Search results for "Similarity solution"
showing 3 items of 3 documents
Group analysis and similarity solutions of the compressible boundary layer equations
1989
In this paper the application of Lie's methods to the equations of the laminar boundary layer is discussed. The momentum and energy equations in Prandtl's form are considered for a steady, viscous, compressible laminar flow with non zero pressure gradient, variable viscosity and thermal conductivity. Group analysis yields similarity solutions for given pressure distributions and particular values of the invariance group parameters (group classification). Crocco's transformation is obtained for the infinite-dimensional group of the Lie's algebra admitted by the equations.
A link between the residual-based gradient plasticity theory and the analogous theories based on the virtual work principle
2009
A link is shown to exist between the so-called residual-based strain gradient plasticity theory and the analogous theories based on the (extended) virtual work principle (VWP). To this aim, the former theory is reformulated and cast in a residual-free form, whereby the insulation condition and the (nonlocal) Clausius–Duhem inequality, on which the theory is grounded, are substituted with equivalent residual-free ingredients, namely the energy balance condition and the residual-free form of the Clausius–Duhem inequality. The equivalence of the residual-free formulation to the original one is shown, also in their ability to cope with energetic size effects and interfacial energy ones. It emer…
Matched asymptotic solution for the solute boundary layer in a converging axisymmetric stagnation point flow
2007
Abstract A novel boundary-layer solution is obtained by the method of matched asymptotic expansions for the solute distribution at a solidification front represented by a disk of finite radius R 0 immersed in an axisymmetric converging stagnation point flow. The detailed analysis reveals a complex internal structure of the boundary layer consisting of eight subregions. The development of the boundary layer starts from the rim region where the concentration, according to the obtained similarity solution, varies with the radius r along the solidification front as ∼ln 1/3 ( R 0 / r ). At intermediate radii, where the corresponding concentration is found to vary as ∼ln( R 0 / r ), the boundary …