Closed form solution to a second order boundary value problem and its application in fluid mechanics

The Adomian decomposition method is used by many researchers to investigate several scientific models. In this Letter, the modified Adomian decomposition method is applied to construct a closed form solution for a second order boundary value problem with singularity.     

Hydromagnetic stability of plane Couette flow of an upper convected Maxwell fluid

Hydrodynamic stability of plane Couette flow of an upper convectedMaxwell fluid is investigated in presence of a transverse magneticfield assuming that the magnetic Prandtl number is sufficientlysmall. The resulting equation is a modified Orr–Sommerfeldequation. The equations of stability are solved numericallyusing Chebyshev collocation method with QZ algorithm. The criticalvalues of Reynolds number, wave number and wave speed are computedand the results are shown through the neutral curves. By increasingthe amount of elasticity to a certain value, it is shown that,as the Hartmann number increases, the minimum critical Reynoldsnumber decreases and it does not increase again in contrastto the Newtonian case.     

Peristaltically induced transport of a MHD biviscosity fluid in a non-uniform tube

We have analyzed an incompressible flow of electrically conducting biviscosity fluid through an axisymmetric non-uniform tube with a sinusoidal wave under the considerations of long wavelength and low Reynolds number. In our analysis we are taking into account the induced magnetic field. The analytic solution has been obtained from which the axial velocity, the axial induced magnetic field and the axial pressure gradient have been derived. The results for the pressure rise ΔP_λ(t), frictional force per wavelength F_λ(t) and the axial induced magnetic field h_z have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the magnetic Prandtl number p_m, the magnetic field parameter M, the Reynolds number Re, the upper limit apparent viscosity coefficient β, and the time averaged mean flow rate θ.     

Effects of Chemical Reaction,Heat, and Mass Transfer on Non-Newtonian Fluid Flow Through Porous Medium in a Vertical Peristaltic Tube

The effect of mass diffusion of chemical species with first-order reaction on peristaltic motion of an incompressible Jeffrey fluid has been investigated. The fluid flows through vertical porous media in the gap between concentric tubes with heat and mass transfer. The inner tube is uniform, while the outer one is a non-uniform tube has a sinusoidal wave traveling down its wall. A perturbation solution, under long-wavelength assumption, is obtained which satisfies the momentum, energy, and concentration equations for the case of small porosity parameter. Numerical results for the behaviors of pressure rise and frictional force per wavelength as well as for the skin friction, Nusselt number, and Sherwood number with other physical parameters are obtained. Several graphs for these results of physical interest are displayed and discussed in detail.     

Numerical study of viscous dissipation effect on free convection heat and mass transfer of MHD non-Newtonian fluid flow through a porous medium

The problem of free convection heat with mass transfer for MHD non-Newtonian Eyring–Powell flow through a porous medium, over an infinite vertical plate is studied. Taking into account the effects of both viscous dissipation and heat source. The temperature and concentration are of periodic variation. The governing non-linear partial differential equations of this phenomenon are transformed into non-linear algebraic system utilizing finite difference method. Numerical results for the velocity, temperature and concentration distributions as well as the skin friction, heat and mass transfer are obtained and reported in tabular form and graphically for different values of physical parameters of the problem. Also, the stability condition is studied.     

Mixed convective heat and mass transfer in a non-Newtonian fluid at a peristaltic surface with temperature-dependent viscosity

We investigate the problem of the unsteady mixed convection peristaltic mechanism. The flow includes a temperature-dependent viscosity with thermal diffusion and diffusion-thermo effects. The peristaltic flow is between two vertical walls, one of which is deformed in the shape of traveling transversal waves exactly like peristaltic pumping and the other of which is a parallel flat plate wall. The equations of momentum, energy, and concentration are subject to a set of appropriate boundary conditions by assuming that the solution consists of two parts: a mean part and a perturbed part. The solution of the perturbed part has been obtained by using the long-wave approximation. The mean part has been solved and coincides with the approximation of Ostrach. The mean part (zeroth order), the first order, and the total solution of the problem have been evaluated numerically for several sets of values of the parameters entering the problem. The skin friction, and the rate of heat and mass transfer at the walls are obtained and illustrated graphically.