Biot and fourier numbers
 

Hi, I have a conjugate heat transfer problem in a oscillating laminar flow.I know the material properites and wonder how can I compute Biot and Fourier numbers? Fluid properties are temprature dependent? How can I obtain heat transfer coeffeienct? and what will be the time for the Fourier number calculation?

Thanks, Selim

Re: Biot and fourier numbers
 

The Biot number is basically a ratio of thermal conductivities and can be obtained by ((Surface Temperature of metal not exposed to fluid - Surface Temperature of Metal exposed to fluid)/(Surface Temperature of Metal exposed to fluid - Temperature of fluid))

i.e. if Biot is a lot less than 1 then the resistance to thermal conduction within the solid is much less than that of the fluid.

As far as Fourier goes, what time are you interested in?

Re: Biot and fourier numbers
 

Selim:

The definitions are ...

Bi = (h*l)/k (l is the characteristic length scale, e.g., thickness of your solid plate)

Fo = (alpha*t)/l^2 (where l and t are the corresponding length and time scales)

Since your problem is oscillatory, you will get different ranges of Biot and Fourier numbers depending on the frequency of your oscillation. I would use the period of oscillation as your time scale.

I assume that you'd be using the Biot number to justify lumped capacitance modelling of your solid. Given the oscillatory nature of your problem, I am also uncertain whether the magnitude of this number alone would be an accurate representation in the steady state case. (For one, I think at higher frequency, heat conduction will dominate).

I think, a more instructive approach would be to write out your governing equation of the plate, and approximate h as a function of the flow velocity (which is oscillatory). Then normalize your equation to obtain a reasonable set of dimensionless parameters, which you can use for your analysis.