关键词: Rayleigh-Benard对流, 相变物质, 线性稳定性, 数值分析

Abstract: The onset of Rayleigh-Benard convection in a fluid layer dispersed with phase-change-material particles was studied numerically by using the linear stability theory.The dimensionless fluctuation of specific heat Q with dimensionless temperature T was given as a form of sine-function Q=1+bsin(ψT).Two kinds of numerical methods were used separately in the calculation of critical Rayleigh number Ra_cr and wave number k_cr.One was the numerical integration method using Simpson 1/3 rule, and the other was the numerical difference method of Runge-Kutta with Newton-Raphson iteration. Both methods showed the same calculation results that the critical Rayleigh number Ra_cr decreased monotonically with increase in the amplitude b of the sine-function, however, the critical wave number kcr did not show much difference with the amplitude b of the sine-function while ψ=π/2, but exponentially increased while ψ=π.

Key words: Rayleigh-Benard对流, 相变物质, 线性稳定性, 数值分析