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Article
Publication date: 3 April 2018

Najib Hdhiri and Brahim Ben Beya

The purpose of this study is to produce a numerical model capable of predicting the mixed convection flows in a rectangular cavity filled with a porous medium and to analyze the…

259

Abstract

Purpose

The purpose of this study is to produce a numerical model capable of predicting the mixed convection flows in a rectangular cavity filled with a porous medium and to analyze the effects of several parameters on convective flow in porous media in a differentially heated enclosure.

Design/methodology/approach

The authors used the finite volume method.

Findings

The authors predicted and analyzed the effects of Richardson number, Darcy number, porosity values and Prandtl number in heat transfer and fluid flow. On other hand, the porosity and Richardson number values lead to reducing the heat transfer rate of mixed convection flow in a porous medium.

Originality/value

A comparison between Darcy–Brinkman–Forchheimer model and Darcy–Brinkman model is discussed and analyzed. The authors finally conclude that the Darcy–Brinkman model overestimates the heat transfer rate.

Details

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

Keywords

Article
Publication date: 16 June 2022

Mohammad Sedigh Kohanpour and Gholamreza Imani

This study aims to investigate lattice Boltzmann (LB) simulation of the fluid flow and heat transfer characteristics of a heated porous elliptic cylinder in uniform flow based on…

Abstract

Purpose

This study aims to investigate lattice Boltzmann (LB) simulation of the fluid flow and heat transfer characteristics of a heated porous elliptic cylinder in uniform flow based on the two-domain scheme. In the present research, the effect of axis ratio (1 ≤ AR ≤ 2), Reynolds number (5 ≤ Re ≤ 40) and Darcy number (10−4Da ≤ 10−2) are studied.

Design/methodology/approach

To perform the LB simulation based on the two-domain scheme, the nonequilibrium extrapolation method is modified to model the heat transfer interfacial conditions required at the curved interface.

Findings

The results show that the axis ratio as well as Reynolds and Darcy numbers significantly affect the fluid flow and heat transfer characteristics of the porous elliptic cylinder. It is shown that for AR > 1, the phenomenon of detached recirculating zone occurs at much higher Darcy numbers compared with the case of the porous circular cylinder (AR = 1). The results show that the location of maximum temperature within the cylinder moves downstream when the Reynolds number, Darcy number and axis ratio increase. It is also concluded that the average Nusselt number of a porous elliptic cylinder is always lower than that of a porous circular cylinder.

Originality/value

The LB simulation of forced convection from a porous cylinder in uniform flow with a curved interface based on the two-domain scheme has not been studied yet.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 August 1995

D. Misra and A. Sarkar

A comparative study is made between different flow models for analysisof natural convection in a differentially heated vertical square cavityfilled with a fluid saturated porous…

Abstract

A comparative study is made between different flow models for analysis of natural convection in a differentially heated vertical square cavity filled with a fluid saturated porous medium. The solution is obtained by using a finite element method. The Darcy‐modified Rayleigh number, Ra*, is varied from 50 to 1000 while the Darcy number, Da, ranges from 5 × 10–7 to 10–2. It is generally observed that for small values of Ra* and Da, all other models converge with the Darcy flow model. However, for large values of Ra* and Da, the Darcy flow model predicts the highest heat transfer rate, and the Brinkman‐Forchheimer extension yields the lowest heat transfer rate whilst prediction from the Brinkman‐extended model lies in between.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 5 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 June 1997

B.V.K. Satya Sai, K.N. Seetharamu and P.A. Aswathanarayana

Presents a numerical study on heat transfer by natural convection in porous media in vertical enclosures with side wall heating. The model for porous media includes inertia terms…

Abstract

Presents a numerical study on heat transfer by natural convection in porous media in vertical enclosures with side wall heating. The model for porous media includes inertia terms and also the Brinkman extension in addition to the Darcy resistance term. A semi‐implicit finite element scheme based on operator splitting method is adopted for solving the time‐dependent system of equations. The first half of the investigations is confined to the low permeability regime where Darcy law holds good. Presents the results for annular and rectangular cavities and proposes correlations for two types of boundary conditions, namely constant wall temperature case and uniform wall heat flux case. In the second half of the investigations, the scheme is applied in a high permeability regime, where the validity of Darcy law becomes questionable. Employs plane rectangular cavities with the two types of boundary conditions mentioned earlier. Highlights the influence of Rayleigh number (Ra) and Darcy number (Da) as separate parameters and proposes correlations for a square cavity for the first time in terms of Ra and Da as separate parameters. Discusses a qualitative study of the effect of aspect ratio on heat transfer as the permeability changes.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 11 September 2018

Hojjat Saberinejad, Ali Keshavarz, Mohammad Payandehdoost, Mohammad Reza Azmoodeh and Alireza Batooei

The purpose of this paper is to numerically investigate the heat transfer enhancement in a tube filled partially with porous media under non-uniform porosity distribution and…

Abstract

Purpose

The purpose of this paper is to numerically investigate the heat transfer enhancement in a tube filled partially with porous media under non-uniform porosity distribution and thermal dispersion effects. The optimum porous thickness ratio [R_(r,Nu)] for the heat transfer enhancement under these conditions with and without considering required pumping power is evaluated.

Design/methodology/approach

The local thermal non-equilibrium and Darcy–Brinkman–Forchheimer models are used to simulated thermal and flow fields in porous region. The tube wall and flow regime are assumed to be isothermal and laminar, respectively. The impacts of Darcy number (Da = 10-6 - 10-1) and inertia parameter (F = 0 − 2) on the Nusselt number and friction factor are studied for non-uniform porosity distribution.

Findings

First, the effect of Nusselt number indicates that there are two different behaviors with respect to uniform and non-uniform porosity for partially and fully filled porous pipe. Second, variable porosity in porous region has significant influence on the optimum thickness ratio with considering required pumping power. For negligible inertia term, it depends on the Darcy number, whereas it is 0.9 at F > 1. Third, the plug flow assumption cannot be valid even at lower Darcy number under non-uniform porosity, while this assumption is applicable at Da < 10-3 for constant porosity distribution in porous region.

Originality/value

According to the best knowledge of authors, the optimum porous thickness ratio for the heat transfer enhancement considering the pressure loss effects under variable porosity has not reported up to now. Also the plug flow assumption in such physics is not discussed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 5 August 2022

N. Keerthi Reddy and M. Sankar

This study aims to numerically study the buoyant convective flow of two different nanofluids in a porous annular domain. A uniformly heated inner cylinder, cooled outer…

Abstract

Purpose

This study aims to numerically study the buoyant convective flow of two different nanofluids in a porous annular domain. A uniformly heated inner cylinder, cooled outer cylindrical boundary and adiabatic horizontal surfaces are considered because of many industrial applications of this geometry. The analysis also addresses the comparative study of different porous media models governing fluid flow and heat transport.

Design/methodology/approach

The finite difference method has been used in the current simulation work to obtain the numerical solution of coupled partial differential equations. In particular, the alternating direction implicit method is used for solving transient equations, and the successive line over relaxation iterative method is used to solve time-independent equation by choosing an optimum value for relaxation parameter. Simpson’s rule is adopted to estimate average Nusselt number involving numerical integration. Various grid sensitivity checks have been performed to assess the sufficiency of grid size to obtain accurate results. In this analysis, a general porous media model has been considered, and a comparative study between three different models has been investigated.

Findings

Numerical simulations are performed for different combinations of the control parameters and interesting results are obtained. It has been found that the an increase in Darcy and Rayleigh numbers enhances the thermal transport rate and strengthens the nanofluid movement in porous annulus. Also, higher flow circulation rate and thermal transport has been detected for Darcy model as compared to non-Darcy models. Thermal mixing could be enhanced by considering a non-Darcy model.

Research limitations/implications

The present results could be effectively used in many practical applications under the limiting conditions of two-dimensionality and axi-symmetry conditions. The only drawback of the current study is it does not include the three-dimensional effects.

Practical implications

The results could be used as a first-hand information for the design of any thermal systems. This will help the design engineer to have fewer trial-and-run cases for the new design.

Originality/value

A pioneering numerical investigation on the buoyant convective flow of two different nanofluids in an annular porous domain has been carried out by using a general Darcy–Brinkman–Forchheimer model to govern fluid flow in porous matrix. The results obtained from current investigation are novel and original, with numerous practical applications of nanofluid saturated porous annular enclosure in the modern industry.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 9 January 2020

Lei Wang, Yang Cai, Wei-Wei Wang, Run-Zhe Liu, Di Liu, Fu-Yun Zhao and Hanqing Wang

This paper aims to numerically investigate the magnetohydrodynamic (MHD) convection heat transfer of nanofluid inside a differentially heated enclosure with various fin…

Abstract

Purpose

This paper aims to numerically investigate the magnetohydrodynamic (MHD) convection heat transfer of nanofluid inside a differentially heated enclosure with various fin morphologies.

Design/methodology/approach

The fluid flow within the cavity was governed by N-S equations while it within porous medium was solved by the non-Darcy model, called the Darcy–Forchheimer model based on representative element-averaging method. Empirical correlations from experimental data are used to evaluate the effective thermal conductivity and dynamic viscosity. Relevant governing parameters, including thermal Rayleigh number (105-107), Hartmann number (0-50), Darcy number (10−6-10−1), thermal conductivity ratio of porous matrix (1-103), nanoparticles volume fraction (0-0.04) and topology designs of porous fins, are sensitively varied to identify their effects and roles on the fluid flow and heat transfer. Particularly, heatlines are used to investigate the mechanism of heat transport.

Findings

Numerical results demonstrate that the predictions of average Nusselt number are augmented by using more porous fins with high permeability, and this effect becomes opposite in tiny Darcy numbers. Particularly, for high Darcy and Rayleigh numbers, the shortest fins could achieve the best performance of heat transfer. In addition, the prediction of average Nusselt number reduces with an increase in Hartmann numbers. An optimal nanoparticles concentration also exists to maximize heat transfer enhancement. Finally, numerical correlations for the average Nusselt number were proposed as functions of these governing parameters.

Practical implications

Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering.

Social implications

Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering. In addition, optimum thermal removals could enhance the lifetime of electronics, therefore reducing the cost of energy and materials.

Originality/value

To the best knowledge of authors, there are not any studies considering the synergetic effects of porous fins on MHD convection of nanofluids. Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 July 1995

Shih‐Wen Hsiao

The problems of transient natural convection from a corrugated plateembedded in an enclosed porous medium is studied numerically. The non‐Darcianeffects as well as the…

Abstract

The problems of transient natural convection from a corrugated plate embedded in an enclosed porous medium is studied numerically. The non‐Darcian effects as well as the acceleration terms are taken into consideration in the momentum equation. The governing equations in terms of vorticity, stream function and temperature are expressed in a body‐fitted coordinates system, which were solved numerically by the finite difference method. Results are presented in terms of streamlines and isotherms, local and average Nusselt numbers, with Darcy‐Rayleigh number ranging from 0 to 1000, and Darcy number from 10–4 to 10–1, for several aspect ratios of the cavity and plate positions. The flow and heat transfer characteristics for a corrugated plate and a flat plate and the numerical results solved with four different mathematical models are also compared.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 5 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Open Access
Article
Publication date: 5 September 2023

Ali Akbar Izadi and Hamed Rasam

Efficient thermal management of central processing unit (CPU) cooling systems is vital in the context of advancing information technology and the demand for enhanced data…

Abstract

Purpose

Efficient thermal management of central processing unit (CPU) cooling systems is vital in the context of advancing information technology and the demand for enhanced data processing speeds. This study aims to explore the thermal performance of a CPU cooling setup using a cylindrical porous metal foam heat sink.

Design/methodology/approach

Nanofluid flow through the metal foam is simulated using the Darcy–Brinkman–Forschheimer equation, accounting for magnetic field effects. The temperature distribution is modeled through the local thermal equilibrium equation, considering viscous dissipation. The problem’s governing partial differential equations are solved using the similarity method. The CPU’s hot surface serves as a solid wall, with nanofluid entering the heat sink as an impinging jet. Verification of the numerical results involves comparison with existing research, demonstrating strong agreement across numerical, analytical and experimental findings. Ansys Fluent® software is used to assess temperature, velocity and streamlines, yielding satisfactory results from an engineering standpoint.

Findings

Investigating critical parameters such as Darcy number (10−4DaD ≤ 10−2), aspect ratio (0.5 ≤ H/D ≤ 1.5), Reynolds number (5 ≤ ReD,bf ≤ 3500), Eckert number (0 ≤ ECbf ≤ 0.1) , porosity (0.85 ≤ ε ≤ 0.95), Hartmann number (0 ≤ HaD,bf ≤ 300) and the volume fraction of nanofluid (0 ≤ φ ≤ 0.1) reveals their impact on fluid flow and heat sink performance. Notably, Nusselt number will reduce 45%, rise 19.2%, decrease 14.1%, and decrease 0.15% for Reynolds numbers of 600, with rising porosity from 0.85 to 0.95, Darcy numbers from 10−4 to 10−2, Eckert numbers from 0 to 0.1, and Hartman numbers from 0 to 300.

Originality/value

Despite notable progress in studying thermal management in CPU cooling systems using porous media and nanofluids, there are still significant gaps in the existing literature. First, few studies have considered the Darcy–Brinkman–Forchheimer equation, which accounts for non-Darcy effects and the flow and geometric interactions between coolant and porous medium. The influence of viscous dissipation on heat transfer in this specific geometry has also been largely overlooked. Additionally, while nanofluids and impinging jets have demonstrated potential in enhancing thermal performance, their utilization within porous media remains underexplored. Furthermore, the unique thermal and structural characteristics of porous media, along with the incorporation of a magnetic field, have not been fully investigated in this particular configuration. Consequently, this study aims to address these literature gaps and introduce novel advancements in analytical modeling, non-Darcy flow, viscous dissipation, nanofluid utilization, impinging jets, porous media characteristics and the impact of a magnetic field. These contributions hold promising prospects for improving CPU cooling system thermal management and have broader implications across various applications in the field.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 34 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 7 June 2019

Yingchun Zhang, Nesrin Ozalp and Gongnan Xie

The purpose of this paper is to investigate the unsteady flow past through a permeable diamond-shaped cylinder and to study the effects of the aspect ratios and Darcy numbers of…

195

Abstract

Purpose

The purpose of this paper is to investigate the unsteady flow past through a permeable diamond-shaped cylinder and to study the effects of the aspect ratios and Darcy numbers of the cylinder.

Design/methodology/approach

The lattice Boltzmann method with D2Q9 lattice model was used to simulate the unsteady flow through permeable diamond-shaped cylinders. The present numerical method is validated against the available data.

Findings

The key findings are that increasing the permeability enhances the suppression of vortex shedding, and that the Strouhal number is directly proportion to the Darcy number, Reynolds number and the aspect ratio of the porous cylinder.

Originality/value

The present study considers unsteady laminar flow past through single permeable diamond-shaped cylinder. According to the authors’ knowledge, very few studies have been found in this field. The present findings are novel and original, which in turn can attract wide attention and citations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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