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 Racr and wave number kcr.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 Racr 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.