Navier’s slip condition on time dependent Darcy-Forchheimer nanofluid using spectral relaxation method

In industrial applications involving metal and polymer sheets, the flow situation is strongly unsteady and the sheet temperature is a mixture of prescribed surface temperature and heat flux. Further, a proper choice of cooling liquid is also an important component of the analysis to achieve better outputs. In this paper, we numerically investigate Darcy-Forchheimer nanoliquid flows past an unsteady stretching surface by incorporating various effects, such as the Brownian and thermophoresis effects, Navier’s slip condition and convective thermal boundary conditions. To solve the governing equations, using suitable similarity transformations, the nonlinear ordinary differential equations are derived and the resulting coupled momentum and energy equations are numerically solved using the spectral relaxation method. Through the systematically numerical investigation, the important physical parameters of the present model are analyzed. We find that the presence of unsteadiness parameter has significant effects on velocity, temperature, concentration fields, the associated heat and mass transport rates. Also, an increase in inertia coefficient and porosity parameter causes an increase in the velocity at the boundary.

Navier Slip and Heat Transfer in a Nanofluid Due to a Stretching/Shrinking Sheet:An Analytical Study

This paper is devoted to the analysis of the heat transfer and Navier’s slip effects in a non-Newtonian Jeffrey fluid flowing past a stretching/shrinking sheet.The nanoparticles,namely,Cu and Al_(2)O_(3)are used with a water-based fluid with Prandtl number 6.272.Velocity slip flow is assumed to occur when the characteristic size of the flow system is small or the flow pressure is very small.By using the similarity transformations,the governing nonlinear PDEs are turned into ordinary differential equations(ODE’s).Analytical results are presented and analyzed for various values of physical parameters:Prandtl number,Radiation parameter,stretching/shrinking parameter and mass transpiration for the flow and heat transfer.The considered problem is relevant to various physical applications in the field of engineering,e.g.,the production of certain materials,the preparation of plastic and rubber sheets and glass blowing.It is shown that the considered nanofluid increases the thermal efficiency.The nanoparticles act as a heater by increasing the solid volume fraction and thermal radiation.Vice versa,they can act as a cooler if the strength of magnetic field is increased.The flow strength decreases by increasing the values of Deborah number.

Axisymmetric Slow Motion of a Prolate Particle in a Circular Capillary with Slip Surfaces

The problem of the steady migration of an axially symmetric prolate particle along its axis of revolution coinciding with the centerline of a circular capillary is investigated semi-analytically in the limit of low Reynolds number,where the viscous fluid may slip at the solid surfaces.A method of distribution of spherical singularities along the axis inside the particle is employed to establish the general solution of the fluid velocity satisfying the boundary conditions at the capillary wall and infinity.The slip condition at the particle surface is then satisfied by using a boundary collocation method to determine the unknown constants in this solution.The hydrodynamic drag force acting on the particle is obtained with good convergence for the cases of a prolate spheroid and a prolate Cassini oval with various values of the slip parameter of the particle,slip parameter of the capillary wall,aspect ratio or shape parameter of the particle,and spacing parameter between the particle and the wall.For the axially symmetric migrations of a spheroid and a Cassini oval in a capillary with no-slip surfaces and of a sphere in a capillary with slip surfaces,our results agree excellently with the numerical solutions obtained earlier.The capillary wall affects the particle migration significantly when the solid surfaces get close to each other.For a specified particle-in-capillary configuration,the normalized drag force exerted on the particle in general decreases with increasing slippage at the solid surfaces,except when the fluid slips little at the capillary wall and the particle-wall spacing parameter is relatively large.For fixed spacing parameter and slip parameters,the drag force increases with an increase in the axial-to-radial aspect ratio(or surface area effective for viscous interaction with the capillary wall)of the particle,but this tendency can be reversed when the particle is highly slippery.