calculator

Detailed Description

This calculator estimates the heat loss due to hot gases escaping from a furnace through openings other than the flue, under positive pressure conditions. The calculation uses furnace draft pressure, opening area, gas and ambient temperatures, a coefficient of discharge, specific gravity, and a correction factor. The method is based on standard industrial practice and is suitable for furnaces operating at positive pressure. Relevant formulas and symbol definitions are documented below.

Leakage Heat Loss

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\begin{equation}\label{eq:leakage-heat-loss} Q = c_{psv} \cdot \text{SCFH} \cdot (T_{\text{leak}} - T_{\text{amb}})\end{equation}

\begin{equation}\label{eq:leakage-cpsv} c_{psv} = 0.0793 \cdot c_{pm}\end{equation}

\begin{equation}\label{eq:leakage-cpm} c_{pm} = 0.2371 - 9 \times 10^{-6} \cdot T_{\text{midpoint}} + 7 \times 10^{-8} \cdot T_{\text{midpoint}}^2 - 3 \times 10^{-11} \cdot T_{\text{midpoint}}^3\end{equation}

\begin{equation}\label{eq:leakage-midpoint} T_{\text{midpoint}} = \frac{T_{\text{leak}} + T_{\text{amb}}}{2}\end{equation}

\begin{equation}\label{eq:leakage-scfh} \text{SCFH} = \text{CFH} \cdot \sqrt{\frac{520}{460 + T_{\text{leak}}}}\end{equation}

\begin{equation}\label{eq:leakage-cfh} \text{CFH} = 1655 \cdot C_{d} \cdot f_{\text{corr}} \cdot (A \cdot 144) \cdot \sqrt{\frac{P}{SG}}\end{equation}

Where:

\(Q\)	Heat loss \([\unit{ \btu\per\hour}]\)
\(c_{psv}\)	Specific heat of gas at average temperature \([\unit{ \btu\per\cubicFoot\degreeFahrenheit}]\)
\(c_{pm}\)	Specific heat of gas at midpoint temperature \([\unit{ \btu\per\pound\degreeFahrenheit}]\)
\(T_{\text{midpoint}}\)	Midpoint temperature \([\unit{ \degreeFahrenheit}]\)
\(T_{\text{amb}}\)	Ambient temperature \([\unit{ \degreeFahrenheit}]\)
\(T_{\text{leak}}\)	Temperature of leaking gases \([\unit{ \degreeFahrenheit}]\)
\(\text{SCFH}\)	Standard cubic feet per hour of leakage \([\unit{ \cubicFoot\per\hour}]\)
\(SG\)	Specific gravity of gas \([\unit{ \unitless}]\)
\(P\)	Furnace draft pressure \([\unit{ \inchWaterColumn}]\)
\(A\)	Opening area \([\unit{ \foot\squared}]\)
\(f_{\text{corr}}\)	Correction factor \([\unit{ \unitless}]\)
\(C_{d}\)	Coefficient of discharge or flow coefficient \([\unit{ \unitless}]\)
\(\text{CFH}\)	Volumetric flow rate of leakage \([\unit{ \cubicFoot\per\hour}]\)

Note

The coefficient of discharge depends on the angle of convergence in degrees. (Source: Eclipse Combustion Engineering Guide, 1986, Chapter 1, Page #6) PDF link

Modules
	Leakage Heat Loss Formula

Files
file	leakage_heat_loss.h

Namespaces
namespace	leakage_heat_loss
	Calculator for total energy loss for gas leakages.

Functions
double	leakage_heat_loss::totalHeatLoss (double draft_pressure, double opening_area, double leakage_gas_temperature, double ambient_temperature, double coefficient_discharge, double specific_gravity, double correction_factor)
	Calculates the total heat loss from hot gas leakage.

Function Documentation

totalHeatLoss()

double leakage_heat_loss::totalHeatLoss	(	double	draft_pressure,
		double	opening_area,
		double	leakage_gas_temperature,
		double	ambient_temperature,
		double	coefficient_discharge,
		double	specific_gravity,
		double	correction_factor
	)

This function computes the heat loss caused by gases leaking from the furnace. The calculation uses:

Parameters

[in]	draft_pressure	Furnace draft pressure \([\unit{\inchWaterColumn}]\)
[in]	opening_area	Opening area \([\unit{\foot\squared}]\)
[in]	leakage_gas_temperature	Temperature of leaking gases \([\unit{\degreeFahrenheit}]\)
[in]	ambient_temperature	Ambient temperature \([\unit{\degreeFahrenheit}]\)
[in]	coefficient_discharge	Coefficient of discharge or flow coefficient \([\unit{\unitless}]\)
[in]	specific_gravity	Specific gravity \([\unit{\unitless}]\)
[in]	correction_factor	Correction factor \([\unit{\unitless}]\)

Returns

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