NUMERICAL ANALYSIS FOR OSCILLATORY NATURAL CONVECTION OF LOW PRANDTL NUMBER FLUID HEATED FROM BELOW

Finite difference numerical computations were carried out for the horizontal fluid layer heated from below and cooled from above for Prandtl numbers from 0.1 to 0.001 and for Rayleigh numbers up to 16,000 (for Pr = 0.01). The aspect ratio (width / height) of a computational regime was generally 4 to allow for the appearance of multiple roll cells. The initiation of oscillatory convection and multiplication in the number of roll cells was detected and found to be affected by the Rayleigh and Prandtl numbers with grid sizes up to 201 × 51. However, the oscillatory characteristics were found to be still dependent on the computational grid size. The critical Rayleigh number for the initiation of oscillation was found by extrapolating to zero grid size. The oscillation appears to occur even just after the initiation of convection at 1708 for Prandtl numbers less than 0.01.