Similarity solution

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

Nonlinear Stefan problem with convective boundary condition in Storm’s materials

Abstract: We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with phase change temperature T f . We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition, and we assume a convective boundary condition at the fixed face x = 0. A unique explicit solution of similarity type is obtained. Moreover, asymptotic behavior of the solution when $${h\rightarrow + \infty}$$ is studied.

Analytical Study of Creeping Flow Past a Composite Sphere: Solid Core With Porous Shell in Presence of Magnetic Field

Abstract: The two-dimensional creeping flow of an electrically conducting fluid past a multiple composite sphere consists of solid sphere with permeable porous shell in presence of applied transverse magnetic field is studied analytically using Stokes and Brinkman equations. The basic governing equations are solved using similarity solution method and closed forms of exact solutions are obtained. Stream lines are discussed for various Hartmann number ( ) and porous parameter ( ). It is observed that the fluid flow is suppressed in presence of magnetic field both in non-porous and porous regions and also the results obtained are in excellent agreement in the absence of the magnetic field

Interaction of a laminar hypersonic boundary layer and a corner expansion wave

Abstract: There are three distinct effects involved in the interaction of a laminar boundary layer and a supersonic corner expansion wave. These are: the upstream influence effect causing some pressure decay ahead of the corner, transverse pressure gradients in the immediate neighborhood of the corner, and the interaction of the boundary layer downstream with the external flow. Arguments are presented to suggest that, when the flow is locally hypersonic and the wall is highly cooled, the dominant effect is the downstream interaction process. Hence the major features can be calculated by using a simple interaction analysis down stream of the corner based on the Prandtl boundary-layer equations and the equations of an inviscid noncentered simple wave. Numerical results are obtained by using the "cold wall" similarity solution to the boundary-layer equations. These show that pressure decay extends over a region which can be many times larger than the original plate length used to generate the boundary layer.

Linear perturbation response of self-similar ablative flows relevant to inertial confinement fusion

Abstract: A family of exact similarity solutions for inviscid compressible ablative flows in slab symmetry with nonlinear heat conduction is proposed for studying unsteadiness and compressibility effects on the hydrodynamic stability of ablation fronts relevant to inertial confinement fusion. Dynamical multi-domain Chebyshev spectral methods are employed for computing both the similarity solution and its time-dependent linear perturbations. This approach has been exploited to analyse the linear stability properties of two self-similar ablative configurations subjected to direct laser illumination asymmetries. Linear perturbation temporal and reduced responses are analysed, evidencing a maximum instability for illumination asymmetries of zero transverse wavenumber as well as three distinct regimes of ablation-front distortion evolution, and emphasizing the importance of the mean flow unsteadiness, compressibility and stratification.

The self-similar rise of a buoyant thermal in very viscous flow

Abstract: An exact similarity solution is obtained for the rise of a buoyant thermal in Stokes flow, in which both the rise height and the diffusive growth scale like t1/2 as time t increases. The dimensionless problem depends on a single parameter Ra = B/(??) – a Rayleigh number – based on the (conserved) total buoyancy B of the thermal, and the kinematic viscosity ? and thermal diffusivity ? of the fluid. Numerical solutions are found for a range of Ra. For small Ra there are only slight deformations to a spherically symmetric Gaussian temperature distribution. For large Ra, the temperature distribution becomes elongated vertically, with a long wake containing most of the buoyancy left behind the head. Passive tracers, however, are advected into a toroidal structure in the head. A simple asymptotic model for the large-Ra behaviour is obtained using slender-body theory. The width of the thermal is found to increase like (?t)1/2, while the wake length and rise height both increase like (RalnRa)1/2(?t)1/2, consistent with the numerical results. Previous experiments suggest that there is a significant transient regime.