Magnetoconvection with Walls of Finite Electrical Conductivity

Abstract

A flow with combined effects of magnetohydrodynamics (MHD) and thermal convection is called magnetoconvection. Its presence drastically affects the nature of flows of electrically conducting fluids such as liquid metals and plasmas. This dissertation investigates magnetoconvection in systems with walls of finite electrical conductivity, a critical aspect in various advanced technologies. The study focuses on understanding the interaction between thermal convection and magnetic fields in electrically conducting fluids, such as liquid metals, within confined spaces. The research aims to provide insights into the flow dynamics and heat transfer characteristics, with particular attention to the effects of wall electrical conductivity.Performing such numerical investigation required a robust and accurate numerical scheme and solver. Thus, using a well tested second order finite difference scheme, a new solver was developed. It is based on the Tensor-product-Thomas (TPT) method. This solver is able to approach and efficiently handle the boundary conditions associated with walls of finite electrical conductivity without iterative processes. The accuracy of the method is verified through comparisons with established results for both electrically conducting and insulating walls. This validation ensures the reliability of the numerical simulations conducted in subsequent chapters.Having a verified and robust numerical solver, a parametric study of the effects of wall electrical conductivity on magnetoconvection is conducted. Different configurations are explored, including cases, where all walls have the same electrical conductivity, and the cases with only specific walls being electrically conductive. The results reveal significant changes in the flow field and heat transfer patterns, underscoring the necessity of considering wall conductivity in magnetoconvection studies.Additionally, the dynamics of an isolated thermal plume affected by strong magnetic fields is studied. This study is conducted for two different plume generation configurations. One configuration results from a point heat source and the other from a line heat source (e.g. thin wire). In the first configuration, the effect of the magnetic field direction is also studied. The results showed that the direction of the magnetic field has a strong effect on the development of the flow. A transverse magnetic field results in a transient, oscillating plume, in which the transient behaviors will decrease by increasing magnetic field intensity. However, a vertical magnetic field results in a completely different behavior.The plume generated by the hot wire also shows the transient, oscillating behavior when a transverse magnetic field is applied to the domain. Velocity and temperature time signals at a series of points were recorded. This data is intended to be used for future experiments, as preliminary experimental results showed a significant difference in the damping caused by the magnetic field.This research contributes to the understanding of magnetoconvection in systems with finite wall conductivity, offering valuable insights into the effect of wall conductivity on the evolution of the internal magnetoconvection flows.