Similarity solution

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

Structure and similarity of nitric oxide production in turbulent diffusion flames

Abstract: On the basis of Favre-averaged equations a similarity solution for the flow field and the mixture field is derived. Using the p.d.f. (probability density function) formulation and an asymptotic expansion for large activation energies of the NO reaction, an algebraic expression for the mean turbulent NO production rate is obtained. The result explains the “rich shift” of NO production by the influence of mixture fraction fluctuations. Integration over the flame yields a formula for the emission index. In the experimental part, the total NO production in vertical diffusion flames of H2, CH4, C3H8, natural gas and a CO/H2 mixture was measured. When the experimental emission index is compared with the theoretical index, a dependence on the diameter appears. This points to an influence of the turbulence length scale. Large coherent structures may be responsible for a reduction in NO production.

Scaling Transformations for Boundary Layer Flow near the Stagnation-Point on a Heated Permeable Stretching Surface in a Porous Medium Saturated with a Nanofluid and Heat Generation/Absorption Effects

Abstract: In this article, a similarity solution of the steady boundary layer flow near the stagnation-point flow on a permeable stretching sheet in a porous medium saturated with a nanofluid and in the presence of internal heat generation/absorption is theoretically studied. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions via Lie-group analysis. Copper (Cu) with water as its base fluid has been considered and representative results have been obtained for the nanoparticle volume fraction parameter \({\phi}\) in the range \({0\leq \phi \leq 0.2}\) with the Prandtl number of Pr = 6.8 for the water working fluid. Velocity and temperature profiles as well as the skin friction coefficient and the local Nusselt number are determined numerically. The influence of pertinent parameters such as nanofluid volume fraction parameter, the ratio of free stream velocity and stretching velocity parameter, the permeability parameter, suction/blowing parameter, and heat source/sink parameter on the flow and heat transfer characteristics is discussed. Comparisons with published results are also presented. It is shown that the inclusion of a nanoparticle into the base fluid of this problem is capable to change the flow pattern.

Curing simulation of thermoset composites

Abstract: This paper deals with the modelling and simulation of resin flow, heat transfer and the curing of multilayer thermoset composite laminates during processing in an autoclave. Darcy's Law and Stokes’ slow-flow equations are used for the flow model and, for approximately isothermal flows, a similarity solution is developed. This permits the decoupling of the velocity and thermal fields. A two-dimensional convection–diffusion heat equation with an internal heat generation term is then solved numerically, together with the equation for the rate of cure, using a finite difference scheme on a moving grid. The simulations are performed with varying composite thicknesses, and a comparison of numerical results with known experimental data confirms the approximate validity of the model.

Mantle plumes - A boundary layer approach for Newtonian and non-Newtonian temperature-dependent rheologies

Abstract: Stress is placed on the temperature dependence of both a linear Newtonian rheology and a nonlinear olivine rheology in accounting for narrow mantle flow structures. The boundary-layer theory developed incorporates an arbitrary temperature-dependent power-law rheology for the medium, in order to facilitate the study of mantle plume dynamics under real conditions. Thermal, kinematic, and dynamic structures of mantle plumes are modelled by a two-dimensional natural-convection boundary layer rising in a fluid with a temperature-dependent power-law relationship between shear stress and strain rate. An analytic similarity solution is arrived at for upwelling adjacent to a vertical isothermal stress-free plane. Newtonian creep as a deformation mechanism, thermal anomalies resulting from chemical heterogeneity, the behavior of plumes in non-Newtonian (olivine) mantles, and differences in the dynamics of wet and dry olivine are discussed.