Wall Heat Loss Calculator

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 calculation follows a top-down approach:

1. Total Heat Loss - Sum of convective and radiative losses, adjusted by correction factor
2. Convective Heat Loss - Heat transfer due to air movement around the wall surface
3. Radiative Heat Loss - Heat transfer due to thermal radiation from the wall surface

Relevant formulas and factors are documented below.

Total Heat Loss

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Total heat loss from wall to ambient environment.

The total heat loss is the sum of convective and radiative components, multiplied by a correction factor to account for operational conditions and uncertainties.

\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

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Heat loss due to natural and forced convection.

Convective heat loss is calculated using the convection coefficient, surface area, and temperature difference. The convection coefficient accounts for geometry (shape factor), operating conditions (duty factor), temperature effects, and wind velocity.

\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 \([\unit{ \degreeFahrenheit}]\)
\(\bar{T}\)	Mean temperature \([\unit{ \degreeFahrenheit}]\)
\(f_\text{shape}\)	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

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\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

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Contains default data for wall types used in wall heat loss calculations.

This database provides default values for shape factors associated with various wall types. The data is used in wall heat loss calculations for process heating systems.

Default Wall Type Data

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The following table lists the default wall types and their shape factor values:

Wall Description	Shape Factor \([\unit{\unitless}]\)
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

Note

Shape factors are used to account for the effect of surface orientation on convective heat transfer.

See also

Wall Heat Loss Calculator Source: [1]

Wall Type Database

Modules
	Wall Total Heat Loss Formula
	Total heat loss from wall to ambient environment.
	Wall Convective Heat Loss Formula
	Heat loss due to natural and forced convection.
	Wall Radiative Heat Loss Formula

Files
file	wall_heat_loss.h

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

Functions
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.

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

• Wall Convective Heat Loss Formula
• wall_shape_factors

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

• Wall Total Heat Loss Formula
• Wall Convective Heat Loss Formula
• Wall Radiative Heat Loss Formula
• wall_shape_factors