Non-axisymmetric Homann stagnation-point flow of Walter’s B nanofluid over a cylindrical disk

The study of non-axisymmetric Homann stagnation-point flow of Walter’s B nanofluid along with magnetohydrodynamic(MHD) and non-linear Rosseland thermal radiation over a cylindrical disk in the existence of the time-independent free stream is considered. Moreover, the notable impacts of thermophoresis and Brownian motion are analyzed by Buongiorno’s model. The momentum, energy, and concentration equations are converted into the dimensionless coupled ordinary differential equations via similarity transformations, which are later numerically solved by altering the values of the pertinent parameters. The numerical and asymptotic solutions for the large shear-to-strain rate ratio γ =a/bfor the parameters of the displacement thicknesses and the wall-shear stress are computed by perturbative expansion and analyzed. Furthermore, the technique bvp4c in MATLAB is deployed as an efficient method to analyze the calculations for the non-dimensional velocities, temperature, displacement thickness, and concentration profiles. It is observed that the two-dimensional displacement thickness parameters α andβ are reduced due to the viscoelasticity and magnetic field effects. Moreover, when the shear-to-strain rate ratio approaches infinity, α is closer to its asymptotic value, while βand the three-dimensional displacement thickness parameter δ1 show the opposite trend.The outcomes of the viscoelasticity and the magnetic field on the skin friction are also determined. It is concluded that ■ reaches its asymptotic behavior when the shearto-strain rate ratio approaches infinity. Meanwhile, ■ shows different results.

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.

Peristaltic Flow of Couple Stress Fluid in a Non-Uniform Rectangular Duct Having Compliant Walls

The present study investigates the peristaltic flow of couple stress fluid in a non-uniform rectangular duct with compliant walls.Mathematical modeling is based upon the laws of mass and linear momentum.Analytic solutions are carried out by the eigen function expansion method under long-wavelength and low-Reynolds number approximations.The features of the flow characteristics are analyzed by plotting the graphs of various values of physical parameters of interest.Trapping bolus scheme is also presented through streamlines.