Computational analysis of multiphase flow of non-Newtonian fluid through inclined channel: heat transfer analysis with perturbation method

Nazeer, Mubbashar; Alqarni, Mohammed Z.; Hussain, Farooq; Saleem, S.

doi:10.1007/s40571-023-00569-y

Cited by 13 publications

(1 citation statement)

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“…In order to achieve this objective, we employ a perturbative approach to solve the Navier-Stokes equations for the surface-wave problem up to the second order, where the wave amplitude is considered to be a small parameter. This method allows for the systematic study of nonlinearity in various fluid phenomena [36][37][38][39][40][41][42][43]. At this stage, the calculation is still completely general; in particular, all the modes are included.…”

Section: Introductionmentioning

confidence: 99%

Comprehensive Perturbation Approach to Nonlinear Viscous Gravity–Capillary Surface Waves at Arbitrary Wavelengths in Finite Depth

Ghahraman

Bene

2023

Fluids

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This study presents a comprehensive analysis of the second-order perturbation theory applied to the Navier–Stokes equations governing free surface flows. We focus on gravity–capillary surface waves in incompressible viscous fluids of finite depth over a flat bottom. The amplitude of these waves is regarded as the perturbation parameter. A systematic derivation of a nonlinear-surface-wave equation is presented that fully takes into account dispersion, while nonlinearity is included in the leading order. However, the presence of infinitely many over-damped modes has been neglected and only the two least-damped modes are considered. The new surface-wave equation is formulated in wave-number space rather than real space and nonlinear terms contain convolutions making the equation an integro-differential equation. Some preliminary numerical results are compared with computational-modelling data obtained via open source CFD software OpenFOAM.

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