Mixed Magneto-Convection in the Generalized Poiseuille-Couette Flows of Nanofluids in a Vertical Channel

This paper investigates axial unsteady flows of nanofluid filling a vertical rectangular channel with a mobile wall with time-dependent velocity. The nanofluid is Boussinesquian and the flow is induced by time-dependent pressure gradient, the buoyancy and Lorentz forces. The magnetic field is applied uniformly and oriented normal to the fluid velocity. The channel walls are maintained at different, constant temperatures. The induced magnetic field included in the analysis as well. For the nanofluid, Buongiorno’s model is employed. The differential equations with partial derivatives that determine the fields of velocity, temperature, volume fraction of nanoparticles and the induced magnetic field are transformed into dimensionless form together with the initial and boundary conditions. A numerical scheme based on the Crank-Nicolson approximation formulas is formulated; the proposed scheme determines the values of the unknown functions at the discretization points by solving some three-diagonal systems of linear algebraic equations. The associate electric field is also determined. The solutions of concrete problems characterized by particular forms of the functions that give the velocity of the wall movement and the pressure gradient are studied and interpreted with the help of numerical values and graphic illustrations.