Vertical heat transport at infinite Prandtl number for micropolar fluid.

Collaborators: M. Caggio (Univ. of L'Aquila), P. Kalita (UJ), K. Mizerski (IGF PAN)

We investigate the upper bound on the vertical heat transport in the fully 3D Rayleigh-Benard convection problem at infinite Prandtl number for a micropolar fluid. Our results are as follows:

(1) We obtain a bound of the Nusselt number given by the cube root of the Rayleigh number, with a logarithmic correction. 

(2) The derived bound is compared with the optimal known one for the Newtonian fluid. It follows that the (optimal) upper bound for the micropolar fluid is less than the corresponding bound for the Newtonian fluid at the same Rayleigh number.

(3) Moreover, strong microrotational  effects can highly suppress the heat transfer.

(4) In the Newtonian limit our purely analytical findings fully agree with estimates and scaling laws obtained from previous theories significantly relying on phenomenology.

--------------------------------------------------------------------------------------------------------------------