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Thermoconvective instability in a vertically oscillating horizontal ferrofluid layer with variable viscosity
Author(s) -
Aanam A Neha,
Siddheshwar P. G.,
Nagouda Smita S.,
Pranesh S.
Publication year - 2020
Publication title -
heat transfer
Language(s) - English
Resource type - Journals
eISSN - 2688-4542
pISSN - 2688-4534
DOI - 10.1002/htj.21840
Subject(s) - ferrofluid , mechanics , nonlinear system , rayleigh number , nusselt number , instability , amplitude , physics , viscosity , magnetic field , work (physics) , rayleigh scattering , classical mechanics , heat transfer , mathematics , thermodynamics , optics , natural convection , reynolds number , quantum mechanics , turbulence
The paper sheds light on the linear and nonlinear stability of a ferrofluid with the temperature and magnetic‐field‐dependent viscosity subjected to an imposed time‐periodic gravity modulation. The perturbations in the system due to external reasons are expanded in terms of the amplitude of modulation in the case of linear stability and a truncated representation of the Fourier series in the case of nonlinear stability. A nonautonomous Lorenz model for the problem is first obtained, and both linear and nonlinear analyses of the system are performed using this. The expression for the critical Rayleigh number, R 0 , and the correction Rayleigh number, R 2 c , is found from the linearized Lorenz model. The Lorenz system of equations is solved for the amplitude to arrive at the Nusselt number ( Nu ), which quantifies the heat transport. In the study we find that the thermorheological effect and the magnetization effect work in unison to destabilize the system, while the magnetorheological effect and the effect of vertical oscillations stabilize the system. The influence of the parameters on the heat transport is the opposite to their effect on the critical Rayleigh number. The results of the paper agree quite well with those of limiting cases.