Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.

Magneto-hydro-dynamics boundary layer viscous flow over a stretching sheet: an approach based on homotopy perturbation me

Abstract: In this paper by means of homotopy perturbation method an approximate solution of the steady magneto-hydrodynamics flow under slip condition over a permeable stretching sheet has been studied. The homotopy perturbation method (HPM) has been used to solve the governing non linear equation to derive an approximate analytical solution. The main feature of the HPM is that it produces analytic expression for the solution to nonlinear differential equations and the obtained analytic solution is in the form of an infinite power series. In this work the analytic solution obtained by using first two terms from HPM solution. The solution is given in a closed form equation and is an approximate solution of the full governing Navier–Stokes equations. The effects of the slip, the magnetic and the mass transfer parameters are discussed. Results show that there is only one physical solution for any combination of the slip, the magnetic, and the mass transfer parameters. The velocity and shear stress profiles are greatly influenced by these parameters.

On Similarity Solution of Heat and Mass Transfer in MHD Powell–Eyring Fluid Over a Non-Linear Stretching Surface

Abstract: The present work deals with flow of fluid caused by stretching of nonlinear permeable surface. The fluid under consideration is incompressible and electrically conducting. Furthermore, in contrast to earlier studies, it is non-Newtonian Powell–Eyring fluid. This is for the reason of better practical applications. The objective is to quantify, through a qualitative mathematical study, the different characteristics of extra heat generated due to presence of magnetic field in the moving fluid and to suggest a remedy for its control through the process of suction. The arising mathematical problem is studied by using the classical magneto hydrodynamic Powell–Eyring model which turns out to be a better mathematical frame for the present physical problem than the previously studied power law models. By applying one parameter group analysis, it is mathematically proved that a similarity solution of the problem exists only if the stretching velocity is proportional to $$x^{1/3}$$ and suction velocity and magnetic field are proportional to $$x^{-1/3}$$ . The governing boundary layer equations are reduced to a system of nonlinear ordinary differential equations using the derived similarity transformation. The approximate analytical solutions are obtained by applying homotopy analysis method. The effect of magnetic field on velocity, temperature and concentration distributions are analyzed empirically and graphically. It is found that the local skin friction increases, on the other hand, the rate of heat transfer and rate of mass transfer decrease with increasing magnetic field.

Hydromagnetic Visco-elastic Boundary Layer Flow Past an Exponentially Stretching Sheet with Suction or Blowing

Abstract: The hydromagnetic visco-elastic boundary layer flow characterized by the Walters Liquid (Model \({\varvec{B}}^{\prime }\)) past an exponentially stretching sheet with suction or blowing has been investigated. Slip velocity is considered instead of no-slip conditions at the boundary. Similarity transformations are obtained by careful inspection to convert the governing partial differential equations into nonlinear self-similar ordinary differential equations. The velocity profiles and the skin-friction coefficient have been computed using MATLAB solver ‘bvp4c’ for various values of flow parameters involved in the solution. The velocity and the skin-friction coefficient have been plotted to observe the visco-elastic, slip velocity, magnetic and suction or blowing parameters effects in the flow field.

Group symmetry analysis for mhd boundary layer flow with diffusion and chemical reaction past a stretching

Abstract: The electrically conducting magnetohydrodynamics (MHD) laminar incompressible boundary layer for the Newtonian fluid past a stretching sheet with diffusion and chemical reaction using group symmetry method is investigated. The symmetry groups admitted by the governing boundary value problem are obtained. Particular attention is paid on the deductive group technique which provides the general group transformation and hence similarity solution of the problem. Finally, with the use of the entailed similarity variables the problem is transformed into a boundary value problem of ODEs and is solved numerically using collocation method.