Here, $Pr=\mu f(\rho cp)f/(\rho fkf)$ is the Prandtl number, $Ra=g(\rho \beta )f(Th\u2212Tc)(\rho cp)fR3/(\mu fkf)$ is the Rayleigh number, $A=\alpha sw/\alpha f$ is the thermal diffusivity ratio, $K=ksw/kf$ is the thermal conductivity ratio, and the functions $H1(\varphi )$, $H2(\varphi )$, $H3(\varphi )$, and $H4(\varphi )$ are given by
Display Formula

(12)$H1(\varphi )=1(1\u2212\varphi Cu\u2212\varphi Al2O3)2.5[1\u2212\varphi Cu\u2212\varphi Al2O3+\varphi Al2O3\rho Al2O3/\rho f+\varphi Cu\rho Cu/\rho f]H2(\varphi )=1\u2212\varphi Cu\u2212\varphi Al2O3+\varphi Al2O3(\rho \beta )Al2O3/(\rho \beta )f+\varphi Cu(\rho \beta )Cu/(\rho \beta )f1\u2212\varphi Cu\u2212\varphi Al2O3+\varphi Al2O3\rho Al2O3/\rho f+\varphi Cu\rho Cu/\rho fH3(\varphi )={\varphi Al2O3kAl2O3+\varphi CukCu\varphi Al2O3+\varphi Cu+2kf+2(\varphi Al2O3kAl2O3+\varphi CukCu)\u22122(\varphi Al2O3+\varphi Cu)kf}\xd7{\varphi Al2O3kAl2O3+\varphi CukCu\varphi Al2O3+\varphi Cu+2kf\u2212(\varphi Al2O3kAl2O3+\varphi CukCu)+(\varphi Al2O3+\varphi Cu)kf}\u22121\xd7{1\u2212\varphi Cu\u2212\varphi Al2O3+\varphi Al2O3(\rho cp)Al2O3/(\rho cp)f+\varphi Cu(\rho cp)Cu/(\rho cp)f}\u22121H4(\varphi )={\varphi Al2O3kAl2O3+\varphi CukCu\varphi Al2O3+\varphi Cu+2kf\u2212(\varphi Al2O3kAl2O3+\varphi CukCu)+(\varphi Al2O3+\varphi Cu)kf}\xd7{\varphi Al2O3kAl2O3+\varphi CukCu\varphi Al2O3+\varphi Cu+2kf+2(\varphi Al2O3kAl2O3+\varphi CukCu)\u22122(\varphi Al2O3+\varphi Cu)kf}\u22121$