A Calculated Study of Porte-Cochere Proximity

Last week I discussed across a common misconception with porte-cochere sprinkler requirements and how code addresses sprinkler protection for these structures.

This week I’m diving a little deeper with some estimates of how a porte-cochere fire would actually affect a main building, based on distance from the building.

It’s important to note that this exercise is largely academic: with the calculations below I’m making some gross assumptions that overly simplify the situation. This has not been vetted with Ph.D. experts nor gone through full scale fire testing. I’m just running some basic numbers with big assumptions to illustrate a point.

Heat Transfer

From what science gives us - heat is transferred by three methods. Conduction, convection, and radiation.
Conduction is the transfer of heat by objects touching each other. The direction of transfer is dictated by hot-to-cooler materials in direct contact.

Convection is the transfer of heat caused by the movement of gas (or a fluid). The direction of transfer is largely dictated by overall movement of the fluid, and for smoke tends to be vertical.

Radiation is the transfer of heat from the emission of electromagnetic waves. The direction of transfer is in all directions, but can reflect and re-emit from other surfaces.

Heat Transfer for a Flame

For a flame, depending on the fuel, most of the heat will be transferred away from the flame source primarily by convection. The chemical reaction (oxidation) of a flame will cause gases to heat. The heated gas’ molecules will become more active and less dense. With less-dense gas than surrounding cooler air, the warm gas will rise up and away from the flame source and carry solid particles forming hot smoke.

Radiation will typically comprise 20-35% of the overall heat release rate for a fire. Radiation transfers heat from the source in all available directions until it contacts another surface. Once in contact with other surfaces, radiation can be absorbed or re-emitted from the surface, depending on the surface material.

Conduction is the least important mode of heat transfer in an open fire. Radiation near a flame’s origin, for example, often emits and heats up adjacent surfaces with more impact than conduction. For wall assemblies, conduction of heat through penetrations becomes important, but for flames in open environments conduction plays only a small role.

Three Porte Cochere Scenarios

100-foot Separation
Now imagine a porte-cochere that is 100 feet (30 m) from the face of a larger main building to the center of the porte-cochere. If the porte-cochere is completely inflamed, how would it transfer heat to the main building?

It would transfer heat only by radiation; and in very small amounts. Assumptions include a 5 megawatt (MW) fire from a wood-built porte-cochere, a 100-foot (30 m) center distance from the main building, an atmospheric transmissivity of 0.95, and a 30% of the overall heat loss as radiation.

Using the Lawson and Quintiere Point-Source Method, the incident radiant flux (a measure of the heat energy per area) is 0.13 kW/sqm.

 
This radiant flux is about 10% of the flux for a 1st degree burn on unprotected skin.

30-foot Separation
Now move the porte-cochere to be 30 feet from the face of the building. Radiation will again transfer heat to the face of the building, but in a much larger amount. Because radiant flux is related to the inverse square of the distance between the targets, this 30-foot distance will actually have a radiant heat flux 10 times greater than a porte-cochere fire 100 feet away. For the same size fire as before but at 30-feet, this could be about enough heat for a 1st degree burn.
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At the 30-foot distance, however, heat transfer to the main building is still primarily by radiation. The hot, buoyant smoke is still primarily driven upward from the porte-cochere and would likely not reach the main building unless strong winds directed the hot gases.
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​10-foot Separation
Now imagine this same porte-cochere, but this time centered only 10 feet (3 m) from the main building. Radiation heat transfer is now 10 times greater than the 30-foot distance, and 100 times greater than the 100-foot distance.

At only 10 feet from a 5 MW fire, the heat flux is enough easily cause 2nd degree burns for unprotected skin.

Additionally, this heat flux is now approaching the critical heat flux for ignition of some building materials. The critical heat flux is the minimum amount of heat, per area, required to cause ignition. There's several factors that contribute to ignition including exposure time, material thermal properties, surface temperatures, and the actual heat flux versus critical heat flux - but for our purposes I'm only showing this critical heat flux for a couple siding materials.

Wood, for instance, has been tested to have a critical heat flux of approximately 10 kW/sqm. Vinyl siding has a critical heat flux of approximately 15 kW/sqm (both values from SFPE Handbook of Fire Protection Engineering, Table A.35, 5th Volume).

When we look at the heat flux already produced by a fire of this size at 10 feet we can see that we're already approaching the critical heat flux for both wood and vinyl.

Actual Separation

Now let's speak in practicality. Porte-cocheres are built to allow visitors to enter and leave cars without exposure to rain or sun. Is a 30-foot or 100-foot separated porte-cochere provide any value to a building? No, of course not. This exercise just shows that with reasonable assumptions, a 10-foot physical separation assuming a 5 MW fire begins to approach the critical flux needed to ignite a nearby building.

Fire Size

Would the actual fire be 5 MW? It's difficult to predict and will vary widely by the materials used and the shape it conforms. A point-source approximation is a large oversimplification given that a wooden canopy would burn in a very different configuration than a condensed pile of wood pallets, for instance.

Convection

What about convection? Up to now we've still only discussed heat transfer by radiation. If a porte-cochere is close enough to a building, convective heat transfer from the hot smoke will begin to contact the main building and heat surfaces along the face of the main building. This could also be aided by wind conditions as well.

As I explored a little last week, a porte-cochere that is only separated inches or a couple feet from a building is hardly any different than a porte-cochere that's attached to the building. That's largely because of convective and radiative heat transfer. The further away the porte-cochere is, the less convective heat transfer plays a role and the lower amount of radiative heat will be transferred.

Fire-Resistive Construction

What if we create a firewall or fire barrier? Both would slow the spread of fire and help prevent the main building from burning. The International Building Code​ relaxes the physical separation with fire-resistive construction, and for good reason. Heat flux becomes much less important when the exterior is of non-combustible construction.

Summary

It can be easy to get lost in code minutiae and live by the black and white lines of what code reads. I find that it's important to remind myself about context about each building and where good engineering judgement plays a role in protecting buildings from fire.

This overly-simplified series of calculations just shows the tiers of radiative heat transfer and how much it is affected by the separation distance. The further away a building is from another, the less convective heat transfer plays a role (if any) and the less radiative heat transfer occurs. 
 
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