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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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Journal ArticleDOI
TL;DR: In this paper, a numerical solution of flow and heat transfer outside a stretching permeable cylinder is presented, where the governing system of partial differential equations is converted to ordinary differential equations by using similarity transformations, which are then solved numerically using the Keller box method.

141 citations

Journal ArticleDOI
TL;DR: In this article, the authors discuss the flow and heat transfer in a two-dimensional boundary layer flow of an electrically conducting nanofluid over a curved stretching sheet coiled in a circle of radius R. The mathematical model of the flow situation under consideration is developed using a curvilinear coordinates system which results in a set of partial differential equations.

140 citations

Journal ArticleDOI
01 Jan 1988
TL;DR: In this paper, it was shown that the instability of the annular flow is responsible for the flickering of large diffusion flames, and the authors have confirmed this phenomenon and proposed a theoretical explanation.
Abstract: Large diffusion flames are known to flicker at a frequency (∼12Hz) that is remarkably insensitive to flow rate, burner size, or gas composition. We have confirmed this phenomenon and propose a theoretical explanation. We note that, in addition to the forced convection associated with a tube-burner diffusion flame, there is strong natural convection generated by the hot gases. This bouyancy-induced flow surrounds the forced component and depends only on the thermomechanical properties of the hot and cold gas, together with g , the gravitational acceleration. We argue that it is the instability (of modified Kelvin-Helmholtz type) of this annular flow that is responsible for the flickering. A paradigm for this flow is defined by the infinite candle , an ideal plane diffusion flame in which the flow field is induced solely by buoyancy. The infinite candle admits a similarity solution. An inviscid, parallel flow stability analysis of this flow-field yields a frequency for which the spatial growth of the disturbance is a maximum. This is within a factor of 2 of the observed frequency.

137 citations

Journal ArticleDOI
TL;DR: In this article, the effects of different shape factors have been investigated for a mixture of water and nanofluid with hybrid nanoparticles (MWCNT-Ag) over a vertical stretching cylinder, while a magnetic field has been applied to the system.
Abstract: In this study, flow of a mixture of water and ethylene glycol (50–50%) with hybrid nanoparticles (MWCNT–Ag) over a vertical stretching cylinder has been investigated. In this research, the fluid passes through a porous media, while a magnetic field has been applied to the system. Furthermore, the effects of thermal radiation, viscous dissipation, and natural convection have been studied. As a novelty, the effects of different shape factors have been investigated. In the first step, the governing equations are extracted from partial differential equations and then converted to ordinary differential equations (ODE) using the similarity solution. In the next step, the fifth-order Runge–Kutta method has been used to solve the related ODEs. The effects of parameters such as magnetic field, radiation parameter, porosity parameter, nanofluid volume fraction, and nanofluid shape factor on dimensionless velocity and temperature profile have been presented for single and hybrid nanofluid. The results showed that at $$\eta$$ = 2.5 for hybrid nanoparticles the shape factors lamina and spherical have the largest difference; lamina is smaller by 6%, also the results demonstrated that at $$\eta$$ = 2 with increasing Ha, the radial velocity reduced 9.68% for hybrid nanoparticles.

137 citations

Journal ArticleDOI
TL;DR: In this paper, an exact similarity solution of the Navier-Stokes equations is obtained, which represents steady axisymmetric stagnation-point flow towards a stretching surface, and it is shown that the flow displays a boundary-layer structure when the stretching velocity of the surface is less than the free stream velocity.
Abstract: An exact similarity solution of the Navier-Stokes equations is obtained. The solution represents steady axisymmetric stagnation-point flow towards a stretching surface. It is shown that the flow displays a boundary-layer structure when the stretching velocity of the surface is less than the free stream velocity. On the other hand, an inverted boundary layer is formed when the surface stretching velocity exceeds the free stream velocity. Temperature distribution in the flow is found when the surface is held at a constant temperature. It turns out that when the surface temperature exceeds the ambient temperature, heat flows from the surface to the fluid near the stagnation point but further away from the stagnation point, heat flows from the fluid to the stretching surface.

136 citations


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