In this study, the influence of temperature and wall slip conditions on the unsteady flow of a viscous, incompressible and electrically conducting nanofluid squeezed between two parallel disks in the presence of an applied magnetic field is investigated numerically. Using the similarity transformation, the governing coupled partial differential equations are transformed into similarity non-linear ordinary differential equations which are solved numerically using the Nachtsheim and Swigert shooting iteration technique together with the sixth order Runge-Kutta integration scheme. The effects of various emerging parameters on the flow characteristics are determined and discussed in detail. To check the reliability of the method, the numerical results for the skin friction coefficient and Nusselt number in the absence of slip conditions are compared with the results reported by the predecessors and an excellent agreement is observed between the two sets of results.
An analysis is presented to investigate the effects of thermal radiation on a convective slip flow of an electrically conducting slightly rarefied fluid, having temperature dependent fluid properties, over a wedge with a thermal jump at the surface of the boundary in the presence of a transverse magnetic field. The reduced equations are solved numerically using the finite difference code that implements the 3-stage Lobatto IIIa formula for the partitioned Runge-Kutta method. Numerical results for the dimensionless velocity and temperature as well as for the skin friction coefficient and the Nusselt number are presented through graphs and tables for pertinent parameters to show interesting aspects of the solution.
The present study investigates the onset of penetrative convection in- duced by selective absorption of radiation in a magnetic nanofluid saturated porous medium. The influence of Brownian motion, thermophoresis, and magnetophoresis on magnetic nanofluid treatment is taken into consideration. The Darcy’s model is selected for the porous medium. We conduct a linear stability analysis to examine the onset of instability and evaluate the results for two different configurations, namely, when the layer is heated from below and when the layer is heated from above. The numerical investigations are carried out by applying the Chebyshev pseudospectral method. The effect of the porosity parameter E, parameter Y (represents the ratio of internal heating to boundary heating), Lewis number Le, concentration Rayleigh number Rn, Langevin parameter αL, width of nanofluid layer d, diffusivity ratio η, and modified diffusivity ratio NA is examined at the onset of convection. The results indicate that the convection commences easily with an increase in the value of Y, Le, and NA but opposite in the case with a decrease in the value of E, αL, η and d for both the two configurations. The parameter Rn advances the onset of convection when the layer is heated from below, while delays the onset of convection when the layer is heated from above.
An investigation made on the effect of Hall currents on double-diffusive convection of a compressible synovial (couple-stress) fluid in the presence of a horizontal magnetic field through a porous layer is considered. The analysis is carried out within the framework of linear stability theory and normal mode technique. A dispersion relation governing the effects of viscoelasticity, compressibility, magnetic field and porous layer is derived. For the stationary convection, a synovial fluid behaves like an ordinary Newtonian fluid due to the vanishing of the viscoelastic parameter. The stable-solute gradient, compressibility, and magnetic field have postponed the onset of convection, whereas Hall currents and medium permeability have not postponed the onset of convection, moreover, a synovial fluid has a dual character in the presence of Hall currents, whereas in the absence of Hall current in synovial fluid have postponed the onset of convection, which is in contrast in case of thermal convection couple-stress fluid with same effects. These analytic results are confirmed numerically and the effects of various parameters are depicted graphically. It has been observed that oscillatory modes are introduced due to the presence of viscoelasticity, magnetic field, porous medium and Hall currents which were non- existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.