Effect of various double frequency modulations on rayleigh benard convection

Abstract

Rayleigh-Bénard convection in Newtonian fluid under different types of modulations are studied in this thesis by replacing the single frequency modulations with two frequency modulations with different amplitude and frequency. Linear and non-linear analysis of Rayleigh-Benard convection is considered under two-frequency gravity, rotation, temperature, magnetic field and internal heat generation modulation. The sixteen combinations of sinusoidal (trigonometric sine) and non-sinusoidal (square, triangular, sawtooth) wave forms of different modulations are considered to study the impact of modulations on the onset of convection and heat transport. The expressions for unmodulated Rayleigh number and correction Rayleigh number in the linear case are obtained from linearized Lorentz model using Venezian approach. To study the impact of different types of modulations and wave forms on the heat transport, the expression for the Nusselt number is obtained by solving the non-linear Lorentz model numerically. From the study it is found that the two-frequency modulations make the system more stable compare to no-modulation and single-frequency modulations. The mixing angle of the two frequency plays major role in deciding the stability of the system. The results pertaining to no-modulation and single frequency are obtained as the limiting cases. Onset of Rayleigh-Bénard Convection and Heat Transfer under Two-frequency newlineRotation Modulation The study investigates the effect of sixteen sinusoidal (sine) and non-sinusoidal combinations (square, triangular, sawtooth) of time-periodic Coriolis force (rotation modulation) on Rayleigh-Bénard convection (RBC) in a Newtonian liquid. The consideration captures the potential effects of two-frequency rotation modulation on stability, newlinespecifically the onset of convection and the amount of heat transfer in the system simultaneously.