Similarity solution

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

Mixed Convection Stagnation-Point Flow Past a Vertical Flat Plate With a Second Order Slip

Abstract: An exact similarity solution of the steady mixed convection flow of a viscous and incompressible fluid in the vicinity of two-dimensional stagnation-point with a second-order slip condition has been investigated. Using appropriate similarity variable, the Navier–Stokes equations coupled with the energy equation governing the flow and heat transfer are reduced to a system of nonlinear ordinary (similarity) equations, which are well-posed. These equations are solved numerically in the buoyancy assisting and opposing flow regions. It is found that a reverse flow region develops in the buoyancy opposing flow case, and dual (upper and lower branch) solutions are found to exist in the case of opposing flow region for a certain range of the negative values of the mixed convection parameter. A stability analysis has been performed, which shows that the upper branch solutions are stable and physically realizable in practice, while the lower branch solutions are not stable and, therefore, not physically realizable in practice. The numerical results have been compared with those reported in the literature, the agreement being excellent.

Similarity Solution for Combined Free-Forced Convection Past a Vertical Porous Plate in a Porous Medium with a Convective Surface Boundary Condition

Abstract: Abstract This paper studies the mathematical implications of the two dimensional viscous steady laminar combined free-forced convective flow of an incompressible fluid over a semi infinite fixed vertical porous plate embedded in a porous medium. It is assumed that the left surface of the plate is heated by convection from a hot fluid which is at a temperature higher than the temperature of the fluid on the right surface of the vertical plate. To achieve numerical consistency for the problem under consideration, the governing non linear partial differential equations are first transformed into a system of ordinary differential equations using a similarity variable and then solved numerically under conditions admitting similarity solutions. The effects of the physical parameters of both the incompressible fluid and the vertical plate on the dimensionless velocity and temperature profiles are studied and analysed and the results are depicted both graphically and in a tabular form. Finally, algebraic expressions and the numerical values are obtained for the local skin-friction coefficient and the local Nusselt number.

Buoyant Plume through a Permeable Porous Layer Located above a Line Heat Source in an Infinite Fluid Space

Abstract: An experimental and analytical study is conducted on the effects of a horizontal porous layer on the development of the buoyant plume arising from a line heat source in an infinite fluid space. Visual observations and the experimental temperature distributions show the expansion and contraction of the plume at the lower and upper interfaces of the permeable layer. Similarity solutions assuming their proper virtual origins can approximately predict the changes of the plume width. Detailed numerical examination indicates that the lateral flow induced near the interfaces causes deviation from the similarity solutions. The vicinity of the interface is understood to be a transition region between the similarity solutions. The numerical analysis adopts the Beavers-Joseph slip boundary condition with the slip coefficient α estimated by α=1/√(e), where e is the porosity of the porous layer. The fairly good agreement between the experimental and numerical results confirms the validity of the slip coefficient.

Asymptotic analysis of drug dissolution in two layers having widely differing diffusivities

Abstract: This paper is concerned with a diffusion-controlled moving-boundary problem in drug dissolution, in which the moving front passes from one medium to another for which the diffusivity is many orders of magnitude smaller. The classical Neumann similarity solution holds while the front is passing through the first layer, but this breaks down in the second layer. Asymptotic methods are used to understand what is happening in the second layer. Although this necessitates numerical computation, one interesting outcome is that only one calculation is required, no matter what the diffusivity is for the second layer.