Transient Taylor–Dean flow in a composite annulus with porous walls partially filled with porous material

Journal of the Egyptian Mathematical Society

Table 2 Numerical values of both the steady and the transient state interfacial velocity (U_i) obtained using the RSA, implicit finite difference, and the exact solution \(\left( {d = 1.5, b = - 0.2, P = 10, {\text{Da}} = 0.02, A^{*} = 1, w = 0.8} \right)\)

S	t	\(\tau_{1}\)			\(\tau_{\lambda }\)
S	t	RSA	IFD	Exact solution	RSA	IFD	Exact solution
− 4	0.08	0.4622	0.4623	0.5773	0.5442	0.5441	0.7232
	0.10	0.5074	0.5074	0.5773	0.6110	0.6111	0.7232
	0.20	0.5715	0.5714	0.5773	0.7232	0.7232	0.7232
	0.40	0.5552	0.5553	0.5773	0.7232	0.7232	0.7232
	0.60	0.5773	0.5773	0.5773	0.7383	0.7383	0.7232
− 2	0.08	0.4092	0.4091	0.5071	0.7385	0.7386	0.6411
	0.10	0.4472	0.4473	0.5071	0.4759	0.4760	0.6411
	0.20	0.5020	0.5019	0.5071	0.5320	0.5319	0.6411
	0.40	0.5071	0.5071	0.5071	0.6409	0.6409	0.6411
	0.60	0.5071	0.5071	0.5071	0.6412	0.6411	0.6411
2	0.08	0.3322	0.3322	0.3915	0.3718	0.3717	0.4687
	0.10	0.3565	0.3566	0.3915	0.4067	0.4068	0.4687
	0.20	0.3890	0.3891	0.3915	0.4621	0.4622	0.4687
	0.40	0.3915	0.3914	0.3915	0.4686	0.4687	0.4687
	0.60	0.3916	0.3916	0.3915	0.4687	0.4687	0.4687
4	0.08	0.3090	0.3090	0.3520	0.3373	0.3373	0.4055
	0.10	0.3276	0.3276	0.3520	0.3636	0.3635	0.4055
	0.20	0.3505	0.3504	0.3520	0.4018	0.4017	0.4055
	0.40	0.3520	0.3521	0.3520	0.4055	0.4055	0.4055
	0.60	0.3520	0.3520	0.3520	0.4055	0.4055	0.4055