Dynamical System Analysis of Thermal Convection in a Horizontal Layer of Nanofluids Heated from Below

Table 4

Comparison between Vadasz case (𝜙=0) and the nanofluid case for 𝜙=0.05 with Pr=10, 𝜆=8/3 for 𝑅 a solitary limit cycle signifying the loss of stability of the steady convection fixed points and the critical value of 𝑅 at which the chaotic behaviour solution occurs.

	𝑅	𝑅
	(limit cycle)	(critical value, chaotic behaviour)
Vadasz	23.474	24.737
(𝜙=0)
Ag	36.918	37.503
Cu	35.769	36.305
Al2O3	34.032	34.490
TiO2	33.352	33.800