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

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

S t \(\tau_{1}\) \(\tau_{\lambda }\)
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