A finite volume, time-marching for solving time-dependent viscoelastic flow in two space dimensions for Oldroyd-B and Phan Thien-Tanner fluids, is presented. A non-uniform staggered grid system is used. The conservati...
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A finite volume, time-marching for solving time-dependent viscoelastic flow in two space dimensions for Oldroyd-B and Phan Thien-Tanner fluids, is presented. A non-uniform staggered grid system is used. The conservation and constitutive equations are solved using the finite volume method with an upwind scheme for the viscoelastic stresses and an hybrid scheme for the velocities. To calculate the pressure field, the semi-implicit method for the pressure linked equation revised method is used. The discretized equations are solved sequentially, using the tridiagonal matrix algorithm solver with under-relaxation. In both, the full approximation storage multigrid algorithm is used to speed up the convergence rate. Simulations of viscoelastic flows in four-to-one abrupt plane contraction are carried out. We will study the behaviour at the entrance corner of the four-to-one planar abrupt contraction. Using this solver, we show convergence up to a Weissenberg number We of 20 for the Oldroyd-B model. No limiting Weissenberg number is observed even though a Phan Thien-Tanner model is used. Several numerical results are presented. Smooth and stable solutions are obtained for high Weissenberg number. Copyright (C) 2002 John Wiley Sons, Ltd.
The plane oscillations of the elliptic cavity filled with a viscous incompressible liquid have been investigated numerically. Characteristic decay time depending on the values of system parameters has been determined,...
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The plane oscillations of the elliptic cavity filled with a viscous incompressible liquid have been investigated numerically. Characteristic decay time depending on the values of system parameters has been determined, the values of parameters at which this time is minimum have been found. Flow patterns of liquid in the cavity are presented.
In this manuscript the influence of local thermal non-equilibrium state on double-diffusive natural convection in a square cavity filled with fluid-saturated porous medium has been addressed numerically. The two dimen...
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In this manuscript the influence of local thermal non-equilibrium state on double-diffusive natural convection in a square cavity filled with fluid-saturated porous medium has been addressed numerically. The two dimensional steady state flow is induced due to maintenance of constant temperature and concentration on the vertical walls and insulation of both horizontal walls of the cavity. Non-Darcy (Darcy-Brinkman-Forchheimer) model has been taken and the complete governing equations are solved by standard simpler algorithm. A comparative study of the effect of the presence of Brinkman term in the momentum equation showed that results under the Darcy model are very close to those for the non-Darcy Brinkman model for relatively low permeable medium (e.g., in this study Da = 10(-4)). From our experiments it has been found that the impact of Lewis number (Le) on the average heat transfer rate of fluid (Nu(f)) and solid (Nu(s)) as well as on the thermal distribution of fluid and solid is not straightforward. It depends on the buoyancy ratio (N) and the value of inter-phase heat transfer coefficient (H). However, Le increases the average mass transfer rate (Sh). Also, for each Le there exist a point in the domain of N where Nu(f) is minimum. Similar points also exist for Nu(s) and Sh. In general, these points are different and depend on the LTNE state parameters, except at Le = 1. For any relatively large value of H, when almost thermal equilibrium state is achieved, the point at which Nu(f) and Nu(s) are minimum is same due to similar thermal distribution of fluid and solid. Also, it has been found that, for the buoyancy aided flow (N > 0), the increase in H up to a threshold value (H-0) decreases Sh as well as Nu(f) but increases Nu(s). The H-0 is found to be a decreasing function of the porosity scaled thermal conductivity ratio (gamma) of fluid and solid phases. Overall, the impact of LTNE state on the heat transfer rate and thermal distribution is significant but it
Recently, an efficient segregated algorithm for incompressible fluid flow and heat transfer problems, called inner doubly iterative efficient algorithm for linked equations (IDEAL), has been proposed by the present au...
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Recently, an efficient segregated algorithm for incompressible fluid flow and heat transfer problems, called inner doubly iterative efficient algorithm for linked equations (IDEAL), has been proposed by the present authors. In the algorithm there exist inner doubly iterative processes for pressure equation at each iteration level, which almost completely overcome two approximations in SIMPLE algorithm. Thus, the Coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of solution process. However, validations have only been conducted for two-dimensional cases. In the present paper the performance of the IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problems is analyzed and a systemic comparison is made between the algorithm and three other most widely used algorithms (simpler, SIMPLEC and PISO). By the comparison of five application examples, it is found that the IDEAL algorithm is the most robust and the most efficient one among the four algorithms compared. For the five three-dimensional cases studied, when each algorithm works at its own optimal under-relaxation factor, the IDEAL algorithm can reduce the computation time by 12.9-52.7% over simpler algorithm, by 45.3-73.4% over SIMPLEC algorithm and by 10.7-53.1% over PISO algorithm. Copyright (C) 2009 John Wiley & Sons, Ltd. C,
Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using simpler algorithm in a non-uniform staggered grid system. It has been shown that for consta...
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The periodically fully developed laminar heat transfer and fluid flow characteristics inside a two-dimensional wavy channel in a compact heat exchanger have been numerically investigated. Calculations were performed f...
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The periodically fully developed laminar heat transfer and fluid flow characteristics inside a two-dimensional wavy channel in a compact heat exchanger have been numerically investigated. Calculations were performed for Prandtl number 0.7, and Reynolds number ranging from 100 to 1,100 on non-orthogonal non-staggered grid systems, based on simpler algorithm in the curvilinear body-fitted coordinates. Effects of wavy heights, lengths, wavy pitches and channel widths on fluid flow and heat transfer were studied. The results show that overall Nusselt numbers and friction factors increase with the increase of Reynolds numbers. According to the local Nusselt number distribution along channel wall, the heat transfer may be greatly enhanced due to the wavy characteristics. In the geometries parameters considered, friction factors and overall Nusselt number always increase with the increase of wavy heights or channel widths, and with the decrease of wavy lengths or wavy pitches. Especially the overall Nusselt number significantly increase with the increase of wavy heights or channel widths, where the flow may become into transition regime with a penalty of strongly increasing in pressure drop.
In the present article, a comprehensive numerical investigation of the magneto-convection in an electrically conducting isotropic, and hydro-dynamically as well as a thermally anisotropic porous cavity, is presented. ...
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In the present article, a comprehensive numerical investigation of the magneto-convection in an electrically conducting isotropic, and hydro-dynamically as well as a thermally anisotropic porous cavity, is presented. The motion of the flow is due to the applied nonuniform heat flux on the bottom wall of the cavity and the insulation of other walls. The non-Darcy model has been adopted that includes Darcy and Brinkman terms in the momentum equations. The coupled governing equations are solved numerically by using the finite volume method (FVM). The impact of periodicity parameter (N), Hartmann number (Ha), and anisotropy parameters (K*, phi, and k*) on the dynamics of flow as well as heat transfer rate have been investigated. From rigorous numerical experiments, it has been found that the structure of streamlines is unicellular except for the inner kernel in some situations. In general, the profile of local heat transfer rate possesses (N - 1) points of singularity for sinusoidal heat flux with periodicity parameter (N), and the profile of local Nusselt number is not symmetric for even values of N. The heat transfer rate is highly affected by a relatively large value of thermal conductivity ratio (k*) as well as Ha, and the absolute difference between the maximum and minimum temperature of the system increases as a function of k* as well as Ha, whereas the strength of flow decreases gradually with increasing Ha.
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