Why is convection heat transfer rate independent of relative velocity?

[indianaronald]

Convection heat transfer rate decided by Newton's cooling law doesn't have a relative velocity between the fluid and the solid surface term. But intuitively doesn't blowing faster on a hot surface make it cool quicker?

 

[mfb]

If convection is very fast, the fluid will not heat much, so heat transfer does not depend on the velocity.

If convection is very slow, the fluid will reach the temperature of the object, and heat transfer is proportional to the velocity.

If convection is somewhere in between, the result is somewhere between those limits.

 

[indianaronald]

What do you mean 'heat transfer is proportional to velocity'. I thought it wasn't. I mean, so convection is dependent on relative velocity?

 

[mfb]

It depends on the convection speed, see my previous post.

Every law has limits of its application. If you try to use a law in a setup where the law does not hold, you should not be surprised if the result is wrong.

 

[indianaronald]

Ok. That answers the question. Thanks.

 

[AlephZero]

Convection DOES depend on the relative velocity. In Newton's law of cooling, that variation changes the value of the heat transfer coefficient.

In a first physics or engineering course on heat transfer, you are oten given the heat transfer coefficient h as a constant value, so you can focus on solving the rest of the problem rather than figuring out what value of h to use.

http://en.wikipedia.org/wiki/Heat_transfer_coefficient has empirical formulas (i.e. derived from experiments, not purely from theory) for heat transfer coefficients for different situations. These are defined in terms of non-dimensional parameters like the Nusselt, Prandtl, Rayleigh and Reynolds numbers (and you can find definitions of what those quantities are in Wikipeida).

The main parameter that contains the "relative flow velocity" is Reynolds number, Re. The other parameters depend mainly on the fluids involved (e.g. whether the heat is convecting into air or water) and also vary a bit with temperature and pressure.

 

[indianaronald]

Thanks. Found out something about a king's law that relates convection heat transfer coefficient to flow velocity.