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Similarity solution
About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.
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TL;DR: In this paper, the axisymmetric Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin.
16 citations
TL;DR: In this article, mathematical and numerical analyses are presented to investigate self-similarity solutions of a two-dimensional MHD boundary layer flow over a permeable surface, and the required boundary conditions to obtain a similarity solution, are detailed.
Abstract: In this paper mathematical and numerical analyses are presented to investigate self-similarity solutions of a two-dimensional MHD boundary layer flow over a permeable surface. Required boundary conditions to obtain a similarity solution, are detailed. In the case of the Nonlinear Density Temperature (NDT) parameter, the self-similarity solution may be multiple, and the requirement of appropriate conditions of the model control parameters, provides a global similarity solution. We will explain the underlying conditions for the existence of a solution, which leads to multiple solutions in the general case. We also give some numerical results to show the MHD influence on the solution stability.
16 citations
TL;DR: In this paper, the steady boundary layer flow and heat transfer induced by a moving permeable semi-infinite flat plate in a parallel free stream is studied. But the surface temperature is assumed to be constant.
Abstract: This paper presents both a numerical and analytical study in connection with the steady boundary layer flow and heat transfer induced by a moving permeable semi-infinite flat plate in a parallel free stream. Both the velocities of the flat plate and the free stream are proportional to x
1/3. The surface temperature is assumed to be constant. The governing partial differential equations are converted into ordinary differential equations by a new similarity transformation. Numerical results for the flow and heat transfer characteristics are obtained for various values of the moving parameter, transpiration parameter and the Prandtl number. Approximate analytical solutions are also obtained when the suction or injection parameter is very large. It is found that dual solutions exist for the case when the fluid and the plate move in the opposite directions.
15 citations
TL;DR: In this paper, the authors developed continuous equations governing steady, laminar, boundary-layer flow and heat transfer in a quiescent non-Newtonian, power-law fluid driven by a stretched porous surface.
15 citations
TL;DR: In this paper, the authors derived an initial-boundary value problem with a nonlocal condition to model mass and charge transport in a controlled potential experiment called chronoamperometry.
Abstract: We derive an initial–boundary value problem with a nonlocal condition to model mass and charge transport in a controlled potential experiment called chronoamperometry. The charge is carried by ions set in motion by a change in the applied electrode potential. The resulting electric current is called the current response. When the charge flux arises from diffusion alone, the model reduces to an initial–boundary value problem for the heat equation. We consider diffusion and migration (motion under the influence of an electric field). This latter component of the total flux gives rise to a nonlinearity in the transport equations. Experimentalists have noted the current response to be proportional to the square root of the time with or without migration. It is shown that the initial–boundary value problem has a unique similarity solution that accounts for this observation.
15 citations