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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: The invariance group of a class of reaction-diffusion equations, where the diffusion coefficient varies as some power of the population density, is studied in this paper, and a general invariant group similarity solution which admits the largest number of group parameters is derived.
Abstract: The invariance group of a class of reaction-diffusion equations, where the diffusion coefficient varies as some power of the population density, is studied. The Lie algebra of the invariance group and the isovector fields which generate the invariance group are established, and then the isovectors are used to derive a "general" invariant group similarity solution which admits the largest number of group parameters. It is also shown that some exact particular analytical solutions previously reported in the literature for special cases of the equation here considered can be rederived from the present solution.
2 citations
01 Dec 2007
2 citations
10 Oct 2011
TL;DR: Abel et al. as discussed by the authors studied the effects of a transverse magnetic field and electric field on momentum and heat transfer characteristics in viscoelastic fluid over a stretching sheet taking into account viscous dissipation and ohmic dissipation.
Abstract: Due to the increasing importance in processing industries and elsewhere when materials whose flow behavior cannot be characterized by Newtonian relationships, a new stage in the evolution of fluid dynamics theory is in progress. An intensive effort, both theoretical and experimental, has been devoted to problems of non-Newtonian fluids. The study of MHD flow of viscoelastic fluids over a continuously moving surface has wide range of applications in technological and manufacturing processes in industries. This concerns the production of synthetic sheets, aerodynamic extrusion of plastic sheets, cooling of metallic plates, etc. (Crane, 1970) considered the laminar boundary layer flow of a Newtonian fluid caused by a flat elastic sheet whose velocity varies linearly with the distance from the fixed point of the sheet. (Chang, 1989; Rajagopal et al., 1984) presented an analysis on flow of viscoelastic fluid over stretching sheet. Heat transfer cases of these studies have been considered by (Dandapat & Gupta, 1989, Vajravelu & Rollins, 1991), while flow of viscoelastic fluid over a stretching surface under the influence of uniform magnetic field has been investigated by (Andersson, 1992). Thereafter, a series of studies on heat transfer effects on viscoelastic fluid have been made by many authors under different physical situations including (Abel et al., 2002, Bhattacharya et al., 1998, Datti et al., 2004, Idrees & Abel, 1996, Lawrence & Rao, 1992, Prasad et al., 2000, 2002). (Khan & Sanjayanand, 2005) have derived similarity solution of viscoelastic boundary layer flow and heat transfer over an exponential stretching surface. (Cortell, 2006) have studied flow and heat transfer of a viscoelastic fluid over stretching surface considering both constant sheet temperature and prescribed sheet temperature. (Abel et al., 2007) carried out a study of viscoelastic boundary layer flow and heat transfer over a stretching surface in the presence of non-uniform heat source and viscous dissipation considering prescribed surface temperature and prescribed surface heat flux. (Khan, 2006) studied the case of the boundary layer problem on heat transfer in a viscoelastic boundary layer fluid flow over a non-isothermal porous sheet, taking into account the effect a continuous suction/blowing of the fluid, through the porous boundary. The effects of a transverse magnetic field and electric field on momentum and heat transfer characteristics in viscoelastic fluid over a stretching sheet taking into account viscous dissipation and ohmic dissipation is presented by (Abel et al., 2008). (Hsiao, 2007) studied
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TL;DR: The classical Barenblatt solution of an initial-boundary value problem (IBVP) to the parabolic Boussinesq equation, which gives a rectangular triangle of full saturation, propagating from a reservoir into an adjacent porous bank with a vertical slope, is shown to coincide with a solution of IBVP to the elliptic Laplace equation with a phreatic surface along which both isobaricity and kinematic conditions are exactly met as mentioned in this paper.
2 citations