In the present study, an analysis is carried out to study twodimensional, laminar boundary layer flow and mass transfer of a micropolar chemically-reacting fluid past a linearly stretching surface embedded in a porous medium. Such a study finds important applications in geochemical systems and also chemical reactor process engineering. The non-linear partial boundary layer differential equations, governing the problem under consideration, have been transformed by a similarity transformation into a system of ordinary differential equations, which is solved numerically by using the galerkin finite element method. The numerical outcomes thus obtained are depicted graphically to illustrate the effect of different controlling parameters on the dimensionless velocity, temperature and concentration profiles. Comparisons of finite element method and finite difference method is also presented in order to test the accuracy of the methods and the results obtained are found to have an excellent agreement. Finally, the numerical values for quantities of physical interest like local Nusselt number and skin friction are also presented in tabular form.
The Present manuscript reports the solution of well known non linear wave mechanics problem called KDV equation, here main emphasis is given on the Mathematical modeling of traveling waves and their solutions in the form of Kortewegde Vries equation (KdV) It is a non-linear Partial Differential Equation (PDE) of third order which arises in a number of physical applications such as water waves, elastic rods, plasma physics etc. We present numerical solution of the above equation using B-spline FEM (Finite Element Method) approach. The ultimate goal of the paper is to solve the above problem using numerical simulation in which the accuracy of computed solutions is examined by making comparison with analytical solutions, which are found to be in good agreement with each other along with that we discussed the physical interpolation of the soliton study in which we found that the travel waves reaches to the maximum magnitude of the velocity in the short time of the interval and there is an uncertainty in the motion of the moving waves. Another important observation we found that the maximum magnitude of the velocity in the most of the time domain is around 1 but in some of the condition waves having a unnatural phenomena which is called the existence of the doubly soliton is seemed frequently. All above observation which is clearly indication of the generic outcome of a weakly nonlinear long-wave asymptotic analysis of many physical systems. The another achievement of the work is to implementation of the cubic Bspline FEM in the above non linear propagating waves phenomena.
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