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Article

El Hassan Ridouane and Antonio Campo

Sets out to discuss laminar free convection characteristics of air confined to a square cavity and a horizontal rectangular cavity (aspect ratio A=2) along with the viable…

Abstract

Purpose

Sets out to discuss laminar free convection characteristics of air confined to a square cavity and a horizontal rectangular cavity (aspect ratio A=2) along with the viable isosceles triangular cavities and right‐angle triangular cavities that may be inscribed inside the two original cavities.

Design/methodology/approach

The three distinct cavities shared the base wall as the heated wall, while the remaining sides and upper walls are cold. The finite volume method is used to perform the numerical computation of the transient conservation equations of mass, momentum and energy. The methodology takes into account the second‐order‐accurate quick scheme for the discretization of the convective term, whereas the pressure‐velocity coupling is handled with the simple scheme. The working fluid is air, which is not assumed as a Boussinesqian gas, so that all influencing thermophysical properties of air are taken as temperature‐dependent. The cavity problem is examined over a variety of height‐based Grashof numbers ranging from 103 to 106.

Findings

Numerical results are reported for the velocity fields, the temperature field as well as the local and mean wall heat fluxes along the heated base wall. It was found that the airflow remains symmetric for the isosceles triangular cavity with aspect ratio A=1 even at high Grashof numbers. In contrast, for an isosceles triangular cavity with an aspect ratio A=2, a pitchfork bifurcation begins to form at a critical Grashof number of 2 × 105, breaking the airflow symmetry. The computed local and mean heat fluxes along the hot base wall are compared for the three configurations under study and the corresponding maximum heat transfer levels are clearly identified for the two aspect ratios A=1 and 2.

Research limitations/implications

As a continuity of this work, there are two avenues that future research could explore and indeed are presently being explored by the authors within these geometries. The first deals with heat transfer enhancement using mixture of gases. The second is to re‐examine the problem under turbulent conditions.

Originality/value

The present study seeks to maximize the convection heat transport in cavities and minimize their sizes. The peculiarity of the derived cavities is their cross‐section area being half of the cross‐section area of the basic cavities.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 16 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Antonio Campo and Mark D. Landon

A detailed review of the archival literature on: fluid dynamics, heat transfer and shape optimization reveals that the optimal shape of natural convective cavities has not…

Abstract

A detailed review of the archival literature on: fluid dynamics, heat transfer and shape optimization reveals that the optimal shape of natural convective cavities has not been investigated so far, and of course, its physical features are not understood. A prominent application of cavities cooled by natural convection arises in the miniaturization of electronic packaging where some type of temperature constraint must be applied at the directly heated wall. This contemporary issue has been addressed in the present work in an elegant manner by linking a code on computational fluid dynamics with a shape optimization code. Once the velocity and temperature fields were accurately computed for an initial cavity with a certain heat load, a two‐step optimization procedure was implemented in a methodical fashion. A first optimization sub‐problem transformed a square cavity into a rectangular cavity, while the second optimization sub‐problem sculpted the shape of the upper horizontal insulated wall in order to bring down the maximum wall temperature of the directly heated vertical wall, i.e. the so‐called “hot spot”. A bird's eye inspection of the numerical results revealed that the first optimization sub‐problem produced a significant reduction in area (volume), while raising the maximum wall temperature of the heated vertical wall by a small amount. The second optimization sub‐problem supplied a remarkable decrease in the maximum wall temperature of the heated vertical wall, carrying with it a moderate increase in area (volume). At the end, the optimal shape of the cavity turns out to be a disfigured vertical rectangular cavity in which the upper insulated wall forming a parabolic‐skewed cap.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 14 no. 6
Type: Research Article
ISSN: 0961-5539

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Article

Venkatadri K., Gouse Mohiddin S. and Suryanarayana Reddy M.

This paper aims to focus on linear and non-linear convection in a lid-driven square cavity with isothermal and non-isothermal bottom surface.

Abstract

Purpose

This paper aims to focus on linear and non-linear convection in a lid-driven square cavity with isothermal and non-isothermal bottom surface.

Design/methodology/approach

It is assumed that the top moving wall is adiabatic and the bottom wall is heated in two modes, and the rest of the walls are maintained at uniform cold temperature. The coupled governing non-linear partial differential equations are solved numerically with MAC algorithm for conducting a parametric study with uniform and non-uniform temperature bottom wall.

Findings

The numerical results are depicted in the form of streamlines, temperature contours and variation of local Nusselt number. The local Nusselt number at the bottom wall of the cavity increases in presence of non-linear temperature parameter as compared with linear temperature parameter and heat transfer reduces with increasing of Ha for uniform and non-uniform heating of bottom wall.

Research limitations/implications

The numerical investigation is conducted for unsteady, two-dimensional natural convective flow in a square cavity. An extension of the present study with the effect of inclination of cavity, wavy walls and triangular cavity will be the interest of future work.

Originality/value

This work studies the effect of magnetic field in the presence of linear convection and non-linear convection. This study might be useful to cooling of electronic components, alloy casting, crystal growth and fusion reactors, etc.

Details

Engineering Computations, vol. 34 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

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Article

Majid Ashouri, Mohammad Behshad Shafii and Hossein Rajabi Kokande

The purpose of this paper is to study the influence of magnetic field on natural convection inside the enclosures partially filled with conducting square solid obstacles…

Abstract

Purpose

The purpose of this paper is to study the influence of magnetic field on natural convection inside the enclosures partially filled with conducting square solid obstacles. Also, the effect of thermal conductivity ratio between the solid and fluid materials is investigated for different number of solid blocks.

Design/methodology/approach

The dimensionless governing equations are transformed into sets of algebraic equations using finite volume method and momentum equations are solved by the SIMPLE algorithm with the hybrid scheme. The validation of the numerical code was conducted by comparing the results of average Nusselt number with previously published works.

Findings

The results indicate that both the magnetic field and solid blocks can significantly affect the flow and temperature fields. It is shown that for a given Rayleigh number, variation of Nusselt number might be increasing or decreasing with change in solid-to-fluid thermal conductivity ratio depending on magnetic field strength and number of solid blocks.

Originality/value

No work has been reported previously on the effect of magnetic field on natural convection flow in a cavity partially filled with square solid blocks. The numerical analysis of conductivity ratio between the solid and fluid materials under the effect of magnetic field have been carried out for the first time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Mahmoud M. El-Gendi and Abdelraheem M. Aly

Boussinesq approximation is widely used in solving natural convection problems, but it has severe practical limitations. Using Boussinesq approximation, the temperature…

Abstract

Purpose

Boussinesq approximation is widely used in solving natural convection problems, but it has severe practical limitations. Using Boussinesq approximation, the temperature difference should be less than 28.6 K. The purpose of this study is to get rid of Boussinesq approximation and simulates the natural convection problems using an unsteady compressible Navier-Stokes solver. The gravity force is included in the source term. Three temperature differences are used namely 20 K, 700 K and 2000 K.

Design/methodology/approach

The calculations are carried out on the square and sinusoidal cavities. The results of low temperature difference have good agreement with the experimental and previous calculated data. It is found that, the high temperature difference has a significant effect on the density.

Findings

Due to mass conservation, the density variation affects the velocity distribution and its symmetry. On the other hand, the density variation has a negligible effect on the temperature distribution.

Originality/value

The present calculation method has no limitations but its convergence is slow. The current study can be used in fluid flow simulations for nuclear power applications in natural convection flows subjected to large temperature differences.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Igor Miroshnichenko, Mikhail Sheremet and Ali J. Chamkha

The purpose of this paper is to conduct a numerical analysis of transient turbulent natural convection combined with surface thermal radiation in a square cavity with a…

Abstract

Purpose

The purpose of this paper is to conduct a numerical analysis of transient turbulent natural convection combined with surface thermal radiation in a square cavity with a local heater.

Design/methodology/approach

The domain of interest includes the air-filled cavity with cold vertical walls, adiabatic horizontal walls and isothermal heater located on the bottom cavity wall. It is assumed in the analysis that the thermophysical properties of the fluid are independent of temperature and the flow is turbulent. Surface thermal radiation is considered for more accurate analysis of the complex heat transfer inside the cavity. The governing equations have been discretized using the finite difference method with the non-uniform grid on the basis of the special algebraic transformation. Turbulence was modeled using the kε model. Simulations have been carried out for different values of the Rayleigh number, surface emissivity and location of the heater.

Findings

It has been found that the presence of surface radiation leads to both an increase in the average total Nusselt number and intensive cooling of such type of system. A significant intensification of convective flow was also observed owing to an increase in the Rayleigh number. It should be noted that a displacement of the heater from central part of the bottom wall leads to significant modification of the thermal plume and flow pattern inside the cavity.

Originality/value

An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyze unsteady turbulent natural convection combined with surface thermal radiation in a square air-filled cavity in the presence of a local isothermal heater. The results would benefit scientists and engineers to become familiar with the analysis of turbulent convective–radiative heat transfer in enclosures with local heaters, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 7
Type: Research Article
ISSN: 0961-5539

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Article

Mikhail Sheremet and Sivaraj Chinnasamy

The purpose of this study is to examine the radiation effect on the natural convective heat transfer of an alumina–water nanofluid in a square cavity in the presence of…

Abstract

Purpose

The purpose of this study is to examine the radiation effect on the natural convective heat transfer of an alumina–water nanofluid in a square cavity in the presence of centered nonuniformly heated plate.

Design/methodology/approach

The square cavity filled with alumina–water nanofluid has a nonuniformly heated plate placed horizontally or vertically at its center. The plate is heated isothermally with linearly varying temperature. The vertical walls are cooled isothermally with a constant temperature, while the horizontal walls are insulated. The governing equations have been discretized using finite volume method on a uniformly staggered grid system. Simulations were carried out for different values of the heated plate nonuniformity parameter (λ = –1, 0 and 1), the nanoparticles solid volume fraction (Φ = 0.01 − 0.04) and the radiation parameter (Rd = 0 – 2) at the Rayleigh number of Ra = 1e+07.

Findings

It is found that the total heat transfer rate is enhanced with an increase in the radiation parameter for both the horizontal and vertical plates. The role of nanoparticles addition to the base fluid can have dual effects on the heat transfer rate by augmenting and dampening for the absence of radiation while it dampens the heat transfer rate for the presence of radiation.

Originality/value

The originality of this work is to analyze steady natural convection in a square cavity filled with a water-based nanofluid in the presence of centered nonuniformly heated plate. The results would benefit scientists and engineers to become familiar with the analysis of convective heat and mass transfer in nanofluids, and the way to predict the properties of nanofluid convective flow in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors, electronics, etc.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Mubbashar Nazeer, N. Ali and T. Javed

The main purpose of this study is to examine the effects of moving wall on the mixed convection flow and heat transfer in a right-angle triangular cavity filled with a…

Abstract

Purpose

The main purpose of this study is to examine the effects of moving wall on the mixed convection flow and heat transfer in a right-angle triangular cavity filled with a micropolar fluid.

Design/methodology/approach

It is assumed that the bottom wall is uniformly heated and the right inclined wall is cold, whereas the vertical wall is adiabatic and moving with upward/downward velocity v0/−v0, respectively. The micropolar fluid is considered to satisfy the Boussinesq approximation. The governing equations and boundary conditions are solved using the Galerkin finite element method. The Penalty method is used to eliminate the pressure term from the momentum equations. To accomplish the consistent solution, the value of the penalty parameter is taken 107. The simulations are performed for a wide range of Richardson number, micropolar parameter, Prandtl number and Reynolds number.

Findings

The results are presented in the form of streamlines, isotherms and variations of average Nusselt number and fluid flow rate depending on the Richardson number, Prandtl number, micropolar parameter and direction of the moving wall. The flow field and temperature distribution in the cavity are affected by these parameters. An average Nusselt number into the cavity in both cases increase with increasing Prandtl and Richardson numbers and decreases with increasing micropolar parameter, and it has a maximum value when the lid is moving in the downward direction for all the physical parameters.

Research limitations/implications

The present investigation is conducted for the steady, two-dimensional mixed convective flow in a right-angle triangular cavity filled with micropolar fluid. An extension of the present study with the effects of cavity inclination, square cavity, rectangular, trapezoidal and wavy cavity will be the interest of future work.

Originality/value

This work studies the effects of moving wall, micropolar parameter, Richardson number, Prandtl number and Reynolds number parameter in a right-angle triangular cavity filled with a micropolar fluid on the fluid flow and heat transfer. This study might be useful to flows of biological fluids in thin vessels, polymeric suspensions, liquid crystals, slurries, colloidal suspensions, exotic lubricants, solar engineering for construction of triangular solar collector, construction of thermal insulation structure and geophysical fluid mechanics, etc.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 10
Type: Research Article
ISSN: 0961-5539

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Article

Mohammed Jami, Ahmed Mezrhab and Hassan Naji

This paper attempts to deal with the presentation of a numerical investigation of the laminar‐free convective heat transfer in a square enclosure containing a solid…

Abstract

Purpose

This paper attempts to deal with the presentation of a numerical investigation of the laminar‐free convective heat transfer in a square enclosure containing a solid cylinder located at an arbitrary position. Effects of the cylinder position on the heat transfer and the flow structures inside the cavity are to be studied and highlighted.

Design/methodology/approach

The numerical code is based on the hybrid scheme with the lattice Boltzmann and the alternating‐directional implicit (ADI) splitting scheme. The energy equation is solved by ADI scheme and the flow field velocities have been computed using the lattice Boltzmann method (LBM). The bounce‐back condition combined with quadratic interpolation is used at solid boundaries.

Findings

The predicted results show that the cylinder location has a significant effect on the heat transfer. It is observed that: when the inner body does not generate heat, most of the heat transfer takes place if the body is located at the center of the enclosure. When the cylinder generates heat and is displaced from the left towards the right and from the lower part towards the upper part of the cavity, the heat transfer rate decreases on the hot wall and increases on the cold wall.

Research limitations/implications

The fluid flow (air) is assumed to be incompressible, laminar and 2D. The viscous heat dissipation is neglected in the energy equation and all physical proprieties are constant except for the density, whose variation with temperature is allowed for in the buoyancy term.

Practical implications

Natural convection in heated enclosures, housing inner bodies has received significant attention because of its interest and importance in industrial applications. Some applications are solar collectors, fire research, electronic cooling, aeronautics, chemical apparatus, building constructions, nuclear engineering, etc.

Originality/value

The paper contributes to the development of the LBM. In particular, it was found that the inherent numerical instabilities of this LBE are not modified by coupling with temperature. This is a good improvement compared to what is observed in the simulations of thermal systems using the full LBE formulation where the energy conservation is taken into account.

Details

Engineering Computations, vol. 25 no. 5
Type: Research Article
ISSN: 0264-4401

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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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