Initiation of thermal convection in finite right circular cylinders

Linear perturbation analyses are extended to determine the lowest Rayleigh number at which convection initiates in a vertical cylinder heated on the bottom and cooled on the top. The critical Rayleigh number for the first mode of convection in a right circular cylinder with a perfectly conducting wall is shown to be three times larger than that in such a cell with a perfectly adiabatic side wall. An adjusted wave number is shown to make the results of Pellew and Southwell applicable to the adiabatic wall in a manner similar to that used by Pnueli and Ostrach for the perfectly conducting side wall. The results are compared with experiment and are in very good agreement.