On Global Instability of Variable Aspect Ratio Channel Flows

Abstract

The linear global stability of a flow of an incompressible fluid through a diverging channel is studied. Stability of such flows in a local context has been studied a long time ago, using the Jeffery-Hamel (JH) similarity profiles and a locally parallel flow approximation. The velocity profiles thus obtained include a parabolic profile of plane Poisuelle flow (PPF), when the divergence angle α = 0. At high α these profiles present a single region of flow reversal at each of the walls. The JH profiles are solutions to steady, laminar, two-dimensional flow of incompressible fluid within an infinite wedge driven by a line source/sink situated at the intersection of the rigid planes that form the wedge. However, these similarity solutions are not valid in finite channels. In this paper the base flow is obtained by solving for the two-dimenisonal Navier-Stokes equation (NSE) using a multi-grid Poisson equation solver (MPES) which employs the vorticity stream-function formulation. Here the stability is carried out using a global approach. The two-dimensional linearized Navier-Stokes equations (LNSE) are solved as a generalized eigenvalue problem using Arnoldi iteration and validated against previously obtained solutions employing the QZ algorithm. The Arnoldi iteration allows for faster computing of the eigenspectrum. This permits complementing our earlier global instability analyses in the small angle-of-divergence limit and extending the work to finite values of this parameter.

Revised and Extended Social Commerce Technology Adoption in e-business of Pakistan

“…According to reports published in January 2018 [13], social media has gained more popularity in Pakistan and it has key social media marketing information for anyone doing business in Pakistan. Social media has produced social marketplace by integrating social networks into online local business firms, letting the customers look for purchases from their social media friends or friends of friends online [14]. Due to growing use of social marketplace by the private and public sector business in Pakistan, this paper intends to investigate opportunities, challenges, and solutions for promising s-commerce.…”

Adoption of social commerce: An empirical analysis in the context of Pakistan

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