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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 stability of dynamically collapsing gas spheres was discussed and a similarity solution for a dynamically collapsing sphere as the unperturbed state was presented. In the similarity solution the gas pressure was approximated by a polytrope of P = Kp'.
Abstract: We discuss the stability of dynamically collapsing gas spheres. We use a similarity solution for a dynamically collapsing sphere as the unperturbed state. In the similarity solution the gas pressure is approximated by a polytrope of P = Kp'. We examined three types of perturbations: bar {JL = 2) mode, spin-up mode, and Ori-Piran mode. When 7 < 1.097, it is unstable against the bar mode. It is unstable against the spin-up mode for any 7. When 7 < 0.961, the similarity solution is unstable against the OriPiran mode. The unstable mode grows in proportion to \t — £o|~, while the central density increases in proportion to pc oc (t — io)~ 2 in the similarity solution. The growth rate,

47 citations

Journal ArticleDOI
TL;DR: In this paper, the local similarity solution procedure was successfully adopted to investigate non-Darcian flow and heat transfer through a boundary layer developed over a horizontal flat plate in a highly porous medium.
Abstract: The local similarity solution procedure was successfully adopted to investigate non-Darcian flow and heat transfer through a boundary layer developed over a horizontal flat plate in a highly porous medium. The full boundary layer equations, which consider the effects of convective inertia, solid boundary, and porous inertia in addition to the Darcy flow resistance, were solved using novel transformed variables deduced from a scale analysis. The results from this local similarity solution are found to be in good agreement with those obtained from a finite difference method. The effects of the convective inertia term, boundary viscous term, and porous inertia term on the velocity and temperature fields were examined in detail. Furthermore, useful asymptotic expressions for the local Nusselt number were derived in consideration of possible physical limiting conditions.

47 citations

Journal ArticleDOI
TL;DR: In this article, a slip-flow boundary condition is deduced, which allows for partial slip at the surface, and the amount of slip, from full slip to no-slip, is controlled by a dimensionless slip coefficient.
Abstract: Axisymmetric stagnation-point flow is considered. A Newtonian fluid impinges orthogonally on a plane surface lubricated by a thin non-Newtonian liquid film of variable thickness. A slip-flow boundary condition is deduced, which allows for partial slip at the surface. The amount of slip, from full slip to no-slip, is controlled by a dimensionless slip coefficient. Similarity solutions are generally prohibited by the slip-flow boundary condition, except for one particular value of the power-law index of the lubricant. Solutions are presented for this case in order to demonstrate the influence of partial slip on the stagnation point flow. With increasing slip and reduced surface stress, a thinning of the viscous boundary layer is observed. The classical Homann flow is recovered in the no-slip limit.

47 citations

Journal ArticleDOI
TL;DR: A compatibility method of finding symmetry and similarity reduction of partial differential equations of Zakharov–Kuznetsov equation and can be applied to other nonlinear evolution equations in mathematical physics.

46 citations

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed the convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxes.
Abstract: The aim of the present paper is to analyze the natural convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxes. To carry out the numerical solution, two steps are performed. The governing partial differential equations are firstly simplified into a set of highly coupled nonlinear ordinary differential equations by appropriate similarity variables, and then numerically solved by the finite difference method. The obtained similarity solution depends on four non-dimensional parameters, i.e., the Brownian motion parameter (N b), the Buoyancy ratio (N r), the thermophoresis parameter (N t), and the Lewis number (Le). The variations of the reduced Nusselt number and the reduced Sherwood number with N b and N t for various values of Le and N r are discussed in detail. Simulation results depict that the increase in N b, N t, or N r decreases the reduced Nusselt number. An increase in the Lewis number increases both of the reduced Nusselt number and the Sherwood number. The results also reveal that the nanoparticle concentration boundary layer thickness is much thinner than those of the thermal and hydrodynamic boundary layers.

46 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202238
202141
202045
201947
201850