Detailed Description

This calculator can be used to calculate fuel savings from improving wall insulation or otherwise reduce heat lost through the walls. Wall losses occur as heat is transferred from the outer surface of the walls or casing of process heating equipment to the surrounding environment. This can occur via convection and radiation. Wall losses are high for systems that are poorly insulated or use poorly designed materials or surfaces. The calculator computes the total heat loss as the sum of convective and radiative heat losses, adjusted by a correction factor. Relevant formulas and factors are documented below. Heat losses due to openings in the unit are covered by the Opening Heat Loss Calculator, Leakage Heat Loss Calculator, or Atmosphere Heat Loss Calculator.

Total Heat Loss

\begin{equation}\label{eq:wall-total-heat-loss} Q_\text{total} = \left(Q_\text{conv} + Q_\text{rad}\right) \cdot f_\text{corr}\end{equation}

Symbols

\(Q_\text{total}\)	Total heat loss \([\unit{ \btu\per\hour}]\)
\(Q_\text{conv}\)	Convective heat loss \([\unit{ \btu\per\hour}]\)
\(Q_\text{rad}\)	Radiative heat loss \([\unit{ \btu\per\hour}]\)
\(f_\text{corr}\)	Correction factor \([\unit{ \unitless}]\)

Convective Heat Loss

\begin{equation}\label{eq:wall-qconv} Q_\text{conv} = h A \Delta T\end{equation}

Convection Coefficient: \begin{equation}\label{eq:wall-h} h = f_\text{shape} \cdot f_\text{duty} \cdot f_{\Delta T} \cdot f_{\bar{T}} \cdot f_\text{wind}\end{equation}

Factors

\begin{equation}\label{eq:wall-duty} f_\text{duty} = \left(\frac{1}{24}\right)^{0.2}\end{equation}

\begin{equation}\label{eq:wall-dTfactor} f_{\Delta T} = (\Delta T)^{0.266}\end{equation}

\begin{equation}\label{eq:wall-Tbarfactor} f_{\bar{T}} = \left(\frac{1}{\bar{T}}\right)^{0.181}\end{equation}

\begin{equation}\label{eq:wall-windfactor} f_\text{wind} = \sqrt{1 + 1.277 \cdot v_\text{wind}}\end{equation}

Temperature Definitions

\begin{equation}\label{eq:wall-dT} \Delta T = T_s - T_a\end{equation}

\begin{equation}\label{eq:wall-Tbar} \bar{T} = \frac{T_s + T_a}{2}\end{equation}

Symbols

\(Q_\text{conv}\)	Convective heat loss \([\unit{ \btu\per\hour}]\)
\(h\)	Convection coefficient \([\unit{ \btu\per\hour\foot\squared\degreeFahrenheit}]\)
\(A\)	Surface area \([\unit{ \foot\squared}]\)
\(\Delta T\)	Temperature difference between surface and ambient \([\unit{ \degreeFahrenheit}]\)
\(f_\text{shape}\)	Shape factor \([\unit{ \unitless}]\)
\(f_\text{duty}\)	Duty factor \([\unit{ \unitless}]\)
\(f_{\Delta T}\)	Temperature difference factor \([\unit{ \unitless}]\)
\(f_{\bar{T}}\)	Mean temperature factor \([\unit{ \unitless}]\)
\(f_\text{wind}\)	Wind factor \([\unit{ \unitless}]\)
\(v_\text{wind}\)	Wind speed \([\unit{ \mile\per\hour}]\)
\(T_s\)	Surface temperature \([\unit{ \degreeFahrenheit}]\)
\(T_a\)	Ambient temperature \([\unit{ \degreeFahrenheit}]\)

Radiative Heat Loss

\begin{equation}\label{eq:wall-qrad} Q_\text{rad} = \varepsilon \sigma A (T_s^4 - T_a^4)\end{equation}

Symbols

\(Q_\text{rad}\)	Radiative heat loss \([\unit{ \btu\per\hour}]\)
\(\sigma\)	Stefan-Boltzmann constant \([\unit{ \btu\per\hour\foot\squared\degreeRankine\tothe{4}}]\)
\(\varepsilon\)	Surface emissivity \([\unit{ \unitless}]\)
\(A\)	Surface area \([\unit{ \foot\squared}]\)
\(T_s\)	Surface temperature \([\unit{ \degreeRankine}]\)
\(T_a\)	Ambient temperature \([\unit{ \degreeRankine}]\)

Shape Factors

Modules
	Wall Total Heat Loss Formula

	Wall Convective Heat Loss Formula

	Wall Radiative Heat Loss Formula

	Wall Shape Factors

Files
file	wall_heat_loss.h

Namespaces
namespace	wall_heat_loss
	Calculates heat losses from walls of process heating equipment to the ambient.

Classes
struct	wall_heat_loss::WallType
	Represents a wall type and its associated shape factor used in heat loss calculations. More...

Functions
const std::vector< WallType > &	wall_heat_loss::wallTypes ()
	Retrieves the predefined shape factors for various wall types.

double	wall_heat_loss::totalHeatLoss (double surface_area, double ambient_temperature, double surface_temperature, double wind_speed, double surface_emissivity, double shape_factor, double correction_factor)
	Calculates the total heat loss from a wall to the ambient (convective + radiative).

double	wall_heat_loss::convectiveHeatLoss (double shape_factor, double wind_speed, double surface_area, double surface_temperature, double ambient_temperature)
	Computes the convective heat loss from the wall to the ambient.

double	wall_heat_loss::radiativeHeatLoss (double surface_emissivity, double surface_area, double surface_temperature, double ambient_temperature)
	Calculates the radiative heat loss from the wall to the ambient.

Variables
const std::array< WallType, 7 >	wall_heat_loss::kWallTypes
	Predefined shape factors for various wall types.

Function Documentation

◆ convectiveHeatLoss()

double wall_heat_loss::convectiveHeatLoss	(	double	shape_factor,
		double	wind_speed,
		double	surface_area,
		double	surface_temperature,
		double	ambient_temperature
	)

Calculates the convective heat loss using an empirical correlation that accounts for surface shape/orientation, duty, temperature difference, mean temperature, and wind speed.

Parameters

[in]	shape_factor	The shape factor corresponding to the wall's surface configuration \([\unit{\unitless}]\)
[in]	wind_speed	Average wind speed measured on the exterior of the wall \([\unit{\mile\per\hour}]\)
[in]	surface_area	Total exterior surface area of the wall \([\unit{\foot\squared}]\)
[in]	surface_temperature	Average surface temperature measured on the exterior of the wall \([\unit{\degreeFahrenheit}]\)
[in]	ambient_temperature	Ambient temperature measured on the exterior of the wall \([\unit{\degreeFahrenheit}]\)

Returns: Convective heat loss \([\unit{\btu\per\hour}]\).

See also

◆ radiativeHeatLoss()

double wall_heat_loss::radiativeHeatLoss	(	double	surface_emissivity,
		double	surface_area,
		double	surface_temperature,
		double	ambient_temperature
	)

Calculates the radiative heat loss using the Stefan-Boltzmann law, based on the fourth power of the absolute temperatures of the surface and ambient, the surface area, and the surface emissivity.

Parameters

[in]	surface_emissivity	Surface emissivity of the wall \([\unit{\unitless}]\)
[in]	surface_area	Total exterior surface area of the wall \([\unit{\foot\squared}]\)
[in]	surface_temperature	Average surface temperature measured on the exterior of the wall \([\unit{\degreeFahrenheit}]\)
[in]	ambient_temperature	Ambient temperature measured on the exterior of the wall \([\unit{\degreeFahrenheit}]\)

Returns: Radiative heat loss \([\unit{\btu\per\hour}]\)

See also: Wall Radiative Heat Loss Formula

◆ totalHeatLoss()

double wall_heat_loss::totalHeatLoss	(	double	surface_area,
		double	ambient_temperature,
		double	surface_temperature,
		double	wind_speed,
		double	surface_emissivity,
		double	shape_factor,
		double	correction_factor
	)

Combines convective and radiative heat loss calculations to provide the total heat loss.

Parameters

[in]	surface_area	Total exterior surface area of the wall \([\unit{\foot\squared}]\)
[in]	ambient_temperature	Ambient temperature measured on the exterior of the wall \([\unit{\degreeFahrenheit}]\)
[in]	surface_temperature	Average surface temperature measured on the exterior of the wall \([\unit{\degreeFahrenheit}]\)
[in]	wind_speed	Average wind speed measured on the exterior of the wall \([\unit{\mile\per\hour}]\)
[in]	surface_emissivity	Surface emissivity of the wall \([\unit{\unitless}]\)
[in]	shape_factor	The shape factor corresponding to the wall's surface configuration \([\unit{\unitless}]\)
[in]	correction_factor	Correction factor for the wall heat loss calculations \([\unit{\unitless}]\)

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

See also

◆ wallTypes()

const std::vector< WallType > & wall_heat_loss::wallTypes ( )

inline

Returns: A vector of WallType structures containing wall descriptions and their corresponding shape factors.

See also: Wall Shape Factors

Definition at line 51 of file wall_heat_loss.h.

Variable Documentation

◆ kWallTypes

const std::array<WallType, 7> wall_heat_loss::kWallTypes

inline

Initial value:

{{{"Horizontal cylinders", 1.016},
                                                  {"Longer vertical cylinders", 1.235},
                                                  {"Vertical plates", 1.394},
                                                  {"Horizontal plate facing up, warmer than air", 1.79},
                                                  {"Horizontal plate facing down, warmer than air", 0.89},
                                                  {"Horizontal plate facing up, cooler than air", 0.89},
                                                  {"Horizontal plate facing down, cooler than air", 1.79}}}

See also: Wall Shape Factors

Definition at line 37 of file wall_heat_loss.h.

Detailed Description

Total Heat Loss

Convective Heat Loss

Radiative Heat Loss

Shape Factors

Modules

Files

Namespaces

Classes

Functions

Variables

Function Documentation

◆ convectiveHeatLoss()

◆ radiativeHeatLoss()

◆ totalHeatLoss()

◆ wallTypes()

Variable Documentation

◆ kWallTypes