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Article

M.A. Antar, Rached Ben-Mansour and Salem Ahmed Al-Dini

There are industrial applications for varying speed lid-driven flow and heat transfer such as the float glass process where the glass film stretches or thickens depending…

Abstract

Purpose

There are industrial applications for varying speed lid-driven flow and heat transfer such as the float glass process where the glass film stretches or thickens depending on the desired thickness. Hence the tin cavity underneath or the nitrogen cavity above is being driven by a variable speed. The purpose of this paper is to simulate such behavior.

Design/methodology/approach

Numerical solution of variable speed lid-driven cavity is carried out with thermal radiation being considered using control volume approach and staggered grid and applying the SIMPLE algorithm. Transient simulation is used for 2D model in the present study. Second order upwind schemes were used for discretization of momentum, energy equations and time.

Findings

Under laminar conditions, thermal radiation plays a significant role in the heat transfer characteristics of the lid-driven cavity. This effect is more significant for blackbody radiation and decreases as the surface emissivity decreases. Nusselt number (Nu) behavior lies between these two limiting case profiles considering constant speed profiles of both maximum and minimum lid velocities, respectively. In addition, local Nu values at the tip where higher than those at the top of the cavity that is stagnant.

Research limitations/implications

The study is limited to laminar flow case.

Practical implications

The applications of this study can be found in float glass process where the glass film stretches or thickens depending on the desired thickness. Hence the tin cavity underneath or the nitrogen cavity above is being driven by a variable speed. Another application involves casting of plastic films. The molten polymer leaves the die with a considerable thickness and high temperature. The film is then trenched to reach its final thickness. In this case, usually there is no actual cavity above or below the film but one can approximate the problem as such. Other similar applications do exist in food drying and processing where the conveyer belt is in portions and their speed may not be the same in different section of the processing oven.

Originality/value

To the best of the authors knowledge, no study in the literature addressed the effect of thermal radiation in lid-driven cavities with variable speed

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Chao Wang, Jinju Sun and Yan Ba

The purpose of this paper is to develop a Vortex-In-Cell (VIC) method with the semi-Lagrangian scheme and apply it to the high-Re lid-driven cavity flow.

Abstract

Purpose

The purpose of this paper is to develop a Vortex-In-Cell (VIC) method with the semi-Lagrangian scheme and apply it to the high-Re lid-driven cavity flow.

Design/methodology/approach

The VIC method is developed for simulating high Reynolds number incompressible flow. A semi-Lagrangian scheme is incorporated in the convection term to produce unconditional stability, which gets rid of the constraint of the convection Courant-Friedrichs-Lewy (CFL) condition; the adaptive time step is used to maintain the numerical stability of the diffusion term; and the velocity boundary condition is readily converted to the vorticity formulation to suit discontinuous boundary treatment. The VIC simulation results are compared with those produced by other gird methods reported in open literature studies.

Findings

The lid-driven cavity flow is simulated from Re = 100 to 100,000. Similar vortex birth mechanisms are exhibited though, but distinct flow characteristics are revealed. At Re = 100 to 7,500, the cavity flow is confirmed steady. At Re = 10,000, 15,000 and 20,000, the cavity flow is periodical with a primary vortex held spatially at the center. In particular, at Re = 100,000 highly turbulent characteristics is first revealed and an analogous primary vortex is formed but in motion rather than stationary, which is caused by the considerable flow separation at all the boundaries.

Originality/value

In the lid-driven cavity, the flow becomes extremely complex and highly turbulent at Re = 100,000, and the analogous primary vortex structure is observed. Boundary layer separation is observed at all walls, producing small vortices and causing the displacement of the analogous primary vortex. Such a finding original and has not yet been reported by other investigators. It may provide a basis for conducting in-depth studies of the lid-driven cavity flow.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Faicel Hammami, Nader Ben-Cheikh, Brahim Ben-Beya and Basma Souayeh

This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume…

Abstract

Purpose

This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume method (FVM) and multigrid acceleration. This study has been performed for certain pertinent parameters; a wide range of the Reynolds number values has been adopted, and aspect ratios ranging from 0.25 to 1 and various velocity ratios from 0.25 to 0.825 have been considered in this investigation. Results show that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Velocity profile for special case of a square cavity (A = 1) was found to be in good agreement between current numerical results and published ones. Flow characteristics inside the cavity have been presented and discussed in terms of streamlines and vorticity contours at a fixed Reynolds number (Re = 5,000) for various aspect ratios (a = 0).

Design/methodology/approach

The numerical method is based on the FVM and multigrid acceleration.

Findings

Computations have been investigated for several Reynolds numbers and aspect ratios A (0.25, 0.5, 0.75, 0.825 and 1). Besides, various velocity ratios (a = 0.25, 0.5, 0.75 and 0.825) at fixed aspect ratios (A = 0.25, 0.5 and 0.75) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity is verified through time history plots for velocity components and phase-space trajectories.

Originality/value

The bifurcations between steady and unsteady states are investigated.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

A. Malleswaran, S. Sivasankaran and M. Bhuvaneswari

The main objective of the present study is to investigate the effects of various lengths and different locations of the heater on the left sidewall in a square lid‐driven cavity.

Abstract

Purpose

The main objective of the present study is to investigate the effects of various lengths and different locations of the heater on the left sidewall in a square lid‐driven cavity.

Design/methodology/approach

The non‐dimensional equations are discretized by the finite‐volume method. The upwind scheme and the central difference scheme are implemented for the convection and the diffusion terms, respectively.

Findings

On increasing the Richardson number, the overall heat transfer is increased whether the length and the location of the heater is considered or not. Among the various lengths of the heater considered, the total heat transfer is better only for the length LH=1/3 of the heater if it is extended from top or bottom of the cavity. In the case of location of the heater, the average heat transfer enhances for center location of the heater. Existence of the magnetic field suppresses the convective heat transfer and the fluid flow.

Practical implications

The results can be used in the cooling of electronic devices and heat transfer improvement in heat exchangers.

Originality/value

The numerical results obtained here focus on the detailed investigation of flow and temperature field in a discretely heated lid‐driven square cavity. The findings will be helpful in many applications such as heat exchangers and cooling of electronic devices.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 23 no. 5
Type: Research Article
ISSN: 0961-5539

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Article

Shainath Ramesh Kalamkar and Jadav Chandra Mandal

The purpose of this paper is to present two low diffusive convective-pressure flux split finite volume algorithms for solving incompressible flows in artificial…

Abstract

Purpose

The purpose of this paper is to present two low diffusive convective-pressure flux split finite volume algorithms for solving incompressible flows in artificial compressibility framework.

Design/methodology/approach

The present method follows the framework similar to advection upwind splitting method of Liou and Steffen for compressible flows which is used by Vierendeels et al. to solve incompressible flow equations. Instead of discretizing the total inviscid flux using upwind scheme, the inviscid flux is first split into convective and pressure parts, and then discretized the two parts differently. The convective part is discretized using upwind method and the pressure part using central differencing. Since the Vierendeels type scheme may not be able to capture the divergence free velocity field due to the presence of artificial dissipation term, a strategy to progressively withdraw the dissipation with time step is proposed here that can ascertain the divergence free velocity condition to the level of residual error. This approach helps in reducing the amount of numerical dissipation due to upwind discretization, which is evident from the numerical test examples.

Findings

Upwind treatment of only the convective part of the inviscid flux terms, instead of the whole inviscid flux term, leads to more accurate solutions even at relatively coarse grids, which is substantiated by numerical test examples.

Research limitations/implications

The method is presently applicable to Cartesian grid.

Originality/value

Although similar formulation is reported by Vierendeels et al., no detailed study of the accuracy is presented. Discretization and solution reconstructions used in the present approach differ from the approach reported by Vierendeels et al. A modification to Vierendeels type scheme is proposed that can help in achieving divergence free velocity condition. Finally the efficacy of the present approach to produce very accurate solutions even on coarse grids is successfully demonstrated using a few benchmark problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 2
Type: Research Article
ISSN: 0961-5539

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Article

T. Javed, Z. Mehmood and Ioan Pop

The purpose of this paper is to analyze numerical results for heat transfer through mixed convection in an incompressible steady lid-driven fluid flow inside a trapezoidal…

Abstract

Purpose

The purpose of this paper is to analyze numerical results for heat transfer through mixed convection in an incompressible steady lid-driven fluid flow inside a trapezoidal cavity in the presence of a uniform magnetic field.

Design/methodology/approach

In this study, the authors have considered three different cases, in which left and right walls of the cavity are tilted at different angles of 0, 30 and 45 degrees, respectively. Both left and right side walls of the cavity are taken cold and the upper wall is insulated and assumed moving with constant speed, whereas the bottom wall is considered to be heated uniformly/non-uniformly. To eliminate pressure term, penalty method is applied to governing Navier–Stokes’ equations. The reduced equations are solved by Galerkin weighted residual technique of finite element method. Grid-independent results are obtained and shown in terms of plots for streamlines, isotherms, Nusselt number and average Nusselt number for a wide range of flow parameters, including Rayleigh numbers Ra, Prandtl number Pr and Hartman number Ha.

Findings

It has been observed that the effects of moving lid become negligible for Ra = 100,000, whereas increasing Rayleigh number results in stronger streamline circulation and convection dominant effects inside the enclosure. Local Nusselt number Nu along the bottom wall is observed to be maximum at edges and it reduces while moving toward the center from edges, and attains minimum value at the center of the bottom wall.

Research limitations/implications

The problem is modeled for laminar and incompressible flow, induced magnetic field has been considered negligibly small and local thermal equilibrium has been assumed.

Originality/value

In this investigation, the authors have presented new and original results for mixed convection flow inside a lid-driven trapezoidal cavity under the influence of a magnetic field. Hence, this study would be important for the researchers working in the area of heat transfer in cavity flows involving magnetic effects to become familiar with the flow behavior and properties.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Leo Lukose and Tanmay Basak

The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of…

Abstract

Purpose

The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of the boundary walls, thermal conditions and/ or kinematics of objects embedded in the cavities and kinematics of external flow field through the ventilation ports. Experimental works on mixed convection have also been addressed.

Design/methodology/approach

This review is based on 10 unified models on mixed convection within cavities. Models 1–5 involve mixed convection based on the movement of single or double walls subjected to various temperature boundary conditions. Model 6 elucidates mixed convection due to the movement of single or double walls of cavities containing discrete heaters at the stationary wall(s). Model 7A focuses mixed convection based on the movement of wall(s) for cavities containing stationary solid obstacles (hot or cold or adiabatic) whereas Model 7B elucidates mixed convection based on the rotation of solid cylinders (hot or conductive or adiabatic) within the cavities enclosed by stationary or moving wall(s). Model 8 is based on mixed convection due to the flow of air through ventilation ports of cavities (with or without adiabatic baffles) subjected to hot and adiabatic walls. Models 9 and 10 elucidate mixed convection due to flow of air through ventilation ports of cavities involving discrete heaters and/or solid obstacles (conductive or hot) at various locations within cavities.

Findings

Mixed convection plays an important role for various processes based on convection pattern and heat transfer rate. An important dimensionless number, Richardson number (Ri) identifies various convection regimes (forced, mixed and natural convection). Generalized models also depict the role of “aiding” and “opposing” flow and combination of both on mixed convection processes. Aiding flow (interaction of buoyancy and inertial forces in the same direction) may result in the augmentation of the heat transfer rate whereas opposing flow (interaction of buoyancy and inertial forces in the opposite directions) may result in decrease of the heat transfer rate. Works involving fluid media, porous media and nanofluids (with magnetohydrodynamics) have been highlighted. Various numerical and experimental works on mixed convection have been elucidated. Flow and thermal maps associated with the heat transfer rate for a few representative cases of unified models [Models 1–10] have been elucidated involving specific dimensionless numbers.

Originality/value

This review paper will provide guidelines for optimal design/operation involving mixed convection processing applications.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Lioua Kolsi, Hakan F. Öztop, Nidal Abu-Hamdeh, Borjini Mohamad Naceur and Habib Ben Assia

The main purpose of this work is to arrive at a three-dimensional (3D) numerical solution on mixed convection in a cubic cavity with a longitudinally located triangular…

Abstract

Purpose

The main purpose of this work is to arrive at a three-dimensional (3D) numerical solution on mixed convection in a cubic cavity with a longitudinally located triangular fin in different sides.

Design/methodology/approach

The 3D governing equations are solved via finite volume technique by writing a code in FORTRAN platform. The governing parameters are chosen as Richardson number, 0.01 ≤ Ri ≤ 10 and thermal conductivity ratio 0.01 ≤ Rc ≤ 100 for fixed parameters of Pr = 0.7 and Re = 100. Two cases are considered for a lid-driven wall from left to right (V+) and right to left (V−).

Findings

It is observed that entropy generation due to heat transfer becomes dominant onto entropy generation because of fluid friction. The most important parameter is the direction of the moving lid, and lower values are obtained when the lid moves from right to left.

Originality

The main originality of this work is to arrive at a solution of a 3D problem of mixed convection and entropy generation for lid-driven cavity with conductive triangular fin attachments.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 4
Type: Research Article
ISSN: 0961-5539

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Article

Y. Guo, R. Bennacer, S. Shen, D.E. Ameziani and M. Bouzidi

The purpose of this paper is to apply the lattice Boltzmann method (LBM) to simulate mixed flow, which combines natural convection for temperature difference and forced…

Abstract

Purpose

The purpose of this paper is to apply the lattice Boltzmann method (LBM) to simulate mixed flow, which combines natural convection for temperature difference and forced convection for lid driven, in a two‐dimensional rectangular cavity over a wide range of aspect ratios (A), Rayleigh numbers (Ra) and Reynolds numbers (Re).

Design/methodology/approach

The LBM is applied to simulate the mixed flow. A multi‐relaxation technique was used successfully. A scale order analysis helped the understanding and predicting the overall heat transfer.

Findings

In the considered lid driven cavity, the Richardson number emerges as a measure of relative importance of natural and forced convection modes on the heat transfer. An expression of the overall heat transfer depending on the cavity slender (A) is deduced. The validity of the obtained expression was checked in mixed convection under the condition of low Richardson number (Ri) and the limitation condition was deduced.

Practical implications

This paper has implications for cooling system optimization and LBM technique development.

Originality/value

This paper presents a new cooling configuration, avoiding critical situation where the opposing effect induce weak heat transfer; and a stable and fast LBM approach allowing complex geometry treatment.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Muneer A. Ismael

This paper investigates a numerical treatment to steady mixed convection in a lid-driven square cavity with arc-shaped moving wall or lid. The horizontal walls are…

Abstract

Purpose

This paper investigates a numerical treatment to steady mixed convection in a lid-driven square cavity with arc-shaped moving wall or lid. The horizontal walls are thermally insulated. The vertical left wall is kept isothermally at high temperature, while the right arc-shaped moving wall is kept isothermally at low temperature.

Design/methodology/approach

Finite difference method in Cartesian coordinates with the upwind scheme is used in numerical solution. The irregular curved boundary has been treated by invoking non-uniform mesh grid with the ability to generate boundary fitted nodes. Jensen’s formulas of Neumann’s boundary condition have derived for the non-uniform mesh grid. The arc-shaped moving wall is considered as a segment of a rotating cylinder; thus, the studied pertinent parameters are the rotational speed of the arc-shaped wall in both aiding and opposing directions ω = −1,000-1,000, the arc-wall radius Ro = 0.5099-1.534 which is governed by its center (X0, Y0) = (1.1, 0.5)-(2.45, 0.5) and the Rayleigh number Ra = 103 − 106.

Findings

The results have shown that for low Rayleigh numbers, the rotational speed enhances heat transfer irrespective to the direction of rotation, while for high Rayleigh numbers, the aiding anticlockwise rotation (negative ω) enhances the heat transfer, while the opposing clockwise rotation (positive ω) manifests a retardation effect on the heat transfer. For a motionless arc-wall, its radius is ineffective for aiding heat transfer, while for non-zero arc-shaped wall speed, the heat transfer is an increasing function of its radius.

Originality/value

The arc-shaped moving wall has never been investigated until now. Therefore, the originality of this paper is due to studying the mixed convection in a lid-driven cavity with moving arc-shaped wall and inspecting the effect of its curvature and rotational speed in both directions on the flow and thermal fields.

Details

Engineering Computations, vol. 34 no. 3
Type: Research Article
ISSN: 0264-4401

Keywords

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