Heat Equation for Compressible Fluids: Valid or Not?

[MattT1991]

Hi everyone,

I am wondering if the heat equation is valid for compressible fluids like air. This is assuming constant 100% humidity.

If it is not then how close is the appoximation.


The model assumes that heat moves through an array of air only by conduction. At the moment I use a psychrometric model to set the boundary Temperaturefor the array from heat flow in, then run the heat equation from that boundary through the array.

Any help asap would be much appreciated,

Thanks,

Matt

 

[boneh3ad]

Assuming that by heat equation you mean $q = -k \nabla T$, then the answer is sometimes. If the gas is stagnant then yes. If it is moving then the equation is much more complicated.

 

[AlephZero]

The model assumes that heat moves through an array of air only by conduction.

That is a big assumption to make for any fluid, and it's nearly always wrong, because temperature changes cause density changes which cause convection currents.

 

[boneh3ad]

that is a big assumption to make for any fluid, and it's nearly always wrong, because temperature changes cause density changes which cause convection currents.

qft...

 

[alphy]

I can tell you that the heat equation is valid for compressible fluids, including air. The equation describes the flow of heat through a material, regardless of whether it is compressible or not. However, the accuracy of the approximation may vary depending on the specific conditions and properties of the fluid.

In the case of air, the model assumes that heat is transferred through conduction, which is a valid assumption for most practical scenarios. However, it is important to note that air is also capable of transferring heat through convection and radiation, which may need to be taken into consideration for more accurate results.

Additionally, the assumption of constant 100% humidity may also affect the accuracy of the model, as humidity can impact the thermal conductivity of air. It would be beneficial to consider the effects of humidity on the heat transfer process in your calculations.

Overall, the heat equation can provide a good approximation for the transfer of heat in compressible fluids like air, but it is important to consider all relevant factors and assumptions for more accurate results. I hope this helps clarify your question.