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The onset of Rayleigh-Bnard 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+ b sin( 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 k _ cr did not show much difference with the amplitude b of the sine-function while ψ =π/2,but exponentially increased while ψ =π.
The onset of Rayleigh-Bnard convection in a fluid layer dispersed with phase-change-material particles was studied numerically by using the linear stability theory. Dimensional fluctuation of specific heat Q with dimensionless temperature T was given as a form of sine- Function Q = 1 + b sin (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 k _ cr did not show much difference with the amplitude b of the sine-function while ψ = π / 2, but exponentially increased while ψ = π.