In the book Basics of Heat and Mass Transfer, the Nusselt number is defined as the ratio of convective heat transfer to pure conduction heat transfer.
But it seems that in the field of heat convection research, Nusselt number has another definition, which is the ratio of total heat transfer to heat transfer by conduction.
The difference between the above two formulas is mainly in the molecule, that is, whether the molecule is convective heat transfer or total heat transfer. I haven't figured out this part yet. The following mainly uses the second formula as an example to illustrate how to calculate the Nusselt number of the system in vertical heat convection and horizontal heat convection.
The specific calculation formula is given in the literature:
Note that here is θ \thetaθ represents the dimensionless temperature.
N u = ⟨ v T − α ∂ T / ∂ y ⟩ V , t α Δ T / H , N u=\frac{\langle v T-\alpha \partial T / \partial y\rangle_{V, t}}{\alpha \Delta_T / H}, No _=a DT/H⟨vT−α∂T/∂y⟩V,t,
where the subscripts V, t represent spatial average and time average. The above formula is a dimensioned result. After it is dimensionless, the calculation formula is:
N u = RaPr ⟨ v ∗ T ∗ ⟩ V , t + 1 N u=\sqrt{\operatorname{RaPr}}\left\langle v^* T^* \right\rangle_{V, t}+1No _=RaPr⟨v∗T∗⟩V,t+1
In fact, there is still one point that I don’t understand very well, that is, why the temperature gradient will be equal to 1 after being averaged and divided by the denominator. If it is pure conduction, the temperature gradient at any place in the whole field should be consistent, because the temperature will be linear. distribution, but now it is convection, will the temperature gradient of the whole field be equal to the pure conduction after being averaged? (I figured out this question last night, so I'll add it here:)
It's actually very simple, it's just that I can't think about it for a while, or IQ is not good. . .