Abstract
Marangoni bio-thermal convection in a layer of nanofluid with gyrotactic microorganisms is investigated. The motion of the nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. The lower boundary of the nanofluid layer is assumed to be a rigid surface at constant temperature and the upper boundary is assumed to be a non-deformable free surface. The stability of the layer is analysed numerically using a Chebyshev spectral method. Two types of nanofluids are studied, namely distilled water/alumina and distilled water/cupric oxide. The physical properties of these nanofluids are modelled by constitutive expressions developed by Hamilton and Crosser, Brinkman and Khanafer and Vafai. Stability boundaries are obtained for appropriate values of the parameters of the problem. The critical eigenvalues are complex-valued, which indicates that the onset of instability is via an oscillatory mode.