Effects of magnetic-field-dependent viscosity at onset of convection in magnetic nanofluids

Convective instability in a thin layer of a magnetic nanofluid heated from below is examined within the framework of linear stability theory. Recent results, in particular those of Blums et al. (J Phys 20:1–5, 2008), have shown the importance of the dependence of the thermophysical properties of magnetic nanofluids on an externally applied magnetic field while studying thermomagnetic convection in a magnetic nanofluid. The model used incorporates the effect of Brownian diffusion, thermophoresis, and magnetophoresis. In addition, we assume that the viscosity of the magnetic nanofluid is a function of the externally applied magnetic field. The resulting eigenvalue problem from the linear stability analysis is solved by employing the Chebyshev pseudospectral method, and the results are discussed for water- and ester-based magnetic nanofluids. A “tight coupling” between buoyancy and magnetic forces has been observed in magnetic nanofluids. The effects of the important parameters of the problem are examined at the onset of convection.