Abstract
Thermal convection is the transport of internal energy by the motion of a fluid. Two types of convection are usually distinguished: free or natural convection and forced convection. Natural convection is a fluid flow whose origin is always a thermal imbalance: it disappears when the temperature gradients vanish.
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Notes
- 1.
Present wording tends to replace the terminology “forced convection” by advection . In this case, temperature is more like a passive scalar and does not, or little, influence the fluid flow.
- 2.
Taking into account their variations with thermodynamic variables would not change the results or the method, but would make the whole derivation more obscure. For this very reason, we shall also neglect the second viscosity ζ.
- 3.
We can make the connection with the coefficient α introduced for the liquids: we have \(\delta \rho /\rho = -\alpha \delta T\), let \(\rho _{1}/\rho _{0} = -\alpha T_{{\ast}}\theta _{1} = -\theta _{1}/\theta _{00}\), therefore \(\alpha = 1/\theta _{00}T_{{\ast}} = 1/T_{l}\).
- 4.
We could, however, approach such a set-up by confining, for example, an oil layer between a layer of mercury in z < 0, and a layer of liquid sodium in z > d!
- 5.
Other solutions may exist where B is not small compared to A, but they are uninteresting for us as we are focusing on the case where A grows first and B follows.
- 6.
We place the boundaries at \(z = \pm \frac{1} {2}\) rather than at z = 0, 1 so as to be able to use the symmetry or the anti-symmetry of the functions with respect to the z = 0 plane.
- 7.
Cahn and Hilliard (1958).
- 8.
This is a metastable chaos.
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Rieutord, M. (2015). Thermal Convection. In: Fluid Dynamics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-09351-2_7
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DOI: https://doi.org/10.1007/978-3-319-09351-2_7
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