On the explicit, purely analytic solution of Von Kármán swirling viscous flow

On a second parameter in the solution of the flow near a rotating disk by homotopy analysis method

“…In the present work we have reworked the solution given in [31]. We have drawn the -curves and found that even for the 40th approximation they are not flat enough to provide a satisfactory choice of .…”

“…The problem of flow due to a rotating disk has been attempted using both the homotopy methods. Yang and Liao [31] gave the solution using the HAM, while Ariel [8] derived the solution using the extended version of the HPM. The solution given by Yang and Liao required as many as 45 terms to obtain a four-digit accuracy, whereas the solution derived by Ariel required only eight terms to obtain a much superior accuracy.…”

“…In their work Yang and Liao [31] applied the classical version of the HAM, which includes a single parameter that is supposed to control the convergence of the series occurring in the solution. It is recommended by Liao [31] in his monograph on the HAM that -curves should be drawn and a value of should be picked from those segments of the curves which are horizontal for the longest lengths.…”

“…It is recommended by Liao [31] in his monograph on the HAM that -curves should be drawn and a value of should be picked from those segments of the curves which are horizontal for the longest lengths. Yang and Liao [31], however, did not follow this recipe and instead chose a fixed value of namely = −1 and kept on increasing the value of N , the order of approximation. Eventually they got a four-digit accuracy for the solution of the normal velocity at infinity.…”

Turbulence modeling of the Von Kármán flow: Viscous and inertial stirrings

“…In the counter-rotating regime, Dijkstra and Van Heijst [9] showed numerically that the transition from the one cell to the two cell structure occurs for a given Reynolds number and corresponds to the appearance of a detached shear layer on the slower disk. Recently, Yang and Liao [10] solved the Von Kármán swirling viscous flow using the homotopy analysis method. The reader is referred to the work of Holodniok et al [11] and to the review of Zandbergen and Dijkstra [12] for a more extensive survey until 1987.…”