The predictability, or lack thereof, of the solar cycle is governed by numerous separate physical processes that act in unison in the interior of the Sun. Magnetic flux transport and the finite time delay it introduces, specifically in the so-called Babcock-Leighton models of the solar cycle with spatially segregated source regions for the α and Ω-effects, play a crucial rule in this predictabi...

We formulate and study numerically a new, parameter-free stabilized finite element method for advectiondiffusion problems. Using properties of compatible finite element spaces we establish connection between nodal diffusive fluxes and one-dimensional diffusion equations on the edges of the mesh. To define the stabilized method we extend this relationship to the advection-diffusion case by solvi...

Abstract: In this paper we study the effects of dissipation in the Couette flow and heat transfer in a drilling fluid, and explore the effects of concentration and the shear-rate and temperature-dependent viscosity, along with a variable thermal conductivity. A brief discussion on the constitutive relations for the stress tensor, the diffusive particle flux vector, and the heat flux vector is p...

To gain control over the diffusive heat flux in a given domain, one needs to engineer a thermal metamaterial with a specific distribution of the generally anisotropic thermal conductivity throughout the domain. Until now, the appropriate conductivity distribution was usually determined using transformation thermodynamics. By this way, only a few particular cases of heat flux control in simple d...

A variational solution to the transient heat flow measure above a closed conductive region of arbitrary perimeter aspect, held at constant temperature, and which is embedded in an otherwise insulating boundary plane, presented. Upon developing general formulation, full range for circular disk conductor considered as example when implementing two term trial function that comprises form based on ...

A new antidynamo theorem for non-stretched twisted magnetic flux tube dynamo is obtained. Though Riemannian curvature cannot be neglected since one considers curved magnetic flux tube axis, the stretch can be neglect since one only considers the limit of thin magnetic flux tubes. The theorem states that marginal or slow dynamos along curved (folded), torsioned (twisted) and non-stretched flux t...

on the onset of triple-diffusive convection in a horizontal layer of nanofluid heated from below and salted from above and below is studied both analytically and numerically. the effects of thermophoresis and brownian diffusion parameters are also introduced through buongiorno model in the governing equations. by using linear stability analysis based on perturbation theory and applying normal m...