Initially Nusselt number was defined for constant fluid thermophysical properties and as, all non dimensionnal numbers, Nusselt is defined using arbitrary choice depending on context, scope of use ...

Now your choice depend on your goal (local or global approach). The usual choice is film temperature.

Thank you Hugo,

Which definition is more practical?

Hi mohammad,

don't have experience in that specific case but as far as I know a local Nusselt number can always be calculated by an energy balance on the surface in this case you only need k_w. But obviously dt/dy|_w changes and so does Nu_x.

I have used a similar approach in the following paper: International Journal of Heat and Mass Transfer. 01/2013; 59:219 - 229. for calculating the local Nusselt numbers around a cylinder. Of course k was a constant in that case but this doesn't change the formulation.

For a simulation it would be quit easy to calculate dt/dy and correspondingly the local values of the Nusselt number then you can integrate this for a mean Nusselt number. Of course it is possible to use an average temperature to advise a mean Nusselt number but then the question is how to calculate the film temperature (1/2 1/3 and other suggestions).

Anyway for engineering purposes I guess using a film temp and an average k would be just fine.

Thanks, what I meant by k_w was k_f|_w, i.e fluid conductivity at the wall temperature

Dear Shankar and Haeri,

Thank you both for your response.

Dear Shankar you are correct, as Haeri said, the k_w is the fluid thermal conductivity at the wall. As the fluid thermal conductivity is variable, the thermal conductivity of free stream is different with that at the wall.

I want to analysis the effect of variable thermal conductivity on the heat transfer over a plate. I think using thermal conductivity of free stream, Nu=hx/k_inf, can show the non-dimensional heat transfer, however, using Nu=hx/k_w, some how, skips the effect of variable thermal conductivity. What do you suggest? Can i conclude that the definition of Nu=hx/k_w is correct?

Thank you again.

Dear Mohammad,

Using that definition does not skip the effects of the variable conductivity. Note that in this case dT/dy would change along the plate and therefore you will need to define a Nu_x which changes along the plate. Note also that defining a Nu in this fashion is not enough and you also need to provide a correlation to relate Nu to for example Pr and Re_x later on. Then the Nu is calculated by this correlation at any point along the plate and is used to calculate (h) to predict the convective heat transfer.

In any case it is just your choice and how you want to present your data. But obviously this definition contains more information than defining an average value.

Dear Sina

You are right. Thank you very much.

if you mean the Nu for fluid at flat plate or inside tube the average Nu cannot change greatly and more effect with variable thermal but the local Nu can be founded by integration the region