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Consider gas flowing at some temperature impinging onto a solid surface at some lower temperature. In this situation one would expect heat to flow from the gas into the surface of the solid. And likewise when the temperature gradient is reversed one would expect heat to flow from the solid to the gas.

Within a solid or from solid to solid I know I can use the solid's coefficient of thermal conduction to predict heat transfer. But what of gases? Do gases also manifest such a property or is there a different property/model required to solve such a problem?

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Every material - regardless of its state - possesses a macroscopic susceptibility for the conduction of heat. The heat flux (amount of heat "flowing" through a unit area per unit time) of an isotropic material, $q$, is given simply by product of the coefficient of thermal conduction, $k$, and the negative gradient of temperature, $T$; $$ \vec{q} = - k \vec{\nabla} T. $$ The negative gradient of temperature encapsulates the direction of heat "flow" that you mentioned, such that heat always flows from the hot matter to the cold matter. In general, the more structured a material is the greater its value of coefficient of thermal conductivity, i.e. gases have low $k$ whilst solids have high $k$.

Edit: The above is perhaps the simplest model and holds only under a plethora of assumptions including (but not limited to) the gas being without convection/currents and there being no phase transitions or ionisation. These models have a tendency to rapidly rise in complexity as more effects are considered and if one wished to realistically model heating of a gas with all known phenomena it would stretch even the most powerful of modern computers.

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  • $\begingroup$ There are some pretty strong caveats to that. If your transfer medium is a fluid (like air) and it is able to move (either due to the temperature or due to a fan/forcing mechanism) that equation won't hold. The heat transfer will be due to convection, which will raise the heat transfer coefficient significantly from just the thermal conductivity of air. $\endgroup$ – JMac Jan 27 '17 at 16:12
  • $\begingroup$ I realise that I make a number of VERY broad assumptions for the sake of my post - there are even a number of further variables that also haven't been touched upon, e.g. phase transitions. Increasing steps of complexity would be to involve the heat equation as well as convective forces etc. In fact, to realistically model the system one would almost certainly require a high end cluster. My answer was just a rough and basic response to put forward the idea of a coefficient of thermal conductivity that is present for all states of matter. $\endgroup$ – DocDave Jan 27 '17 at 16:27
  • $\begingroup$ I just mentioned it because he used the term "flowing over" which may have referred to heat transfer but also could have implied convection. It also seemed very relevant as convection is one of the 3 traditional modes of heat transfer. He also specifically asked if there was another model besides conduction when dealing with gasses. There absolutely is and you never addressed that. $\endgroup$ – JMac Jan 27 '17 at 16:32
  • $\begingroup$ The wording I focussed on was "Within a solid [...] I know I can use the solid's coefficient of thermal conduction to predict heat transfer. But what of gases? Do gases also manifest such a property?", to which the answer is simply yes. $\endgroup$ – DocDave Jan 27 '17 at 16:45
  • $\begingroup$ "Or is there a different property or model to solve such problem". That's the part I mean. His question to me was actually trying to figure out if fluids could transfer heat through other methods. It seems negligent to not even mention convection while also saying air has low conductivity. It's true, but only stagnant air has its heat transfer governed by conduction. That conduction value is misleading unless you also point out that often times there us a forced or free convection that increases it's heat transfer over pure conduction. $\endgroup$ – JMac Jan 27 '17 at 16:50
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Gasses and fluids in general aren't confined to heat transfer through conduction in the way solids are.

Gasses and liquids do have a conductivity ascoiciated with them, but there can also be more at play. The fluid is also able to move, which means that as it's heated it can be replaced with fluid at a lower temperature. This increases the heat transfer between the media quite a bit compared to conduction(gasses have low thermal conductivity)

The process is called convection and for simplified 1D heat transfer it has a "convection coefficient" which acts the same as conductivity does in conduction, although convection is more complicated and values aren't easily searched in a table.

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  • $\begingroup$ When I read this question I imagined a blowtorch heating a metal surface. I assumed that the flow rate of gas does not change with time. Ie the system is in a way "static". I am not 100 % sure but in this case, Doc Dave's answer is probably correct, with different values of k in the gas region and solid region. $\endgroup$ – user3728501 Jan 27 '17 at 17:26
  • $\begingroup$ Oops I meant to add that as an answer - but does anyone have any comments on what I suggest here? $\endgroup$ – user3728501 Jan 27 '17 at 17:26
  • $\begingroup$ So a TRUE coefficient of thermal conductivity for gases probably better assessed with convection (mixing).Otherwise the formation of a heat depleted boundary layer near a solid surface for example acts like an insulator $\endgroup$ – docscience Jan 27 '17 at 20:14
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Following properties are relevant as I can think of.

  • gas/solid temperatures
  • gas/solid thermal conductivities
  • gas/solid heat capacities
  • gas viscosity
  • gas flow rate
  • gas jet size (diameter)
  • gas jet angle
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When I read this question I imagined a blowtorch heating a metal surface. I assumed that the flow rate of gas does not change with time. Ie the system is in a way "static". I am not 100 % sure but in this case, Doc Dave's answer is probably correct, with different values of k in the gas region and solid region.

Perhaps someone with more expertise can comment on this?

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  • $\begingroup$ A blowtorch heating a metal surface is convection, not conduction. You still wouldn't be using the thermal conductivty of the gas for that. When you have a moving fluid as one of the transfer media it is considered convection. The heat transfer becomes governed by the fluid dynamics as well as conduction of the medium. DocDave's answer is under the assumption that air is stagnant. That's all well and good; but it is important to note the difference between stagnant gas and moving gas. Stagnant air is a good insulator. Air forced to move is a good conductor. The difference is important. $\endgroup$ – JMac Jan 27 '17 at 17:32
  • $\begingroup$ That doesn't respond to the model I am proposing in the above answer. Also stating "a blowtorch heating a metal surface is convection not conduction" doesn't make any sense. They are two different phenomena. Gasses conduct heat - conduction is the diffusion of heat energy throughout a medium. Conduction is thermal energy driven motion of a fluid. $\endgroup$ – user3728501 Jan 27 '17 at 18:28
  • $\begingroup$ It's going to be hard to find the heat transfer from a blowtorch without considering convection. There's conduction on the metal side, but you'll never know the heat transfer from a flame without considering convection (and some other factors with the blowtorch). $\endgroup$ – JMac Jan 27 '17 at 18:48
  • $\begingroup$ In the model I'm considering there is no convection. If gas is being blasted out of a blowtorch and the flow doesn't change with time, which might be physically unrealistic but let's roll with it, then since the flow doesn't change with time and the timescale of convection is presumably a lot longer than the timescale of a jet of gas leaving a blowtorch, then presumably we can neglect it. $\endgroup$ – user3728501 Jan 27 '17 at 18:54
  • $\begingroup$ That's not how this works. If you have a blowtorch blowing on a piece of metal, the way it transfers heat is convection. You don't have hot gas sitting still against the metal, you can't consider it like that. The hot gas is flowing onto it and therefore has convective properties. You could model it as a steady heat source. The problem is; that would just be figuring out the convection. Steady state convection is the type that entry level heat transfer usually deals with. $\endgroup$ – JMac Jan 27 '17 at 18:58

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