Thermal Convective Instability of Fluid Heated Suddenly at the Lower Boundary

Abstract

A linearized theory of stability is applied to the problem of the onset of thermal convection in a semi-infinite fluid of constant temperature whose horizontal lower boundary is heated suddenly and thereafter kept at a higher constant temperature. On basis of the assumption that the basic temperature profile is quasi-stationary, a neutral stability curve is obtained and the critical Rayleigh number is found to be 1340. Amplified disturbance whose growth rate is equal to that of the thickness of the heated layer is also investigated. Results are compared with other theoretical and experimental results.