Convectional Onset in Ferrofluid Layer Through a Darcy-brinkman Porous Medium
Rajan Singh *
Department of Mathematics, School of Sciences, IFTM University, Moradabad-244102, India.
Nidhi Tiwari
Department of Mathematics, School of Sciences, IFTM University, Moradabad-244102, India.
B.K. Singh
Department of Mathematics, School of Sciences, IFTM University, Moradabad-244102, India.
Atanu Nag
Department of Physics, School of Sciences, IFTM University, Moradabad-244102, India.
Anshul Dubey
Department of Mathematics, School of Sciences, IFTM University, Moradabad-244102, India.
*Author to whom correspondence should be addressed.
Abstract
This chapter considers the analysis of the instabilities of convection through a porous medium in a layer of incompressible ferrofluid when the layer is subjected to a uniform magnetic field along with an external heat source. The Darcy-Brinkman model is used to study porous media. The perturbation method is used in combination with the normal mode method to analyse the influence of various integrated factors involved in the stability/instability of the considered system. The case of exponential variation in stratification is considered, and the dependence of the growth rate on the kinematic viscosity, medium porosity, medium permeability, heat source, Darcy-Brinkman number, and Alfvén squared velocity is also analytically demonstrated. The cases of stable stratification and unstable stratification are also analysed to determine the stabilisation as well as destabilisation effects of the system under certain constraints.
Keywords: Ferrofluids, magnetic field, Darcy-Brinkman porous medium, heat source