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 fab May 13, 2005 02:28

total pressure influence on heat transfer

Hi,

Shouldn't the heat transfer coefficient between a solid wall and a fluid change for a different total pressure, i.e. the density, of the fluid?

I wonder if anybody has an idea how the total pressure has an impact on the heat transfer coefficient; any diagramm or formula?

Best Regards! fab

 Alexey May 17, 2005 03:15

Re: total pressure influence on heat transfer

hi fab,

By definition heat transfer coefficient (alfa) is:

alfa = H / (Tfluid - Twall), [W/(m^2*K)],

(I assume that Tfluid > Twall),

where

H is the heat flux [W/m^2], Tfluid is the fluid temperature in the bulk of flow, Twall is the wall temperature.

Heat flux is:

H=lambda * dT/dy,

where lambda is the heat conductivity coeff. and y is the axis nornal to the wall.

As you can see there is no direct dependence from total pressure here. Only from temperature and its gradient at the wall.

Alexey.

 fab May 17, 2005 06:45

Re: total pressure influence on heat transfer

Hi,

isn't that the heat transition coefficient? The heat transfer coefficient depends also on the structure/velocity of the moving fluid. And it should depend on the pressure too; I mean the more molecules are hitting each other the more energy is transferred. Or is that totally wrong?

Greetings! fab

 Harry Fulmer May 17, 2005 08:04

Re: total pressure influence on heat transfer

When y+<11.5 (i.e. laminar) the Stanton number = 1/Pr.Re So yes, looking at k, wall distance and local dT works, the rest of the boundary layer would be explicitly modelled, e.g. the convection of heat away form the surface via the boundary and bulk flow.

When y+>11.5 in the turbulent region the Taylor-Prandlt analogy dictates that heat flux is proportional to momentum fluxSo the Stanton number has to include the effects of wall shear stress which means we have to account for things like fluid velocity near the wall, turbulence near the wall etc.

Generally at a wall HTC = Stanton number x rho x Cp x u

It's via this relationship that Pressure->density comes into play, not so much in the HTC itself.

 fab May 18, 2005 10:33

Re: total pressure influence on heat transfer

Hi,

thanks! So the HTC depends linearly on the density? But then it shouldn't be neglected!?

Greetings! fab

 Harry Fulmer May 19, 2005 03:57

Re: total pressure influence on heat transfer

It's not the HTC as such, more the amount of heat that is convected form the surface is linearly dependent on rho. It depends on how you think of HTC, derived or a function of the local wall conditions. Me, I think of it as the efficiency by which heat is removed, the dT incurred for any given heat removed.

 fab May 19, 2005 05:09

Re: total pressure influence on heat transfer

If I understand you correct, it would have a linear impact on natural convection problems!?

fab

 Harry Fulmer May 19, 2005 06:07

Re: total pressure influence on heat transfer

For natural convection (assuming from say a fixed T vertical wall) changing just the ambient density will have a non-linear affect on HTC due to the coupling between HTC, Q and fluid speed. In reality if you change the ambient density then thermal coductivity and specific heat wil also be changed. A very coupled problem.

 fab May 19, 2005 09:24

Re: total pressure influence on heat transfer

Hi,

thanks for your explanations! Do you have any hint about papers concerning that special topic? I really would like to know which order of magnitude the influence will be depending on rho ...

Regards! fab

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