Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis

Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis

The migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. The partial differential equation depends on the permeability of the medium which is assumed to be a function of the voidage. It is shown that the partial differential equation admits, as well as translations in time and space, ot...

Dual Solutions for Nonlinear Flow Using Lie Group Analysis

`The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method h...

Lie Group Analysis of a Flow with Contaminant-Modified Viscosity

Analysis of Block Preconditioners for Models of Coupled Magma/Mantle Dynamics

This article considers the iterative solution of a finite element discretisation of the magma dynamics equations. In simplified form, the magma dynamics equations share some features of the Stokes equations. We therefore formulate, analyse and numerically test a Elman, Silvester and Wathen-type block preconditioner for magma dynamics. We prove analytically and demonstrate numerically the optima...

Inclined Lorentzian force effect on tangent hyperbolic radiative slip flow imbedded carbon nanotubes: lie group analysis

The present paper focuses on numerical study for an inclined magneto-hydrodynamic effect on free convection flow of a tangent hyperbolic nanofluid embedded with Carbon nanotubes (CNTs) over a stretching surface taking velocity and thermal slip into account. Two types of nanoparticles are considered for the study; they are single and multi-walled nanotubes. The presentation of single-parameter g...