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2

The rate of temperature change will be the power per unit mass times the specific heat. So if you have a certain mass of water $M$ flowing per second, at a velocity $v$, losing $\Delta P$ pressure per second, then work done is $v\Delta P A$ and $A = \frac{M}{\rho v}$ . Then with a heat capacity $c$ (about 4.2 kJ/kg/K for water), and the relationship between ...

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The dimensionless Rayleigh number characterizes buoyancy driven convection. When the Rayleigh number is below a critical value, heat transfer is primarily by conduction (e.g. no Benard convection cells). When the Rayleigh number is above the critical value, heat transfer is primarily by convection (e.g. Benard convection cells spontaneously form and ...

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As far as I remember, the RB convection system very far away from the onset has not been analytically studied to a great extent. There has been quite a bit of numerical work studying pattern formation and structure generation (finally leading to chaotic turbulence). Far from the onset, I suppose one might see ergodicity breaking with periodic orbits and ...

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