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Article
Publication date: 19 December 2022

Damodara Priyanka, Pratibha Biswal and Tanmay Basak

This study aims to elucidate the role of curved walls in the presence of identical mass of porous bed with identical heating at a wall for two heating objectives: enhancement of…

Abstract

Purpose

This study aims to elucidate the role of curved walls in the presence of identical mass of porous bed with identical heating at a wall for two heating objectives: enhancement of heat transfer to fluid saturated porous beds and reduction of entropy production for thermal and flow irreversibilities.

Design/methodology/approach

Two heating configurations have been proposed: Case 1: isothermal heating at bottom straight wall with cold side curved walls and Case 2: isothermal heating at left straight wall with cold horizontal curved walls. Galerkin finite element method is used to obtain the streamfunctions and heatfunctions associated with local entropy generation terms.

Findings

The flow and thermal maps show significant variation from Case 1 to Case 2 arrangements. Case 1 configuration may be the optimal strategy as it offers larger heat transfer rates at larger values of Darcy number, Dam. However, Case 2 may be the optimal strategy as it provides moderate heat transfer rates involving savings on entropy production at larger values of Dam. On the other hand, at lower values of Dam (Dam ≤ 10−3), Case 1 or 2 exhibits almost similar heat transfer rates, while Case 1 is preferred for savings of entropy production.

Originality/value

The concave wall is found to be effective to enhance heat transfer rates to promote convection, while convex wall exhibits reduction of entropy production rate. Comparison between Case 1 and Case 2 heating strategies enlightens efficient heating strategies involving concave or convex walls for various values of Dam.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 16 March 2020

Abdelraheem M. Aly

The purpose of this study is to simulate the natural convection of a heated square shape embedded in a circular enclosure filled with nanofluid using an incompressible smoothed…

Abstract

Purpose

The purpose of this study is to simulate the natural convection of a heated square shape embedded in a circular enclosure filled with nanofluid using an incompressible smoothed particle hydrodynamics (ISPH) method.

Design/methodology/approach

In the ISPH method, the evaluated pressure was stabilized by using a modified source term in solving the pressure Poisson equation. The divergence of the velocity was corrected, and the dummy particles were used to treat the rigid boundary. Dummy wall particles were initially settled in outer layers of the circular enclosure for preventing particle penetration and reducing the error of truncated kernel. The circular enclosure was partially filled with a porous medium near to the outer region. The single-phase model was used for the nanofluid, and the Brinkman–Forchheimer-extended Darcy model was used for the porous medium. Dummy wall particles were initially settled in outer layers of circular enclosure for preventing particle penetration and reducing error from the truncated kernel on the boundary.

Findings

The length of the inner square shape plays an important role in enhancing the heat transfer and reducing the fluid flow inside a circular enclosure. The porous layer represents a resistance force for the fluid flow and heat transfer, and, consequently, the velocity field and temperature distributions are reduced at the outer region of the circular cylinder. Then, the radius of the inner square shape, Darcy parameter and radius of the porous layer were considered the main factors for controlling the fluid flow and heat transfer inside a circular enclosure. The average Nusselt number decreases as the inner square length, radius of the porous layer and solid volume fraction increase.

Originality/value

The stabilized ISPH method is corrected for simulating the natural convection from an inner hot square inside a nanofluid-filled circular enclosure saturated with a partial layer of a porous medium.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 4 January 2016

Abderrahim Bourouis, Abdeslam Omara and Said Abboudi

The purpose of this paper is to provide a numerical study of conjugate heat transfer by mixed convection and conduction in a lid-driven enclosure with thick vertical porous layer…

Abstract

Purpose

The purpose of this paper is to provide a numerical study of conjugate heat transfer by mixed convection and conduction in a lid-driven enclosure with thick vertical porous layer. The effect of the relevant parameters: Richardson number (Ri=0.1, 1, 10) and thermal conductivity ratio (Rk=0.1, 1, 10, 100) are investigated.

Design/methodology/approach

The studied system is a two dimensional lid-driven enclosure with thick vertical porous layer. The left vertical wall of the enclosure is allowed to move in its own plane at a constant velocity. The enclosure is heated from the right vertical wall isothermally. The left and the right vertical walls are isothermal but temperature of the outside of the right vertical wall is higher than that of the left vertical wall. Horizontal walls are insulated. The governing equations are solved by finite volume method and the SIMPLE algorithm.

Findings

From the finding results, it is observed that: for the two studied cases, heat transfer rate along the hot wall is a decreasing function of thermal conductivity ratio irrespective of Richardson numbers contrary to the heat transfer rate along the fluid-porous layer interface which is an increasing function of thermal conductivity ratio. At forced convection dominant regime, the difference between heat transfer rate for upward and downward moving wall is insensitive to the thermal conductivity ratio. For downward moving wall, average Nusselt number is higher than that of upward moving wall.

Practical implications

Some applications: building applications, furnace design, nuclear reactors, air solar collectors.

Originality/value

From the bibliographic work and the authors’ knowledge, the conjugate mixed convection in lid-driven partially porous enclosures has not yet been investigated which motivates the present work that represent a continuation of the preceding investigations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 2 February 2024

Deepika Parmar, S.V.S.S.N.V.G. Krishna Murthy, B.V. Rathish Kumar and Sumant Kumar

This study aims to analyze the impact of fractional derivatives on heat transfer and entropy generation during transient free convection inside various complex porous enclosures

Abstract

Purpose

This study aims to analyze the impact of fractional derivatives on heat transfer and entropy generation during transient free convection inside various complex porous enclosures, such as triangle, L-shape and square-containing wavy surfaces. These porous enclosures are saturated with Cu-water nanofluid and subjected to the influence of a uniform magnetic field.

Design/methodology/approach

In the present study, Darcy’s model is used for the momentum transport equation in the porous matrix. Additionally, the Caputo time fractional derivative is introduced in the energy equation to assess the heat transfer phenomenon. Furthermore, the total entropy generation has been computed by combining the entropy generation due to fluid friction (Sff), heat transfer (Sht) and magnetic field (Smf). The complete mathematical model is further simulated using the penalty finite element method, and the Caputo time derivative term is approximated using the L1 scheme. The study is conducted for various ranges of the Rayleigh number (102Ra104), Hartmann number (0Ha20) and fractional order parameter (0<α<1) with respect to time.

Findings

It has been observed that the fractional order parameter α governs the characteristics of entropy generation and heat transfer within the selected range of parameters. The Bejan number associated with heat transfer (Beht), fluid friction (Beff) and magnetic field (Bemf) further demonstrate the dominance of flow irreversibilities. It becomes evident that the initial evolution state of streamlines, isotherms and local entropy varies according to the choice of α. Additionally, increasing Ra values from 102 to 104 shows that the heat transfer rate increases by 123.8% for a square wavy enclosure, 7.4% for a triangle enclosure and 69.6% for an L-shape enclosure. Moreover, an increase in the value of Ha leads to a reduction in heat transfer rates and entropy generation. In this case, Bemf1 shows the dominance of the magnetic field irreversibility in the total entropy generation.

Practical implications

Recently, fractional-order models have been widely used to express numerous physical phenomena, such as anomalous diffusion and dispersion in complex viscoelastic porous media. These models offer a more accurate representation of physical reality that classical models fail to capture; this is why they find a broad range of applications in science and engineering.

Originality/value

The fractional derivative model is used to illustrate the flow pattern, heat transfer and entropy-generating characteristics under the influence of a magnetic field. Furthermore, to the best of the author’s knowledge, a fractional-derivative-based mathematical model for the entropy generation phenomenon in complex porous enclosures has not been previously developed or studied.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 34 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: 28 November 2019

Mohammad Ghalambaz, Kasra Ayoubi Ayoubloo and Ahmad Hajjar

This paper aims to investigate melting heat transfer of a non-Newtonian phase change material (PCM) in a cylindrical enclosure-space between two tubes using a deformed mesh method.

Abstract

Purpose

This paper aims to investigate melting heat transfer of a non-Newtonian phase change material (PCM) in a cylindrical enclosure-space between two tubes using a deformed mesh method.

Design/methodology/approach

Metal foam porous layers support the inner and outer walls of the enclosure. The porous layers and clear space of the enclosure are filled with PCM. The natural convection effects during the phase change are taken into account, and the governing equations for the molten region and solid region of the enclosure are introduced. The governing equations are transformed into non-dimensional form and then solved using finite element method. The results are compared with the literary works and found in good agreement. The non-Newtonian effects on the phase change heat transfer and melting front are studied.

Findings

The results show that the increase of non-Newtonian effects (the decrease of the power-law index) enhances the heat melting process in the cavity at the moderate times of phase change heat transfer. The temperature gradients in porous metal foam over the hot wall are small, and hence, the porous layer notably increases the melting rate. When the melting front reaches the cold porous layer, strong non-linear behaviors of the melting front can be observed.

Originality/value

The phase change heat transfer of non-Newtonian fluid in a cylindrical enclosure partially filled with metal foams is addressed for the first time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 12 August 2021

Nirmalendu Biswas, Dipak Kumar Mandal, Nirmal K. Manna, Rama Subba Reddy Gorla and Ali J. Chamkha

The aims of this study is to numerically investigate the thermal phenomena during magnetohydrodynamic (MHD) free convection in an oblique enclosure filled with porous media…

Abstract

Purpose

The aims of this study is to numerically investigate the thermal phenomena during magnetohydrodynamic (MHD) free convection in an oblique enclosure filled with porous media saturated with Cu–Al2O3/water hybrid nanofluid and heated at the left wavy wall. The thermophysical phenomena are explored thoroughly by varying the amplitude (λ) and undulation (n) of the wavy wall and the inclination of the enclosure (γ) along with other pertinent physical parameters. Darcy–Rayleigh number (Ram), Darcy number (Da), Hartmann number (Ha) and nanoparticle volumetric fraction (ϕ). The effect of all parameters has been analyzed and represented by using heatlines, isotherms, streamlines, average Nusselt number and local Nusselt number.

Design/methodology/approach

The finite volume method is used to work out the transport equations coupled with velocity, pressure and temperature subjected to non-uniform staggered grid structure after grid-sensitivity analysis by an indigenous computing code and the semi-implicit method for pressure linked equations (SIMPLE) algorithm. The solution process is initiated following an iterative approach through the alternate direction implicit sweep technique and the tridiagonal matrix algorithm (TDMA) algorithm. The iterative process is continued until successive minimization of the residuals (<1e-8) for the governing equations.

Findings

This study reveals that the increase in the heating surface area does not always favor heat transfer. An increase in the undulation amplitude enhances the heat transfer; however, there is an optimum value of undulation of the wavy wall for this. The heat transfer enhancement because of the wall curvature is revealed at higher Ram, lower Da and Ha and lower volume fraction of nanoparticles. In general, this augmentation is optimum for four undulations of the wavy wall with an amplitude of λ = 0.3. The heat transfer enhancement can be more at the cavity inclination   γ = 45°.

Research limitations/implications

The technique of this investigation could be used in other multiphysical areas involving partial porous layers, conducting objects, different heating conditions, wall motion, etc.

Practical implications

This study is to address MHD thermo-fluid phenomena of Cu–Al2O3/water-based hybrid nanofluid flow through a non-Darcian porous wavy cavity at different inclinations. The amplitude and number of undulations of the wavy wall, permeability of the porous medium, magnetic field intensity, nanoparticle volumetric fraction and inclinations of the enclosure play a significant role in the heat transfer process. This analysis and the findings of this work can be useful for the design and control of similar thermal systems/devices.

Originality/value

Many researchers have examined the problem of buoyancy-induced free convection in a wavy-porous cavity packed with regular fluids or nanofluids. However, the effect of magnetic fields along with the amplitude (λ) at different undulations (n) of the heated wavy wall of an inclined enclosure is not attended so far to understand the transport mechanisms. Most often, the evolutions of the thermo-fluid phenomena in such complex geometries invoking different multiphysics are very intricate. Numerical implementations for simulations and subsequent post-processing of the results are also challenging.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 28 July 2021

Abdeslam Omara, Mouna Touiker and Abderrahim Bourouis

This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a…

Abstract

Purpose

This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting.

Design/methodology/approach

The domain of interest is a partially square porous enclosure with sinusoidal wall heating and cooling. The fluid flow, heat and mass transfer dimensionless governing equations associated with the corresponding boundary conditions are discretized using the finite volume method. The resulting algebraic equations are solved by an in-house FORTRAN code and the SIMPLE algorithm to handle the non-linear character of conservation equations. The validity of the in-house FORTRAN code is checked by comparing the current results with previously published experimental and numerical works. The effect of the porous layer thickness, the spatial frequency of heating and cooling, the Darcy number, the Rayleigh number and the porous to fluid thermal conductivity ratio is analyzed.

Findings

The results demonstrate that for high values of the spatial frequency of heating and cooling (f = 7), temperature contours show periodic variations with positive and negative values providing higher temperature gradient near the thermally active wall. In this case, the temperature variation is mainly in the porous layer, while the temperature of the clear fluid region is practically the same as that imposed on the left vertical wall. This aspect can have a beneficial impact on thermal insulation. Besides, the porous to fluid thermal conductivity ratio, Rk, has practically no effect on Shhot wall, contrary to Nuinterface where a strong increase is observed as Rk is increased from 0.1 to 100, and much heat transfer from the hot wall to the clear fluid via the porous media is obtained.

Practical implications

The findings are useful for devices working on double-diffusive natural convection inside non-homogenous cavities.

Originality/value

The authors believe that the presented results are original and have not been published elsewhere.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 25 February 2021

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 the…

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. 31 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 29 August 2019

Shantanu Dutta, Arup Kumar Biswas and Sukumar Pati

The purpose of this paper is to analyze the natural convection heat transfer and irreversibility characteristics in a quadrantal porous cavity subjected to uniform temperature…

Abstract

Purpose

The purpose of this paper is to analyze the natural convection heat transfer and irreversibility characteristics in a quadrantal porous cavity subjected to uniform temperature heating from the bottom wall.

Design/methodology/approach

Brinkmann-extended Darcy model is used to simulate the momentum transfer in the porous medium. The Boussinesq approximation is invoked to account for the variation in density arising out of the temperature differential for the porous quadrantal enclosure subjected to uniform heating on the bottom wall. The governing transport equations are solved using the finite element method. A parametric study is carried out for the Rayleigh number (Ra) in the range of 103 to 106 and Darcy number (Da) in the range of 10−5-10−2.

Findings

A complex interaction between the buoyant and viscous forces that govern the transport of heat and entropy generation and the permeability of the porous medium plays a significant role on the same. The effect of Da is almost insignificant in dictating the heat transfer for low values of Ra (103, 104), while there is a significant alteration in Nusselt number for Ra ≥105 and moreover, the change is more intense for larger values of Da. For lower values of Ra (≤104), the main contributor of irreversibility is the thermal irreversibility irrespective of all values of Da. However, the fluid friction irreversibility is the dominant player at higher values of Ra (=106) and Da (=10−2).

Practical implications

From an industrial point of view, the present study will have applications in micro-electronic devices, building systems with complex geometries, solar collectors, electric machinery and lubrication systems.

Originality/value

This research examines numerically the buoyancy driven heat transfer irreversibility in a quadrantal porous enclosure that is subjected to uniform temperature heating from the bottom wall, that was not investigated in the literature before.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

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