Abstract: The problem of magnetohydrodynamics boundary layer flow and heat transfer on a permeable stretching surface in a second grade nanofluid under the effect of heat generation and partial slip is studied theoretically. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the PDE’s are transformed into a set of ODE’s with the help of local similarity transformations. The differential equations are solved by variational finite element method. The effects of different controlling parameters on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The comparison confirmed excellent agreement. The present study is of great interest in coating and suspensions, cooling of metallic plate, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers technology, materials processing exploiting.
Abstract: This work is focused on the steady boundary layer flow
near the forward stagnation point of plane and axisymmetric bodies
towards a stretching sheet. The no slip condition on the solid
boundary is replaced by the partial slip condition. The analytical
solutions for the velocity distributions are obtained for the various
values of the ratio of free stream velocity and stretching velocity, slip
parameter, the suction and injection velocity parameter, magnetic
parameter and dimensionality index parameter in the series forms with
the help of homotopy analysis method (HAM). Convergence of the
series is explicitly discussed. Results show that the flow and the skin
friction coefficient depend heavily on the velocity slip factor. In
addition, the effects of all the parameters mentioned above were more
pronounced for plane flows than for axisymmetric flows.
Abstract: The present contribution deals with the
thermophoretic deposition of nanoparticles over a rapidly rotating
permeable disk in the presence of partial slip, magnetic field, thermal
radiation, thermal-diffusion, and diffusion-thermo effects. The
governing nonlinear partial differential equations such as continuity,
momentum, energy and concentration are transformed into nonlinear
ordinary differential equations using similarity analysis, and the
solutions are obtained through the very efficient computer algebra
software MATLAB. Graphical results for non-dimensional
concentration and temperature profiles including thermophoretic
deposition velocity and Stanton number (thermophoretic deposition
flux) in tabular forms are presented for a range of values of the
parameters characterizing the flow field. It is observed that slip
mechanism, thermal-diffusion, diffusion-thermo, magnetic field and
radiation significantly control the thermophoretic particles deposition
rate. The obtained results may be useful to many industrial and
engineering applications.