Three-dimensional numerical simulation of ferrofluid magnetoconvection in cubical enclosure heated with an inner spherical hot block

Abstract

In this study, three-dimensional computational analysis is performed to investigate the magnetoconvection of ferrofluid ([Formula: see text]-water) within a cubical enclosure heated by an inner spherical hot block. The ferrofluid, considered as a working fluid, is modeled as a single-phase fluid. The inner spherical block is put at high temperature while all the remaining walls of the enclosure are exposed to low temperature. Two radii values ([Formula: see text] and [Formula: see text]) of the inner hot sphere are examined. Governing equations with corresponding boundary conditions are solved numerically applying a second-order accurate finite volume method on a staggered grid system, using an accelerated multigrid model. Simulations are carried out based on various flow-governing parameters such as Rayleigh number [Formula: see text], Hartmann number [Formula: see text] and ferrofluid nanoparticle volume fraction [Formula: see text]. The effects of the pertinent parameters in the performance of the system are also studied. The flow and thermal fields, the local and surface-averaged Nusselt numbers on the sphere and the enclosure for both configurations are detailed. The flow remains steady and laminar for all Rayleigh numbers regardless of the sphere radius. Obviously, heat transfer rate improves with [Formula: see text] augmentation and minimizes with Ha decrease. At the highest Ra and lowest Ha, higher inner sphere radius shows significantly better heat transfer rate (more than [Formula: see text]). Useful correlations are presented to quantify the surface-averaged heat transfer rate through the cubical enclosure.