The second-law analysis of convective pattern change in a rectangular cavity

Natural convection in a rectangular cavity is examined, utilizing the second law of thermodynamics. Through an application of the second law the rate of entropy generation associated with the convective pattern changes is evaluated for the onset of natural convection in a cavity with free boundaries, for which an exact solution is sought, as well as with rigid boundaries which is studied numerically. Entropy to be generated from the perturbed temperature and velocity fields is shown to depend on AR (aspect ratio of the cavity), Ra-c (the critical Rayleigh number) and a nondimensional parameter, Omega, which is related to the ratio of entropy generation by viscous friction to that by thermal transport. The convective pattern change is related to a change in the spatial distributions of the rate of entropy generation due to heat transfer and due to dissipation, demonstrating that an application of the second law helps examine convective pattern changes quantitatively by dealing with temperature and velocity fields in a unified manner.