Open AccessConvection instability of non-Newtonian Walter's nanofluid along a vertical layer
Author(s) -
Galal M. Moatimid,
Mohamed A. Hassan
Publication year - 2017
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2016.09.001
Subject(s) - viscoelasticity , newtonian fluid , mathematics , dispersion relation , instability , nanofluid , mechanics , non newtonian fluid , stability (learning theory) , convection , elasticity (physics) , nonlinear system , classical mechanics , mathematical analysis , physics , thermodynamics , heat transfer , optics , quantum mechanics , machine learning , computer science
The linear stability of viscoelastic nanofluid layer is investigated. The rheological behavior of the viscoelastic fluid is described through the Walter's model. The normal modes analysis is utilized to treat the equations of motion for stationary and oscillatory convection. The stability analysis resulted in a third-degree dispersion equation with complex coefficients. The Routh–Hurwitz theory is employed to investigate the dispersion relation. The stability criteria divide the plane into several parts of stable/unstable regions. This shows some analogy with the nonlinear stability theory. The relation between the elasticity and the longitudinal wave number is graphically analyzed. The numerical calculations show that viscoelastic flows are more stable than those of the Newtonian ones