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1

Comparative analysis of numerical simulations of blood flow through the segment of an artery in the presence of stenosis

Shaikh Fozia, Shaikh Asif Ali, Hincal Evren, Qureshi Sania

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 2

49--61

EN

A mathematical model is developed to study the characteristics of blood flowing through an arterial segment in the presence of a single and a couple of stenoses. The governing equations accompanied by an appropriate choice of initial and boundary conditions are solved numerically by Taylor Galerkin’s time-stepping equation, and the numerical stability is checked. The pressure, velocity, and stream functions have been solved by Cholesky’s method. Furthermore, an in-depth study of the flow pattern reveals the separation of Reynolds number for the 30 and 50% blockage of single stenosis and 30% blockage of multi-stenosis. The present results predict the excess pressure drop across the stenosis site than it does for the inlet of the artery with single and multiple stenosis and the increase in the velocity is observed at the center of the artery.

2

Lubrication of asymmetric rollers considering viscosity as function of mean temperature

Lanka Swetha, Sajja Venkata Subrahmanyam, Prasad Dhaneshwar

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 2

49--63

EN

A theoretical analysis of an asymmetric roller bearing system with cavitation that is hydro-dynamically lightly loaded and lubricated by a thin, incompressible fluid is presented. The lubricant adheres to the non-Newtonian Bingham plastic fluid concept, in which the viscosity of the fluid should change depending on the mean film temperature. The continuity and momentum equations, which regulate fluid flow, are first solved analytically and then numerically using MATLAB. Through graphs and tables, some key bearing features are addressed and further explained. This leads to the conclusion that there is a discernible difference between Newtonian and non-Newtonian fluids in terms of pressure, temperature, load, and traction. The findings are good in line with the body of literature.

3

Near-resonant regimes of a moving load on a pre-stressed incompressible elastic half-space

Kudaibergenov Askar, Kudaibergenov Askat, Prikazchikov Danila

Acta Mechanica et Automatica

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2021

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Vol. 15, no. 1

30--36

EN

The article is concerned with the analysis of the problem for a concentrated line load moving at a constant speed along the surface of a pre-stressed, incompressible, isotropic elastic half-space, within the framework of the plane-strain assumption. The focus is on the near-critical regimes, when the speed of the load is close to that of the surface wave. Both steady-state and transient regimes are considered. Implementation of the hyperbolic–elliptic asymptotic formulation for the surface wave field allows explicit approximate solution for displacement components expressed in terms of the elementary functions, highlighting the resonant nature of the surface wave. Numerical illustrations of the solutions are presented for several material models.

4

Formulas for the H/V ratio of Rayleigh waves in incompressible pre-stressed half-spaces

Chi Vinh P. C., Tuan T. T., Hue L. T.

Archives of Mechanics

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2018

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Vol. 70, nr 2

131--150

EN

In this paper, the propagation of a Rayleigh wave in an incompressible pre-stressed elastic half-space is considered. The main aim is to derive exact formulas for the H/V ratio, the ratio of the amplitude of the horizontal displacement to the amplitude of the vertical displacement of the Rayleigh wave. First, the H/V ratio equations are obtained using the secular equation and the relation between the H/V ratio and the Rayleigh wave velocity. Then, the exact formulas for the H/V ratio have been derived for a general strain-energy function by analytically solving the H/V ratio equations. These formulas are then specified to several particular strain-energy functions. Since the obtained formulas are exact and totally explicit, they will be a good tool for nondestructively evaluating pre-stresses of structures before and during loading.

5

A dynamically adaptive lattice Boltzmann method for thermal convection problems

Feldhusen K., Deiterding R., Wagner C.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 4

735--747

EN

Utilizing the Boussinesq approximation, a double-population incompressible thermal lattice Boltzmann method (LBM) for forced and natural convection in two and three space dimensions is developed and validated. A block-structured dynamic adaptive mesh refinement (AMR) procedure tailored for the LBM is applied to enable computationally efficient simulations of moderate to high Rayleigh number flows which are characterized by a large scale disparity in boundary layers and free stream flow. As test cases, the analytically accessible problem of a two-dimensional (2D) forced convection flow through two porous plates and the non-Cartesian configuration of a heated rotating cylinder are considered. The objective of the latter is to advance the boundary conditions for an accurate treatment of curved boundaries and to demonstrate the effect on the solution. The effectiveness of the overall approach is demonstrated for the natural convection benchmark of a 2D cavity with differentially heated walls at Rayleigh numbers from 103 up to 108. To demonstrate the benefit of the employed AMR procedure for three-dimensional (3D) problems, results from the natural convection in a cubic cavity at Rayleigh numbers from 103 up to 105 are compared with benchmark results.

6

Thermal and mass diffusion on hydromagnetic flow from a vertical surface with induced magnetic field

Sharma B. K., Singh S., Chaudhary R. C.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 4

1135-1146

EN

The viscous incompressible electrically conducting fluid past an infinite porous vertical plate under the combined buoyancy effects of thermal and mass diffusion has been studied under the action of transverse applied magnetic field taking into account the induced magnetic field, when the plate is subjected to constant heat and mass fluxes (CHFlCMF). The analytical solutions are found for velocity field, temperature distribution, induced magnetic field, current density, concentration field and the expressions for shear stress and rate of heat transfer are obtained and discussed in detail with the help of figures.

7

A contravariant velocity based implicit multilevel method for simulating the whole process of incompressible flow transition arround Joukowsky airfoils

Liu Z., Liu C., Xiong G.

Applied Mechanics and Engineering

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1998

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Vol. 3, no 1

111-161

EN

A contravanant velocity based incompressible Navier-Stokes governing system is derived to generate an implicit multi-level method so that we can simulate the receptivity and flow transition in cases with complex geometnes. The two- and three- dimensional development of leading-edge receptivity and flow transition in a 2-D Joukowsky airfoil boundary layer are investigated by direct numencal simulation (DNS) using this system. The numencal investigation is based on the so-called spatial approach. The numencal results agree very well with linear stability theory (LST) and the experimental results for the flat plate case. They also agree well with the result obtained by other researchers for the 2-D elliptic leadingedge receptivity case. Some new phenomena for the transition around Joukowsky airfoils are abserved. The details of this approach are described.