Fluid temperature change over cold surface?

[dgarza6]

For my research I am trying to study the temperature change of a warm fluid (air) flowing over a cold surface, but I have not studied fluid mechanics. Does anyone know of an equation that can be used to analyze this problem? To give some reference, the hot air is 49 Celsius and the cold air is 0 Celsius with a fluid velocity of 200 mph. Thanks!

 

[NFuller]

The first thing you need to know is the Reynolds number of the system. This may allow for a simpler form of the Navier-Stokes equation to be used. If the Reynolds number is very small, then the Stokes equation is valid. If the Reynolds number is very large, then the Euler equations are valid. If the Reynolds number has moderate magnitude, then you have to solve the full Navier-Stokes equation.

Once you have the velocity profile of the fluid, you can find the heat flow using the advection-diffusion equation.

 

[Nidum]

At 200 mph air speed you will need to have a very clear idea of what 'flowing over' means . Depending on the geometry of the problem the flow dynamics and the actual conditions for heat transfer might be difficult to determine .

Please show us a sketch of the actual configuration .

 

[dgarza6]

The first thing you need to know is the Reynolds number of the system. This may allow for a simpler form of the Navier-Stokes equation to be used. If the Reynolds number is very small, then the Stokes equation is valid. If the Reynolds number is very large, then the Euler equations are valid. If the Reynolds number has moderate magnitude, then you have to solve the full Navier-Stokes equation.

Once you have the velocity profile of the fluid, you can find the heat flow using the advection-diffusion equation.

Thanks! This helps a lot.

 

[dgarza6]

At 200 mph air speed you will need to have a very clear idea of what 'flowing over' means . Depending on the geometry of the problem the flow dynamics and the actual conditions for heat transfer might be difficult to determine .

Please show us a sketch of the actual configuration .

The situation is warm air flowing over a cold wing and calculating the temperature change of the air.

 

[dgarza6]

Thanks! This helps a lot.

Quick follow-up question. What range of values are considered small, moderate and large for the Reynold's number?

 

[NFuller]

A small Reynolds number is $Re<<1$ like $10^{-3}$
A Large Reynolds number is $Re>>1$ like $10^{3}$
A moderate Reynolds number is $Re\sim 1$ like $10$

For the situation of air moving across an airfoil at high speed, the Reynolds number is likely large but you still need to make sure. This would allow for the flow to be divided into two regions across a boundary layer and separate the Navier-Stokes equation into parabolic PDEs.

 

[Nidum]

Your diagram file won't open in any software that I have available . Could you please convert it to .jpg or .png format and just upload it here ?

 

[dgarza6]

Your diagram file won't open in any software that I have available . Could you please convert it to .jpg or .png format and just upload it here ?

This should do it.

 

[Nidum]

OK . Thanks .

 

[Nidum]

You show an aerofoil with a flat bottom and with the air only flowing over the top surface ? Is this correct ?

In any case I think that finding a solution to this problem which can be put in equation form is not a realistic prospect for anything like real aerofoil profiles¹ even if you do only consider air flow over the top surface .

You could analyse a range of aerofoil sections and flow conditions systematically - one at a time - and generate a chart of results which you could then find fit curves to describe .

Anyway there are problems enough in analysing just one configuration .

Personally I would strive to set up a parametric model in CFD . There would be difficulties to overcome but I think that it could be done .

Note 1 : You may be able to do it for simplified aerofoil sections which have a very low thickness to chord ratio and very basic profiles such as arcs . You would essentially be making the approximation that the aerofoil surface was so nearly flat that it could be treated as such .

 

[russ_watters]

This should do it.

Can I just say I love how it appears you have six tabs open in your browser where you researched terms people threw at you in the thread...?

Anyway, carry-on...

 

[NFuller]

One more piece of advice, from looking at what you've posted, this problem will likely need to be solved numerically as @Nidum suggested. The easiest route would be to use some pre-packaged fluid dynamics software such as Comsol.

 

[boneh3ad]

Really, this task has no closed-form solution and a relatively high level of fluid dynamics knowledge would be required to solve it. In my opinion, the simplest method would be to use publicly-available data about the pressure distribution of the wing section (easy to find for NACA profiles) to approximate the boundary layer. It would be relatively straightforward to do using something like Hartree profiles for perhaps a senior-level or early graduate engineering student who has taken a viscous flow course.

Using a prepackaged software is a bad idea here, in my opinion. Garbage in, garbage out. Unless @dgarza6 knows how gridding and inflow conditions work and affect the answer, using a commercial CFD package is likely to produce a bad answer, and you need some degree of fluid mechanics knowledge to be able to see the bad answer for what it is.

Either way, you would need some fairly advanced fluid mechanics background in order to solve the problem numerically on your own. The former approach has the advantage of teaching the user about fluids in the process, whereas the latter approach assumes that knowledge and would be unforgiving to someone who didn't know what they were doing. Either way, it's a relatively big task.