Conductive Heat TransferHeat flux through a wall and thermal penetration time

What this calculates

This sheet uses a simple conduction equation to calculate the heat transfer through a solid object. The answer is reported in units of heat flux, or kW/m2. So, think of this not as the total amount of energy that escapes from a fire and moves through a wall, but the total amount of energy in that specific small area of the wall that we are interested in. This is useful for determining ignition of adjacent items, which will often be somewhere on the order of 20 kW/m2.

How to use it

Choose a representative wall material from the dropdown box at the bottom of the variables section. Enter the thickness of the wall, the hot-side temperature and the cool-side temperature in in the yellow cells.

The spreadsheet will report the heat flux that reaches the far side of the wall/object from the hot area, and the time it takes the heat wave to penetrate all the way through in cell (thermal penetration time).

Variables

q″: Heat flux conducted through the wall [kW/m²]
k: Thermal conductivity of wall material [kW/m·K]
T₂: Temperature on the hot side [K]
T₁: Temperature on the cold side [K]
L: Wall thickness [m]
t: Thermal penetration time [s]
α: Thermal diffusivity = k / (ρc) [m²/s]
ρ: Density of wall material [kg/m³]
c: Specific heat of wall material [kJ/kg·K]

Equations

$$ q = rac{ k \, (T_2 - T_1) }{ L } $$Conductive heat flux (Quintiere, eq. 3-1)

$$ t = \frac{ L^{2} }{ 16 \, \alpha }, \quad \alpha = \frac{k}{\rho \, c} $$Thermal penetration time (Quintiere, p. 52)

Discussion

The dropdown menu is set up to pick a material from a prefilled list of thermal properties. The thermal properties that it looks up come from Quintiere’s “Principals of Fire behavior” table 3-1. Concrete (high) and Concrete (low) are not two distinct materials but represent the range of values reported in that table.

This equation works well for a broad range of applications, but it does have its limits. If you enter a highly conductive item (like steel) and give it a very thin thickness, you are likely to obtain heat flux values that are thousands of kW/m2. When you start seeing this, consider that the heat transfer through the wall is quite high and quite fast, but don’t be overconfident in the exact number you are seeing there; for our purposes it is higher than it needs to be to ignite most things.

Worked example

Example

A 4” thick brick wall is exposed to a flame on one side. The flame temperature is 1000 degrees C and the ambient temperature on the cool side of the brick wall is 20 degrees C. What is the heat flux to the cold side of the wall from the flame, and how long is the thermal penetration time?

Choose “Brick” from the dropdown menu and set the length (or wall thickness) to 4 inches in the “L” cell. Enter the hot side and cold side temperatures in the remaining yellow cells.

The spreadsheet should calculate a heat flux to the cold side of about 6.7 kW/m2 with a thermal penetration time of 1257.3 seconds.

References

Quintiere, J. G., Principles of Fire Behavior, conductive heat transfer eq. 3-1 (p. 49) and thermal penetration time (p. 52). The spreadsheet form divides both sides by area so the result is given as a flux (kW/m²) rather than total energy.
Material thermal properties (k, c, ρ, kρc) from Quintiere, Table 3-1.