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Article
Publication date: 25 June 2019

Nirmal Kumar Manna, Nirmalendu Biswas and Pallab Sinha Mahapatra

This study aims to enhance natural convection heat transfer for a porous thermal cavity. Multi-frequency sinusoidal heating is applied at the bottom of a porous square…

Abstract

Purpose

This study aims to enhance natural convection heat transfer for a porous thermal cavity. Multi-frequency sinusoidal heating is applied at the bottom of a porous square cavity, considering top wall adiabatic and cooling through the sidewalls. The different frequencies, amplitudes and phase angles of sinusoidal heating are investigated to understand their major impacts on the heat transfer characteristics.

Design/methodology/approach

The finite volume method is used to solve the governing equations in a two-dimensional cavity, considering incompressible laminar flow, Boussinesq approximation and Brinkman–Forchheimer–Darcy model. The mean-temperature constraint is applied for enhancement analysis.

Findings

The multi-frequency heating can markedly enhance natural convection heat transfer even in the presence of porous medium (enhancement up to ∼74 per cent). Only the positive phase angle offers heat transfer enhancement consistently in all frequencies (studied).

Research limitations/implications

The present research idea can usefully be extended to other multi-physical areas (nanofluids, magneto-hydrodynamics, etc.).

Practical implications

The findings are useful for devices working on natural convection.

Originality/value

The enhancement using multi-frequency heating is estimated under different parametric conditions. The effect of different frequencies of sinusoidal heating, along with the uniform heating, is collectively discussed from the fundamental point of view using the average and local Nusselt number, thermal and hydrodynamic boundary layers and heatlines.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 10
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 17 June 2019

Muhammad Raees Ul Haq, Hang Xu and Liang Zhao

The purpose of this study is to obtain the numerical as well as regularity results for the nonlinear elliptic set of equations arising in the study of fluid flow in…

Abstract

Purpose

The purpose of this study is to obtain the numerical as well as regularity results for the nonlinear elliptic set of equations arising in the study of fluid flow in microchannel induced by the pressure in the presence of interfacial electrokinetic effects.

Design/methodology/approach

For the numerical study, the authors implemented traditional FDM approach, and for the regularity results they used the classical energy estimates. The interfacial electrokinetic effects result in an additional source term in classical momentum equation, hence affecting the characteristics of the flow and heat transfer. The sinusoidal temperature variation is assumed on side walls.

Findings

The results were obtained for various combinations of physical parameters appearing in the governing equations. This study concludes that in the presence of electric double layer, the average heat transfer rate reduces along with larger values of Reynolds number. It is observed that the heat transfer increases with the increase in amplitude ratio and phase deviation. The flow behavior and heat transfer rate inside the microchannel are also strongly affected by the presence of κ (kappa).

Originality/value

To the best of the authors’ knowledge, the problem of heat transfer through microchannel in combination with sinusoidal temperature variation at boundary with electric double layer effects has not been considered previously. Hence, this paper focuses on the influence of the sinusoidal boundary temperature distributions on both sidewalls of a rectangular microchannel through parallel plates with electrokinetic effects on the pressure-driven laminar flow. In addition, a detailed mathematical analysis is also to be carried out to verify the regularity of this model with the proposed boundary conditions. The study used the classical energy method to get the regularity results.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 10
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 6 February 2017

Huey Tyng Cheong, S. Sivasankaran and M. Bhuvaneswari

The purpose of this paper is to study natural convective flow and heat transfer in a sinusoidally heated wavy porous cavity in the presence of internal heat generation or…

Abstract

Purpose

The purpose of this paper is to study natural convective flow and heat transfer in a sinusoidally heated wavy porous cavity in the presence of internal heat generation or absorption.

Design/methodology/approach

Sinusoidal heating is applied on the vertical left wall of the cavity, whereas the wavy right wall is cooled at a constant temperature. The top and bottom walls are taken to be adiabatic. The Darcy model is adopted for fluid flow through the porous medium in the cavity. The governing equations and boundary conditions are solved using the finite difference method over a range of amplitudes and number of undulations of the wavy wall, Darcy–Rayleigh numbers and internal heat generation/absorption parameters.

Findings

The results are presented in the form of streamlines, isotherms and Nusselt numbers for different values of right wall waviness, Darcy–Rayleigh number and internal heat generation parameter. The flow field and temperature distribution in the cavity are affected by the waviness of the right wall. The wavy nature of the cavity also enhances the heat transfer into the system. The heat transfer rate in the cavity decreases with an increase in the internal heat generation/absorption parameter.

Research limitations/implications

The present investigation is conducted for steady, two-dimensional natural convective flow in a wavy cavity filled with Darcy porous medium. The waviness of the right wall is described by the amplitude and number of undulations with a well-defined mathematical function. An extension of the present study with the effects of cavity inclination and aspect ratio will be the interest for future work.

Practical implications

The study might be useful for the design of solar collectors, room ventilation systems and electronic cooling systems.

Originality/value

This work examines the effects of sinusoidal heating on convective heat transfer in a wavy porous cavity in the presence of internal heat generation or absorption. The study might be useful for the design of solar collectors, room ventilation systems and electronic cooling systems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 2
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 18 July 2019

Dalia Sabina Cimpean and Ioan Pop

This paper aims to develop a numerical study of the steady natural convection in an inclined square porous cavity filled by a nanofluid with sinusoidal temperature…

Abstract

Purpose

This paper aims to develop a numerical study of the steady natural convection in an inclined square porous cavity filled by a nanofluid with sinusoidal temperature distribution on the side walls and adiabatic conditions on the upper and lower walls.

Design/methodology/approach

Governing equations transformed in terms of the dimensionless variables using the Darcy–Boussinesq approximation have been solved numerically using a central finite-difference scheme. The Gaus-Siedel iteration technique was used for the system of discretized equations. The two-phase nanofluid model including the Brownian diffusion and thermophoresis effects has been considered for simulation of nanofluid transport inside the cavity.

Findings

The numerical results of streamlines, isotherms and isoconcentrations are investigated and the effect of different important parameters, such as inclination angle of the cavity, amplitude ratio of the sinusoidal temperature or phase deviation, is discussed. The results obtained for no inclination of the cavity are compared and successfully validated with previous reported results of the literature. The important findings of the study are focused on the changes made by the inclination angle and the periodic thermal boundary conditions, on the heat and fluid flow.

Originality/value

The originality of the present study is given by the mathematical model presented for an inclined cavity, the numerical solution with new results for inclined cavity and the applications for design of solar energy devices such as solar collectors in which the boundary conditions vary with time because of changes in weather conditions.

Details

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

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Article
Publication date: 20 September 2018

Mikhail A. Sheremet, Ioan Pop and Alin V. Rosca

The purpose of this study is a numerical analysis of transient natural convection in an inclined square cavity filled with an alumina-water nanofluid under the effects of…

Abstract

Purpose

The purpose of this study is a numerical analysis of transient natural convection in an inclined square cavity filled with an alumina-water nanofluid under the effects of sinusoidal wall temperature and thermal radiation by using a single-phase nanofluid model with empirical correlations for effective viscosity and thermal conductivity.

Design/methodology/approach

The domain of interest includes the nanofluid-filled cavity with a sinusoidal temperature distribution along the left vertical wall. Horizontal walls are supposed to be adiabatic, while right vertical wall is kept at constant low temperature. Temperature of left wall varies sinusoidally along y-coordinate. It is assumed in the analysis that the thermophysical properties of the fluid are independent of temperature and the flow is laminar. The governing equations have been discretized using the finite difference method with the uniform grid. Simulations have been carried out for different values of the Rayleigh number, cavity inclination angle, nanoparticles volume fraction and radiation parameter.

Findings

It has been found that a growth of radiation parameter leads to the heat transfer enhancement and convective flow intensification. At the same time, an inclusion of nanoparticles illustrates a reduction in the average Nusselt number and fluid flow rate.

Originality/value

The originality of this work is to analyze unsteady natural convection in a square cavity filled with a water-based nanofluid in the presence of a sinusoidal temperature distribution along one wall. 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. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 8 October 2018

Purushothaman Pichandi and Satheesh Anbalagan

The purpose of this paper is to propose an effective numerical approach for solving the natural convection in a two-dimensional square enclosure by using the single…

Abstract

Purpose

The purpose of this paper is to propose an effective numerical approach for solving the natural convection in a two-dimensional square enclosure by using the single relaxation time-Bhatnagar, Gross and Krook (SRT-BGK) model (D2Q9) and lattice Boltzmann method (LBM).

Design/methodology/approach

Navier–Stroke equation is replaced by lattice Boltzmann method, and the numerical approach was simulated using LBM. LBM is a linear equation so, it reduces the computational time. The governing equations are solved using the SRT-BGK model. To achieve better numerical stability and accuracy, the momentum and energy equations are solved using two-dimensional nine-directional (D2Q9) lattice arrangement.

Findings

The results are presented at different convection mechanism with constant Prandtl number = 0.71, and the result is validated with reported literature. Numerical investigation is performed and accurate results are obtained; the range of Pr = 0.71, various Rayleigh number, phase change, periodicity parameter and amplitude ratio with three different blockage ratios. The present study is performed using LBM.

Research limitations/implications

To extend this work, the influence of natural convection, various selections of Prandtl number and Rayleigh number, periodicity and the effect of aspect ratio with mounted number of blockages could be included.

Practical implications

This research article will be useful for the study of fluid flow and heat transfer in hot and cold fluid interaction over the solid object. Like gear hardening with various sizes of gear blocks, material processing with hot and cold fluid interactions inside the furnace wall, solar panels high and low density fluid variation, indoor hot and cold fluid thermal environments, inside nuclear reactors heat and heavy water fluid interaction, cooling of electronic equipments and various chemical engineering applications.

Social implications

This paper will be useful for studying fluid flow and heat transfer within a square enclosure, and it gives practical information in engineering and heat transfer applications.

Originality/value

The present work is the first to investigate using LBM for selected parameters to apply a natural convection with imposed sinusoidal wave for different convection mechanisms.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 9
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 7 June 2013

Ö. Türk and M. Tezer‐Sezgin

The purpose of the paper is to obtain finite element method (FEM) solution of steady, laminar, natural convection flow in inclined enclosures in the presence of an oblique…

Abstract

Purpose

The purpose of the paper is to obtain finite element method (FEM) solution of steady, laminar, natural convection flow in inclined enclosures in the presence of an oblique magnetic field. The momentum equations include the magnetic effect, and the induced magnetic field due to the motion of the electrically conducting fluid is neglected. Quadratic triangular elements are used to ensure accurate approximation for second order derivatives of stream function appearing in the vorticity equation.

Design/methodology/approach

Governing equations in terms of stream function and vorticity are solved by FEM using quadratic triangular elements. Vorticity boundary conditions are obtained through Taylor series expansion of stream function equation by using more interior stream function values to improve the accuracy. Isothermally heated or cooled and/or adiabatic conditions for the temperature are imposed. Results are obtained for Rayleigh number values and Hartmann number values up to 1000000 and 100, respectively.

Findings

It is observed that streamlines form a thin boundary layer close to the heated walls as Ha increases. The same effect is seen in the vorticity contours, and isotherms are not affected much. As Ra increases streamlines are deformed moving from the heated walls through cooled walls. Vorticity starts to develop boundary layers close to heated and adjacent walls. Isotherms are pushed towards the sinusoidally heated wall whereas in the case of linearly heated left and bottom walls they expand towards cooled part of the cavity as Ra increases.

Originality/value

The application of FEM with quadratic elements for solving natural convection flow problem under the effect of a magnetic field is new in the sense that the results are obtained for large values of Rayleigh and Hartmann numbers.

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
Publication date: 6 July 2018

Ismail Arroub, Ahmed Bahlaoui, Abdelghani Raji, Mohammed Hasnaoui and Mohamed Naïmi

The purpose of this paper is to investigate numerically mixed convection of Al2O3-water nanofluids flowing through a horizontal ventilated cavity heated from below by a…

Abstract

Purpose

The purpose of this paper is to investigate numerically mixed convection of Al2O3-water nanofluids flowing through a horizontal ventilated cavity heated from below by a temperature varying sinusoidally along its lower wall. The simulations focus on the effects of different key parameters, such as Reynolds number (200 ≤ Re ≤ 5,000), nanoparticles’ concentration (0 ≤ ϕ ≤ 0.1) and phase shift of the heating temperature (0 ≤ γ ≤ π), on flow and thermal patterns and heat transfer performances.

Design/methodology/approach

The Navier–Stokes equations describing the nanofluid flow were discretized using a finite difference technique. The vorticity and energy equations were solved by the alternating direction implicit method. Values of the stream function were obtained by using the point successive over-relaxation method.

Findings

The simulations were performed for two modes of imposed external flow (injection and suction). The main findings are that the dynamical and thermal fields are affected by the parameters Re, ϕ, γ and the applied ventilation mode; the addition of nanoparticles leads to an improvement of heat transfer rate and an increase of mean temperature inside the enclosure; the heat exchange performance and the better cooling are more pronounced in suction mode; the phase shift of the heating temperature may lead to periodic solutions for weaker values of Re and contributes to an increase or a decrease of heat transfer depending on the value of ϕ and the convection regime.

Originality/value

To the best of the authors’ knowledge, the problem of mixed convection of a nanofluid inside a vented cavity using the injection or suction technics and submitted to non-uniform heating conditions has not been treated so far.

Details

Engineering Computations, vol. 35 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 4 March 2021

Harun Zontul, Hudhaifa Hamzah and Besir Sahin

This paper aims to exhibit a numerical study to analyze the influence of a periodic magnetic source on free convection flow and entropy generation of a ferrofluid in a…

Abstract

Purpose

This paper aims to exhibit a numerical study to analyze the influence of a periodic magnetic source on free convection flow and entropy generation of a ferrofluid in a baffled cavity. In this study, ferrofluid nanofluid was selected due to its ability to image magnetic domain structures within the cavity. The non-uniform magnetic source is considered as a sinusoidal distribution in the vertical direction.

Design/methodology/approach

The finite volume technique is used to evaluate the steady two-dimensional partial differential equations that govern the flow with its corresponding boundary conditions.

Findings

The obtained results indicate that a significant increase in the average Nusselt number can be achieved with the use of the periodic magnetic source instead of a uniform case. In addition, the effectiveness of the adiabatic baffle notably depends on its position and Rayleigh number. Regardless of the values of period and Hartmann numbers, the periodic magnetic source has a higher entropy generation and lower Bejan number than the uniform magnetic source.

Originality/value

The novelty of this research lies in applying a periodic magnetic source on the natural convection of ferrofluids in a baffled cavity.

Details

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

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Article
Publication date: 3 April 2017

K. Janagi, S. Sivasankaran, M. Bhuvaneswari and M. Eswaramurthi

The aim of the present study is to analyze the natural convection flow and heat transfer of cold water around °C in a square porous cavity. The horizontal walls of cavity…

Abstract

Purpose

The aim of the present study is to analyze the natural convection flow and heat transfer of cold water around °C in a square porous cavity. The horizontal walls of cavity are adiabatic, and the vertical walls are maintained at different temperatures. The right side wall is maintained at temperature θc, and the left side wall is maintained at sinusoidal temperature distribution.

Design/methodology/approach

The Brinkman–Forchheimer-extended Darcy model for porous medium is used to study the effects of density inversion parameter, Rayleigh number and impact of Darcy number and porosity. The finite volume method is used to solve the governing equations.

Findings

The heat transfer rate is increased on increasing the Darcy number and porosity. Also, the convective heat transfer rate is decreased first and then increased on increasing the density inversion parameter.

Research limitations/implications

The numerical computations have been carried out for the Darcy number ranging of 10(−4)Da ≤ 10(−1), the porosity ranging of 0.4 ≤ ε ≤ 0.8 and the density inversion parameter ranging of 0 ≤ Tm ≤ 1 and keeping Ra = 106.

Practical implications

The results can be used in the cooling of electronic components, thermal storage system and in heat exchangers.

Originality/value

The choice of consideration of sinusoidal heating and density maximum effect produces good result in flow field and temperature distribution. The obtained results can be used in various fields.

Details

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

Keywords

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