# Would a solid door handle get hotter than a hollow one if there is a fire behind the door?

I am a designer (mechanical engineer) who works for a fire company. My boss asked me to develop and build a new door handle and lock mechanism. Which I did successfully. It has a 16mm Solid vertical handle on the right of the door.

My boss came and viewed the work the first thing out of his mouth was "We will need a hollow handle so that it doesn't get as hot." At this point we had a discussion as to whether changing the handle from solid to hollow would change the maximum temperature.

I argued that by only changing from solid to hollow none of the heat transfer mechanisms will decrease (convection, conduction & radiation) and that only the time it takes to reach maximum temperature (or ambient) will change.

If I am wrong can you please explain why. It just seems like I have the correct answer here.

UPDATE: 07/08/15

Not too sure if all the people who answered this will see this I hope so. Thanks for your time.

Your answers were very good and what I expected. I totally agree a solid handle stores more energy. Which when touched will be available for transfer into your hand and the longer the handle is touched the more of this energy gets transferred and the more the user gets "burned". Veritasium did a great youtube video on this.

Fun fact, in the fire standards there is no maximum temperature requirement for any part of the fire, be it being touched by the user or not.

• What do you mean by "maximum temperature"? There's a melting point for materials, but that's not influenced in any way by the shape. I'm not sure what the actual question is. – ACuriousMind Aug 5 '15 at 21:56
• I believe he means equilibrium temperature based on some fire-standard temperature differential across the door. – Bill N Aug 5 '15 at 21:58
• With things being approximately equal between the two viewpoints, this could be a good time to agree with the boss and move on. – David White Aug 6 '15 at 3:41
• @Nathan Would you choose the same material for a hollow and a solid handle? – WalyKu Aug 7 '15 at 7:41
• @Kurtovic. It would be nice to pick a better material, but honestly. You only really get what you can make in the factory. Price drives everything, steel is cheap and its a known quantity. – Nathan Wilkinson Aug 11 '15 at 7:48

Let's take the extremes as examples. Image you had an immensely dense solid door handle that has reached thermal equilibrium with the fire on the hot side of the door. The handle would have an equally immense heat capacity. If you touch that handle, then it would certainly feel very hot and burn your hand. On the other hand (no pun intended), image you had a very very thin hollow door handle, say 1 atom thin at a very low density. Again suppose it was in thermal equilibrium with the fire on the other side. Although at the same temperature as the other handle, being so thin and of low-density, it would hold very little heat energy. So if you touched it, your hand would quickly absorb and dissipate all the heat and not get burned.

So the issue is not the temperature difference of the two handles, but the extensive (total) heat capacity of the two handles. So your boss is right, a hollow handle is safer.

Another intuitive example. Which would feel colder in your hands, a super thin frozen bubble of ice, or a solid ice sphere?

Note: I feel very qualified to answer this because I have a PhD in Molecular Thermodynamics and I'm a certified fire-fighter/EMT at my local volunteer fire station.

• Your answers were very good and what I expected. I totally agree a solid handle stores more energy. Which when touched will be available for transfer into your hand and the longer the handle is touched the more of this energy gets transferred and the more the user gets "burned". Veritasium did a great youtube video on this. youtube.com/watch?v=hNGJ0WHXMyE Fun fact, in the fire standards there is no maximum temperature requirement for any part of the fire, be it being touched by the user or not. – Nathan Wilkinson Aug 7 '15 at 2:28
• @KevinVW I agree that what you said is totally true. But as it stands now, we don't build door handles that are one atom thick. The practical thickness of a door handle would be much larger, what brings a higher thermal capacity. The thing to consider is what would be the difference in energy transfer to the hand, for a use case where the handle is hold ~1 sec. Now the question comes to be, what the impact of the minimum practical thickness vs. solid door handle would be in this situation. My guess is that the impact wouldn't be that big. – WalyKu Aug 7 '15 at 7:38

You're both right.

Suppose I have a long metal bar which I keep at some reference temperature $T_0$ on the one side, then due to various heat exchanges with their environment it comes to a temperature $T$ on the operative side.

Now let's septuple the system: we'll have one in the center and 6 around it, corresponding to the "filled in" tube. Still, the operative side will come to the temperature $T$, assuming that we have not changed the heat exchanges with the door and atmosphere much. (In practice the center will not have the convective transport away from it that you'd otherwise have, so in fact the temperature does rise a little bit. But we're not going to compare the 7x system to the 1x system, so let's ignore this effect for a second.)

Now let's pull out the central bar without disturbing the other ones. Again, $T_0$ on the one side, $T$ on the other. In this respect you're pretty much correct.

However, if you're trying to minimize the amount that you get burned, which would you rather touch?

The one with 6 bars can transmit only $6/7$ of the heat energy per unit time that the one with 7 bars can, at least in this zeroth-order theory that we're talking about. That saves you 14% of the heat transported into your hand, which might save you from getting burned and certainly will feel a bit "cooler" to the touch.

So in this respect your boss is more correct.

Here is a link to a hollow-tube stainless steel door handle touted as heat-resistant: http://www.alibaba.com/product-detail/Heat-Resistent-Stainless-Steel-Door-Handle_642007359.html?spm=a2700.7724857.35.1.xs2tqC.

Because stainless steel is an alloy, electrons in its outer shell don't circulate as freely as those in pure elemental metal. They tend to bump against the impurities in the alloy, so they don't conduct heat as well. But what you're really interested in is the hollow shape.

The hollow shape reduces the cross-sectional area through which heat is conducted. Thermal energy transferred by conduction is proportional to the cross sectional area of the solid times the difference in heat from hot surface to cold surface and the time of transfer, and inversely proportional to the distance between the surfaces.

Q ∝ A(Th − Tc)t / d

Q is the thermal energy transferred through the doorknob

A is the cross sectional area of the conductor

Th is the temperature of the hot side

Tc is the temperature of the cold side

t is the time duration of heat transfer

d is the distance from the hot side to the cold side of the conductor

The less area there is for the heat to pass through, the slower will be its passage. So a hollow door handle will transfer less heat per unit time than a solid handle. Will they both reach the same maximum temperature? Eventually yes, but a few extra minutes of relative coolness can allow someone to grip the doorknob in time to make a difference.

I think your boss has the right idea.

[Incidentally, the thermal conductivity constant for stainless steel is 16 to 24 (W/m)/K. Compare this to 109 to 121 for brass, and you see why stainless steel is the better material for a heat resistant doorknob. Here is a link to thermal conductivity constants for various materials: https://en.wikipedia.org/wiki/List_of_thermal_conductivities.]

I suspect the boss is right, but I'm not sure to what degree.

If the other side of the door gets hot, a hollow handle will have greater thermal resistance than solid, since there is less material to conduct to the cooler side. Since the radiative and convective losses on the cool side will remain the same, the hollow handle should be cooler, at least as you move away from the door. Plus, for medium temperatures, a hand will cool the handle more quickly, there ought to be a range where the hollow handle will inflict less-serious burns on a grasping hand.

Like I say, though, I've no idea of exactly how much.