The Onset of Buoyancy and Surface Tension Driven Convection in a Ferrofluid Layer by Influence of General Boundary Conditions

Mahesh Kumar Ramachandraiah,Savitha Basavaraju

doi:10.4236/ojfd.2022.121003

Abstract

This paper investigated the buoyancy and surface tension-driven ferro-thermal-convection (FTC) in a ferrofluid (FF) layer due to influence of general boundary conditions. The lower surface is rigid with insulating to temperature perturbations, while the upper surface is stress-free and subjected to general thermal boundary condition. The numerically Galerkin technique (GT) and analytically regular perturbation technique (RPT) are applied for solving the problem of eigenvalue. It is analyzed that increasing Biot number, decreases the magnetic and Marangoni number is to postponement the onset. Additionally, magnetization nonlinearity parameter has no effect on FTC in the non-existence of Biot number. The results under the limiting cases are found to be in good agreement with those available in the literature.

Highlights

Until recently, there were liquids which could be magnetized to be comparable with the magnetization of magnetic nanoparticles
This paper investigated the buoyancy and surface tension-driven ferro-thermal-convection (FTC) in a ferrofluid (FF) layer due to influence of general boundary conditions
The numerically Galerkin technique (GT) and analytically regular perturbation technique (RPT) are applied for solving the problem of eigenvalue when both the surfaces insulated to temperature perturbations

Summary

Introduction

There were liquids which could be magnetized to be comparable with the magnetization of magnetic nanoparticles. A very less number of researches address the effects of Bouyancy and surface tension forces on FTC (see [10] [11]) with viscosity variations ([12] [13] [14] [15]), heat source strength ([16] [17]) and Coriolis force Shivakumara et al [20] studied the onset of FTC in a horizontal FF layer with temperature dependent viscosity in exponentially. The study of penetrative FTC in a saturated porous layer is studied by Nanjundappa et al [21] with the internal heating source and applied Brinkman extended Darcy model in the momentum equation. Nanjundappa and co-workers ([22] [23] [24]) analyzed the internal heat generation effect on the onset of FTC in a FF saturated porous layer. Savitha et al [25] investigated the penetrative FTC in a FF-saturated high porosity anisotropic porous layer via uniform internal heating. The numerically Galerkin technique (GT) and analytically regular perturbation technique (RPT) are applied for solving the problem of eigenvalue when both the surfaces insulated to temperature perturbations

Formulation of the Problem

Numerical Solution

Numerical Results and Discussion

Conclusions