scispace - formally typeset
Search or ask a question
Topic

Similarity solution

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


Papers
More filters
Journal ArticleDOI
TL;DR: In this article, the authors considered different one-phase Stefan problems for a semi-infinite slab, involving a moving phase change material as well as temperature dependent thermal coefficients, and proved the existence of at least one similarity solution imposing a Dirichlet, Neumann, Robin or radiative-convective boundary condition at the fixed face.
Abstract: Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a Dirichlet, Neumann, Robin or radiative–convective boundary condition at the fixed face. The velocity that arises in the convective term of the diffusion–convection equation is assumed to depend on temperature and time. In each case, an equivalent ordinary differential problem is obtained giving rise to a system of an integral equation coupled with a condition for the parameter that characterizes the free boundary, which is solved through a double-fixed point analysis. Some solutions for particular thermal coefficients are provided.

9 citations

01 Jan 2014
TL;DR: In this article, the effects of thermal radiation on the behavior of nanofluid over a stretching sheet were investigated numerically by using the fourth-order Runge-Kutta method along with shooting technique.
Abstract: In this article, the unsteady stagnation point flow and heat transfer of a nanofluid over a stretching sheet with the effects of magnetic field and porous media is investigated numerically. The effects of thermal radiation are also considered. In contrast to the conventional no-slip condition at the surface, Navier’s slip condition has been applied. The behaviour of the nanofluid was investigated for three different nanoparticles in the water-base fluid, namely, copper, alumina, and titanium. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations, which are then solved numerically by using the fourthorder Runge-Kutta method along with shooting technique. The results corresponding to the dimensionless velocity and temperature profiles, also the skin friction and the reduced Nusselt number are displayed graphically for various pertinent parameters.

9 citations

Journal ArticleDOI
TL;DR: In this paper, a self-similar solution for stratified flow through a non-rectangular channel is derived, where the bottom of the channel is constrained to be flat, assuming first multi-layer stratification, and second continuous stratification.
Abstract: A self-similar solution describing stratified flow through a non-rectangular channel is derived. The solution shown here is an extension of Wood's (1968) solution for stratified withdrawal through a rectangular channel. We consider a restricted set of geometries (where the bottom of the channel is constrained to be flat) and calculate the flow, assuming first multi-layer stratification, and second continuous stratification. In the case of two-layer flow we prove that the self-similar solution is the only possible solution. The analytical solutions are corroborated by three-dimensional numerical model simulations.

9 citations

Journal ArticleDOI
TL;DR: In this paper, a theoretical and experimental study of the propagation of gravity currents in porous media with variations in the topography over which they flow is presented, motivated in part by the sequestration of carbon dioxide in saline aquifers.
Abstract: We present a theoretical and experimental study of the propagation of gravity currents in porous media with variations in the topography over which they flow, motivated in part by the sequestration of carbon dioxide in saline aquifers. We consider cases where the height of the topography slopes upwards in the direction of the flow and is proportional to the power of the horizontal distance from a line or point source of a constant volumetric flux. In two-dimensional cases with , the current evolves from a self-similar form at early times, when the effects of variations in topography are negligible, towards a late-time regime that has an approximately horizontal upper surface and whose evolution is dictated entirely by the geometry of the topography. For , the transition between these flow regimes is reversed. We compare our theoretical results in the case with data from a series of laboratory experiments in which viscous glycerine is injected into an inclined Hele-Shaw cell, obtaining good agreement between the theoretical results and the experimental data. In the case of axisymmetric topography, all topographic exponents result in a transition from an early-time similarity solution towards a topographically controlled regime that has an approximately horizontal free surface. We also analyse the evolution over topography that can vary with different curvatures and topographic exponents between the two horizontal dimensions, finding that the flow transitions towards a horizontally topped regime at a rate which depends strongly on the ratio of the curvatures along the principle axes. Finally, we apply our mathematical solutions to the geophysical setting at the Sleipner field, concluding that topographic influence is unlikely to explain the observed non-axisymmetric flow.

9 citations

Journal ArticleDOI
TL;DR: In this article, the first-, second-, and third-order statistics of the flows are calculated and discussed, and the radial profiles of such statistics, as well as that of the turbulent kinetic energy balance and other second-order transport equations are examined at two axial distances.
Abstract: In this study, direct numerical simulations of a turbulent free jet (Re = 2000), a lazy plume (), and a forced plume (Re = 1684, Ri = 0.025) are compared. The evolution of the various fluxes and the so-called source parameter, Γ, are examined as a function of distance from the source. The first-, second-, and third-order statistics of the flows are calculated and discussed. The radial profiles of such statistics, as well as that of the turbulent kinetic energy balance and other second-order transport equations are examined at two axial distances, one axial distance before the flows have adjusted to their similarity solution, and the other beyond the similarity adjustment length scale. Vortical structures are visualised and discussed along with entrainment. The source term Γ was not found to monotonically decrease with axial distance from the source as predicted by past researchers. While the mean flow and turbulent velocity statistics of the simulated lazy and forced plumes took on similar behaviour far f...

9 citations


Trending Questions (1)
Network Information
Related Topics (5)
Reynolds number
68.4K papers, 1.6M citations
89% related
Turbulence
112.1K papers, 2.7M citations
88% related
Boundary layer
64.9K papers, 1.4M citations
87% related
Partial differential equation
70.8K papers, 1.6M citations
87% related
Boundary value problem
145.3K papers, 2.7M citations
84% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202238
202141
202045
201947
201850