Implicit finite difference solution for the magneto-hydro-dynamic unsteady free convective flow and heat transfer of a third-grade fluid past a porous vertical plate

Approximate Solution for the Thin Film Flow Problem of a Third Grade Fluid Using Spline Collocation Method

“…Now in order to obtain a solution to equation (6) with the boundary conditions given in equations (7) and (8), we fit a straight line y(x) = mx + c through the boundary points, which is of course an initial guess, and the moments These moments are now utilized to evaluate y i , i = 0, 1, 2... n, through the relation (16) along with the two additional equations from boundary conditions. This can be finished by solving merely a tridiagonal system of equations.…”

“…Many Numerical and analytical techniques have been developed to solve nonlinear differential equations by many researchers. These methods include the artificial parameter methods by He [1], the variational iteration method by He [2], the homotopy analysis method by Liao [3], the optimal homotopy asymptotic method (OHAM) by Marinca and Herisanu [4], the optimum homotopy asymptotic method by Mabood [5], an implicate finite difference method by Itishree et al [6], the spline collocation method [7], etc. In this paper, we considered the steady uni-dimensional flow of an incompressible third grade fluid down a uniform inclined plane, for the third grade fluid, the first four terms of Taylor series are using the stress rate of strain relation.…”

“…from relation (12) if a curve is initially fitted to the data and two extra conditions are considered to complete the system.Here our objective is to solve the differential equation(6) with the help of relation (15). Let us express the equation(6) in the form…”

Spectral-homotopy analysis of MHD non-orthogonal stagnation point flow of a nanofluid

“…Most researchers have used the semi-analytical and numerical methods such as the Runge-Kutta methods [1], finite difference methods [2], finite element methods [3] and spectral methods [4] to solve this type of equations. In recent years, for solving nonlinear differential equations, several analytical and semi-analytical methods have been established such as the variational iteration method [5,6], Adomian decomposition method [7], differential transform method [8], homotopy analysis method (HAM) [9][10][11][12][13], and the spectral-homotopy analysis (SHAM) [14,15] and more recently, the successive linearization method [16,17].…”

Analysis of Unsteady MHD Thin Film Flow of a Third Grade Fluid with Heat Transfer down an Inclined Plane

“…The third grade fluid model attempt to include such characteristics of viscoelastics fluids. Many authors have successfully analysed the nonlinear differential equation governing the flow of a third grade fluid [1][2][3]. He [4][5][6] introduced a new perturbation method which is a combination of regular perturbation method and homotopy as used in topology.…”