Homotopy Perturbation Method and the Stagnation Point Flow

The laminar steady flow of an incompressible, viscous fluid near a stagnation point has been computed using the homotopy perturbation method (HPM). Both the cases, (i) two-dimensional flow and (ii) axisymmetric flow, have been considered. A sequence of successive approximations has been obtained in the solution, and the convergence of the sequence is achieved by using the Padé approximants. It is found that there is a complete agreement between the results obtained by the HPM and the exact numerical solution

New Analytical and Numerical Solutions for Mixed Convection Boundary-Layer Nanofluid Flow along an Inclined Plate Embedded in a Porous Medium

Two different analytical and numerical methods have been applied to solve the system describing the mixed convection boundarylayer nanofluids flow along an inclined plate embedded in a porous medium, namely, homotopy perturbation method (HPM) and Chebyshev pseudospectral differentiation matrix (ChPDM), respectively. Further, ChPDM is used as a control method to check the accuracy of the results obtained by HPM. The analytical method is applied using a new way for the deformed equations, and the resulted solution was expressed in terms of a well-known entire error function. In addition, using only two terms of the homotopy series, the approximate analytical solution is compared with the numerical solution obtained by the accurate ChPDM approach. The results reveal that good agreements have been achieved between the two approaches for various values of the investigated physical parameters

Current Perspective on the Study of Liquid-Fluid Interfaces: From Fundamentals to Innovative Applications

Fluid interfaces are promising candidates for confining different types of materials - e.g., polymers, surfactants, colloids, and even small molecules - and for designing new functional materials with reduced dimensionality. The development of such materials requires a deepening of the Physico-chemical bases underlying the formation of layers at fluid interfaces, as well as on the characterization of their structures and properties. This is of particular importance because the constraints associated with the assembly of materials at the interface lead to the emergence of equilibrium and dynamics features in the interfacial systems, which are far from those conventionally found in the traditional materials. This Special Issue is devoted to studies on fundamental and applied aspects of fluid interfaces, trying to provide a comprehensive perspective on the current status of the research field

Comment on: “The three-dimensional flow past a stretching sheet and the homotopy perturbation method”, by P.D. Ariel, Computers and Mathematics with Applications 54 (2007) 920–925

AbstractIn his application of the homotopy perturbation (HP) method to the problem of the three-dimensional flow past a stretching sheet, P.D. Ariel [The three-dimensional flow past a stretching sheet and the homotopy perturbation method, Comput. Math. Appl. 54 (2007) 920–925] encountered secular terms in the second order approximation, which he could not avoid. It is shown here that these secular terms can be removed by coordinate straining. Moreover, the form of an HP solution, which is free from secular terms at all levels of approximation, and which can be determined recursively, is indicated