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The extrudate swell phenomenon is analysed by solving, simultaneously, the Navier‐Stokes equations along with the continuity equation by means of a finite volume method. In this work, the planar jet flows of incompressible viscous Newtonian and power‐law fluids for Reynolds numbers as high as 75 are simulated. The method uses the velocity components and pressure as the primitive variables and employs an unstructured triangular grid and triangular or polygonal control volume for each separate variable. The numerical results show good agreement with previously reported experimental and numerical results. Shear thickening results in an increase in swelling ratio, while the introduction of surface tension results in a describes in swelling ratio.

The purpose of this paper is to present a numerical method for the simulation of steady and unsteady incompressible laminar flows, including convective heat transfer.

A node centered, finite volume discretization technique is applied on hybrid meshes. The developed solver, is based on the artificial compressibility approach.

A sufficient number of representative test cases have been examined for the validation of this numerical solver. A wide range of the various dimensionless parameters were applied for different working fluids, in order to estimate the general applicability of our solver. The obtained results agree well with those published by other researchers. The strongly coupled solution of the governing equations showed superiority compared to the loosely coupled solution as inviscid effects increase.

Convective heat transfer is dominant in a wide variety of practical engineering problems, such as cooling of electronic chips, design of heat exchangers and fire simulation and suspension in tunnels.

A comparison between the strongly coupled solution and the loosely coupled solution of the Navier-Stokes and energy equations is presented. A robust upwind scheme based on Roe’s approximate Riemann solver is proposed.

The purpose of this paper is the development of a robust numerical scheme for fluid flow simulations in complex domains with open boundaries.

A modified pressure correction algorithm is presented. The proposed modifications are derived through a step-by-step analysis of the importance of mass continuity enforcement in pressure correction methods, the boundary conditions of the pressure correction equation and the special nature of open boundaries.

The algorithm is validated by performing steady state laminar flow simulations in two backward facing step geometries with progressively truncated outlet channels. The efficiency of the methodology is demonstrated by simulating the pulsatile flow field in a patient specific iliac bifurcation reconstructed by medical imaging data.

The proposed numerical scheme provides accurate and mass conserving solutions in complex domains with open boundaries. The proposed methodology may be directly implemented in any computational domain without any prerequisites regarding the location or type of domain boundaries.

The purpose of this paper is to investigate the feasibility of solving turbulent flows based on smoothed finite element method (S-FEM). Then, the differences between S-FEM and finite element method (FEM) in dealing with turbulent flows are compared.

The stabilization scheme, the streamline-upwind/Petrov-Galerkin stabilization is coupled with stabilized pressure gradient projection in the fractional step framework. The Reynolds-averaged Navier-Stokes equations with standard k-epsilon model are selected to solve turbulent flows based on S-FEM and FEM. Standard wall functions are applied to predict boundary layer profiles.

This paper explores a completely new application of S-FEM on turbulent flows. The adopted stabilization scheme presents a good performance on stabilizing the flows, especially for very high Reynolds numbers flows. An advantage of S-FEM is found in applying wall functions comparing with FEM. The differences between S-FEM and FEM have been investigated.

The research in this work is limited to the two-dimensional incompressible turbulent flow.

The verification and validation of a new combination are conducted by several numerical examples. The new combination could be used to deal with more complicated turbulent flows.

The applications of the new combination to study basic and complex turbulent flow are also presented, which demonstrates its potential to solve more turbulent flows in nature and engineering.

This work carries out a great extension of S-FEM in simulations of fluid dynamics. The new combination is verified to be very effective in handling turbulent flows. The performances of S-FEM and FEM on turbulent flows were analyzed by several numerical examples. Superior results were found compared with existing results and experiments. Meanwhile, S-FEM has an advantage of accuracy in predicting boundary layer profile.

The effects of steady fluid flow through double bell‐shaped constrictions in tubes were investigated numerically for the Reynolds number range of 5 to 400. The double constrictions studied were for similar first and second constrictions of 1/3, 1/2 and 2/3. A dimensionless constriction spacing of 1.0 was considered. Study showed that the major part of the mean dimensionless pressure drop in the constricted tube occurs predominantly across the first constriction when flow moves towards the valley region formed by the two constrictions. Minimum pressures along the constricted tubes occurs downstream of each constrictions. When the constriction magnitudes increased, the pressure drop across the same length of the tube increases exponentially. The effect of increasing the Reynolds number for all the constriction values considered here is to increase the spreading of the recirculation region between the valley region of the constrictions. The recirculation region formed between the two constrictions has a deminishing effect on the generation of wall vorticity near the second constriction. The effects are more pronounce when the recirculatory flow from the first constriction has spread over the second constriction. In general, a peak wall vorticity is found slightly upstream of each of the constrictions. When the Reynolds number is increased, the peak wall vorticity increases and its location moved upstream. It is noted for the cases considered here that the peak wall vorticity generated by the first constriction is always greater than the peak wall vorticity generated by the second constriction.

A control‐volume based method for the numerical calculation of axisymmetric incompressible fluid flow and heat transfer is presented. The proposed method extends the staggered grid approach to unstructured triangular meshes. The velocities are stored at the vertices and the edges of a triangle, pressure and temperature are stored at the vertices. Accordingly, velocities are interpolated in a quadratic way, pressure and temperature linearly. The accuracy of the proposed method is examined for a number of different testproblems. Compared to a linear interpolation scheme implemented in the same code, more accurate solutions and smaller computation times are obtained for the proposed quadratic scheme. The method was designed for and is about to be applied to the numerical simulation of crystal growth.

The purpose of this paper is to develop and test an implicit scheme, accurate to the second order, for solving full Navier‐Stokes equations for three dimensional problems, using parallel algorithm.

Parallel solution to the 3‐D incompressible full Navier‐Stokes equations is presented, based on two fractional steps in time and finite element in space. The accuracy of the scheme is second order in both time and space domains. Large time‐step sizes, with Courant‐Friedrichs‐Lewy (CFL) numbers much larger than unity, are taken since the momentum equation is solved implicitly. A fourth order artificial viscosity term is added. In order to stabilize the numerical solution, fourth order artificial viscosity term is used for high Reynolds number flows. The domain decomposition technique is implemented for parallel solution to the problem with matching and non‐overlapping sub‐domains. It is aimed to study both a 3D free and mixed convection problems using the developed scheme. The segregate solution for temperature field is calibrated by a 3‐D free convection problem. Then the flow case where the forced convection is one order of magnitude higher than the free convection is studied.

It is observed that the long time solution to the flow field shows oscillatory behaviour as the Reynolds number of the flow doubled while keeping the ratio of the forced to free convection fixed. The solution using a parallel algorithm gives satisfactory results, in terms of computation time and accuracy, for the natural convection problem in cubic cavity, and, the forced cooling of a room with chilled ceiling having a parabolic geometry as presented at the end. It is observed that doubling the Reynolds number, while keeping all the parameters unchanged, varies the flow behaviour completely.

A code previously developed and published by the author only solved momentum equation and studied the velocity field. In this study, full Navier Stokes equation is solved and the code is calibrated with a well‐known 3D free‐convection for two different Rayleigh number cases and then 3D mixed convection problem is studied for two cases. Re=2000 case results, solved both by the scheme in this study and by commercial code, presented an interesting physics of the problem. For Re=2000 case, continuous cooling of the room is not possible. Doubling the Reynolds number, raising it from 1000 to 2000, while keeping all the parameters unchanged, varies the flow behaviour completely.

The purpose of this study is to investigate the problem of pulsatile flow in a porous annulus for small Reynolds number.

The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the homotopy analysis method (HAM). The analytic solutions of non‐linear differential equation are constructed in the series form. The convergence of the series solutions is carefully analyzed.

Graphical results are presented to investigate the influence of different parameters on the flow behavior. Comparison between the solutions obtained by the HAM and the numerical solution shows good agreement.

An analysis for study on flow of an incompressible viscous fluid in the region lying between two concentric porous cylinders, under the assumption that a periodic pressure gradient is imposed across the annulus and that there is a uniform small transfer across two walls is presented. The HAM solutions are obtained for the equations governing the fluid flow.

The purpose of this paper is to theoretically study the problem of the peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct under the effects of Hall and ion slip. An incompressible and magnetohydrodynamics fluid is also taken into account. The governing equations are modelled under the constraints of low Reynolds number and long wave length. Recent development in biomedical engineering has enabled the use of the periastic flow in modern drug delivery systems with great utility.

Numerical integration is used to analyse the novel features of volumetric flow rate, average volume flow rate, instantaneous flux and the pressure gradient. The impact of physical parameters is depicted with the help of graphs. The trapping phenomenon is presented through stream lines.

The results of Newtonian fluid model can be obtained by taking out the effects of Jeffrey parameter from this model. No-slip case is a special case of the present work. The results obtained for the flow of Jeffrey fluid reveal many interesting behaviours that warrant further study on the non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear-thinning reduces the wall shear stress.

The results of this paper are new and original.