A series method for the solution of laminar boundary layers on moving surfaces

An analytical treatment for the exact solutions of MHD flow and heat over two–three dimensional deforming bodies

“…Unlike the numerical variations in the open literature, the fundamental purpose here is to gain exact analytical solutions either in the closed-form or in the infinite series form, at least. Within this aim, first, exponential type series solutions are shown to exist (after the works of [74,38]), having finite or infinite terms in the expansion depending on the prevailing parameters of the fields of flow and heat. Special closed-form solutions are shown to be possible when the series terminates.…”

“…Therefore, solution of the boundary value problem (4) is reduced to finding two roots k and a 1 from equations (9) and (10). This is a great advance as also stated in [38,74] to be further exploited in what follows. It is worthy to mention that the physical quantity f 00 ð0Þ at this stage is given by…”

“…It was first noted by Ackroyd [74] that taking into account the infinity boundary condition in (4), it is natural to assume a solution in the exponentially decaying format…”

“…Hence, the objectives are initially to represent the governing equations of severally worked stretching/shrinking bodies by a universal system, containing several parameters of physical interest. The next objective is to derive exact analytical solutions of the exponential form (after the works of [74,38]) and of the algebraic form (after the works of [22,31,75]). Within this purpose, the general exponential series formula is shown to lead to well-known solutions in some special cases.…”

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

“…The idea dates back to Cochran [24] who showed that a scale factor characterizes the flow, and he then went on to calculate the same. Ackroyd [4], in general, showed that the flows caused by moving boundaries in unbounded domains have a scale factor associated by them, and it greatly helps in getting a more efficient solution by taking this fact into account. Accordingly, we have developed a two-parameter solution, the second parameter being the scale factor.…”