Symbol	Description	Unit
$q$	Heat flux	W/m²
$k$	Thermal conductivity	W/(m·K)
$h$	Convection coefficient	W/(m²·K)
$T$	Temperature	K
$\varepsilon$	Emissivity	—
$\sigma$	Stefan-Boltzmann constant	5.67×10⁻⁸ W/(m²·K⁴)

Activity Levels and Unit Conversions

The heat emission formula for animals in a relaxed state is:

$H = 6.6 m^{0.75}$

where $H$ is the heat emission in Btu per hour (Btu/h) and $m$ is the mass in pounds (lb).

For animals in moderate activity, multiply the result by 2:

$H_{\text{moderate}} = 2 \times 6.6 m^{0.75}$

Unit Conversions

When using SI units, apply these conversions:

Mass: $1 \, \text{lb} = 0.4536 \, \text{kg}$
Heat emission: $1 \, \text{Btu/h} = 0.293 \, \text{W}$

To adapt the formula for metric units, convert mass to pounds first: if $m_{\text{kg}}$ is mass in kg, then $m_{\text{lb}} = m_{\text{kg}} / 0.4536$ . Substitute into the formula to get $H$ in Btu/h, then convert to watts by multiplying by 0.293 if needed.

References

Original Source

Heat Emission Formula Details

The basic heat emission formula for animals in a relaxed state is: $H = 6.6 m^{0.75}$

where:

$H$ is the heat emission in Btu per hour (Btu/h)
$m$ is the mass or weight in pounds (lbs)

Activity Adjustment Factor

For animals in moderate activity, multiply the relaxed state heat emission by a factor of *2. $H_{\text{moderate}} = 2 \times H_{\text{relaxed}} = 2 \times (6.6 m^{0.75})$

Key Unit Conversions

The following conversions are essential for applying this formula in different unit systems:

Mass: 1 pound (lb) = 0.4536 kilograms (kg)
Power (Heat Flow): 1 British thermal unit per hour (Btu/h) = 0.293 Watts (W)

Practical Application Notes

The heat emission from animals varies significantly based on their activity state. While the base formula provides estimates for animals in a relaxed state, applying a multiplication factor is essential for more accurate thermal load calculations in occupied spaces.

For moderate activity, multiply the calculated heat emission by a factor of 2. $H_{\text{moderate}} = 2 \times H_{\text{relaxed}}$

Unit Conversion Reference

For seamless calculation, the following conversions are provided:

Animal Weight: 1 lb = 0.4536 kg
Heat Emission: 1 Btu/h = 0.293 W

Source: engineeringtoolbox.com

Reference Charts

For a comprehensive lookup of heat emissions from common animals in relaxed state (both imperial and metric units), refer to the downloadable chart:

Animal Heat Emission Chart (PDF) — provides pre-calculated values for various animal types and weights

Formula Application Summary

The baseline formula applies to animals in a relaxed state:

$H = 6.6 \, m^{0.75}$

Condition	Modification
Relaxed state	Use formula as-is
Moderate activity	Multiply result by *2

The formula estimates metabolic heat production, which equals heat emission at thermal equilibrium. For livestock facility ventilation design, moderate activity is the more realistic assumption.

Unit Conversion Factors

For converting the imperial units commonly used in the base formula:

Weight: 1 lb = 0.4536 kg
Heat Emission Rate: 1 Btu/h = 0.293 W

Base Formula (Metric Notation)

The formula for heat emission from animals in a relaxed state, expressed with SI units:

$H = 6.6 \cdot m^{0.75}$

Where:

$H$ is the heat emission (Btu/h)
$m$ is the animal's mass (lb)

To use metric units directly, convert the constant or the final result using the factors above.

Additional Notes

The base heat emission formula for animals in a relaxed state, H = 6.6 m^0.75, assumes standard conditions. For animals in a state of moderate activity, the heat emission should be estimated by applying a *multiplying factor of 2 to the result calculated from the base formula.

The associated Heat Emission Chart provides pre-calculated values for common animals in both imperial and metric units, offering a quick reference for engineering estimates.

Source: engineeringtoolbox.com