Effect of Magnetically Controlled Viscosity on Double-Diffusive Convection in Magnetic Nanofluids
摘要
This chapter investigates double-diffusive convection ( \(\mathcal {D}_{convec}\) ) in magnetically responsive nanofluids ( \({M}_{g}\mathcal {N}_{f}\) ) composed of stratified horizontal layers, particularly using water based \({M}_{g}\mathcal {N}_{f}\) ( \(\mathcal {W}_{b}-{M}_{g}\mathcal {N}_{f}\) ) and ester based \({M}_{g}\mathcal {N}_{f}\) ( \(\mathcal {E}_{b}-{M}_{g}\mathcal {N}_{f}\) ) where viscosity is modified under external magnetic fields. The research framework emphasizes how combined thermal and solutal gradients initiate convection, with special attention to magnetic control over viscosity. A rigorous mathematical formulation has been developed to examine the onset and progression of convective disturbances. Three dominant microlevel transport mechanisms—Brownian motion, thermophoresis (following Buongiorno’s 2006 model), and magnetophoresis—are integrated into the modeling of heat and mass transfer in \({M}_{g}\mathcal {N}_{f}\) . A linear stability analysis results in an eigenvalue problem, resolved numerically using the Chebyshev pseudospectral QZ method. Simulations are conducted for both \(\mathcal {W}_{b}-{M}_{g}\mathcal {N}_{f}\) and \(\mathcal {E}_{b}-{M}_{g}\mathcal {N}_{f}\) under gravity-influenced domains with mixed boundary conditions. Parametric investigations consider the effects of the Lewis number, Langevin parameter, solutal Rayleigh number, and concentration Rayleigh number. Neutral and critical stability boundaries ( \(\mathcal {N}_{s}\mathcal {C}_{urves}\) and \(\mathcal {C}_{s}\mathcal {C}_{urves}\) ) are derived to illustrate how magnetic modulation of viscosity affects both thermal and solutal convective mechanisms within the nanofluid system.