Slow velocity fluid flow problems in small diameter channels have many important applications in science and industry. Many researchers have modeled the flow through renal tubule, hollow fiber dialyzer and flat plate dialyzer using Navier Stokes equations with suitable simplifying assumptions and boundary conditions. The aim of this article is to investigate the hydrodynamical aspects of steady, axisymmetric and slow flow of a general second-order Rivlin-Ericksen fluid in a porous-walled circular tube with constant wall permeability. The governing compatibility equation have been derived and solved analytically for the stream function by applying Langlois recursive approach for slow viscoelastic flows. Analytical expressions for velocity components, pressure, volume flow rate, fractional reabsorption, wall shear stress and stream function have been obtained correct to third order. The effects of wall Reynolds number and certain non-Newtonian parameters have been studied and presented graphically. The obtained analytical expressions are in agreement with the existing solutions in literature if non-Newtonian parameters approach to zero. The solutions obtained in this article may be considered as a generalization to the existing work. The results indicate that there is a significant dependence of the flow variables on the wall Reynolds number and non-Newtonian parameters.
This article aims to study Newtonian fluid flow modeling and simulation through a rectangular channel embedded in a semicircular cylinder with the range of Reynolds number from 100 to 1500. The fluid is considered as laminar and Newtonian, and the problem is time independent. A numerical procedure of finite element’s least Square technique is implemented through COMSOL multiphysics 5.4. The problem is validated through asymptotic solution governed through the screen boundary condition. The vortex length of the recirculating region formed at the back of the cylinder and orientation of velocity field and pressure will be discussed by three horizontal and four vertical lines along the recirculating region in terms of Reynolds number. It was found that the two vortices of unequal size have appeared and the lengths of these vortices are increased with the increase Reynolds number. Also, the empirical equations through the linear regression procedure were determined for those vortices. The orientation of the velocity magnitude as well as pressure along the lines passing through the center of upper and lower vortices are the same.
The current article is an understanding of heat transfer and non-Newtonian fluid flow with implications of the power-law fluid on a facing surface of the circular cylinder embedded at the end of the channel containing the screen. The cylinder is fixed with an aspect ratio of 4:1 from height to the radius of the cylinder. The simulation for the fluid flow and heat transfer was obtained with variation of the angle of screen 63 , Reynolds number 1000 Re 10,000 and the power-law index 0.7 1.3 n by solving the two-dimensional incompressible Navier-Stokes equations and the energy equation with screen boundary condition and slip walls. The results will be in a good match with asymptotic solution given in the literature. The results are presented through graph plots for the non-dimensional velocity, temperature, mean effective thermal conductivity, heat transfer coefficient, and the local Nusselt number on the front surface of the circular cylinder. It was found that the ratio between the input velocity to the present velocity on the surface of the circular cylinder remains consistent and reaches up to a maximum of 2.2% and the process of heat transfer does not affect by the moving of the screen and clearly with the raise of power-law indexes the distribution of the heat transfer upsurges. On validation with two experimentally derived correlations, it was also found that the results obtained for the shear-thinning fluid are more precise than the numerically calculated results for the Newtonian as well as shear-thickening cases. Finally, we suggest the necessary measures to enrich the the development of convection when observing with the strong effects influenced by screens or screen boundary conditions.
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