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...