Eur. Phys. J. Plus (2020) 135: 138
https://doi.org/10.1140/epjp/s13360-020-00224-y

Regular Article

Linear and nonlinear stability of thermal convection in Newtonian dielectric liquid with field-dependent viscosity

¹ Department of Mathematics, Bangalore University, Bangalore, Karnataka, 560056, India
² Department of Computer Science and Engineering, PES University, Bangalore, Karnataka, 560085, India
³ Department of Mathematics, Atria Institute of Technology, Bangalore, Karnataka, 560024, India

^* e-mail: bhavyashivaraj@gmail.com

Received: 2 July 2019
Accepted: 13 January 2020
Published online: 28 January 2020

Abstract

The present study deals with a linear and weakly nonlinear stability analyses of thermal convection in a variable viscosity Newtonian dielectric liquid. The generalised Lorenz model is obtained by using the Galerkin method. Using this model, the Nusselt number is calculated in the regular (non-chaotic) regime and onset of chaotic motion is also studied. Temperature dominance over an electric field dominance in influencing viscosity is shown to hasten onset of convection and to thereby enhance the heat transport. Electric field dominance can be used to delay thermal convection and thereby to diminish heat transport. The effect of electric Rayleigh number is to diminish the Nusselt number and its effect on chaotic motion is to advance onset. Subcritical instability is shown to be possible in the system. The dielectric liquid plays an important role in thermal systems like transformers that require a coolant.