Magneto convection for a nanofluid layer with local thermal non-equilibrium (LTNE) model: A realistic approach

Abstract

Linear thermal instability of a horizontal nanofluid layer considering thermally non-equilibrium effect by applying magnetic field is investigated. Analysis is done with more practical boundary conditions on volume fraction of nanoparticles i.e. zero nanoparticle flux is considered across free-free boundaries. A two-temperature model has been introduced in order to consider the influence of thermally non-equilibrium phases (fluid and particle). Local thermal non-equilibrium (LTNE) means that there is a difference in temperature between the two phases that cannot be neglected. LTNE model has acquainted three parameters modified thermal diffusivity ratio, modified thermal capacity ratio and Nield number in addition to the Chandrasekhar number which was introduced due to magnetic field. Results are interpreted analytically as well as graphically. It is found that system stability enhances by enhancing the values of Chandrasekhar number, modified thermal diffusivity ratio, modified thermal capacity ratio and falls with the rise in Nield number, Lewis number, concentration Rayleigh number and modified diffusivity ratio. Critical wave number tends to its local thermal equilibrium (LTE) when there is no interaction among the particle and fluid phases and also when both the phases act as a single phase due to having identical temperatures. Further, critical values of two different nanomaterials (alumina and copper) immersed in base fluid water is compared. It is found that with in thermally non-equilibrium conditions among the phases along with revised boundary conditions copper–water nanofluid is having higher critical values (critical wave number as well as critical Rayleigh number) than alumina-water nanofluid in the presence of magnetic field. Thus, stability of copper nanomaterials is more pronounced as compared to alumina nanomaterials under the above said conditions.