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Article

Leo Lukose and Tanmay Basak

The purpose of this paper is to study thermal (natural) convection in nine different containers involving the same area (area= 1 sq. unit) and identical heat input at the…

Abstract

Purpose

The purpose of this paper is to study thermal (natural) convection in nine different containers involving the same area (area= 1 sq. unit) and identical heat input at the bottom wall (isothermal/sinusoidal heating). Containers are categorized into three classes based on geometric configurations [Class 1 (square, tilted square and parallelogram), Class 2 (trapezoidal type 1, trapezoidal type 2 and triangle) and Class 3 (convex, concave and triangle with curved hypotenuse)].

Design/methodology/approach

The governing equations are solved by using the Galerkin finite element method for various processing fluids (Pr = 0.025 and 155) and Rayleigh numbers (103 ≤ Ra ≤ 105) involving nine different containers. Finite element-based heat flow visualization via heatlines has been adopted to study heat distribution at various sections. Average Nusselt number at the bottom wall ( Nub¯) and spatially average temperature (θ^) have also been calculated based on finite element basis functions.

Findings

Based on enhanced heating criteria (higher Nub¯ and higher θ^), the containers are preferred as follows, Class 1: square and parallelogram, Class 2: trapezoidal type 1 and trapezoidal type 2 and Class 3: convex (higher θ^) and concave (higher Nub¯).

Practical implications

The comparison of heat flow distributions and isotherms in nine containers gives a clear perspective for choosing appropriate containers at various process parameters (Pr and Ra). The results for current work may be useful to obtain enhancement of the thermal processing rate in various process industries.

Originality/value

Heatlines provide a complete understanding of heat flow path and heat distribution within nine containers. Various cold zones and thermal mixing zones have been highlighted and these zones are found to be altered with various shapes of containers. The importance of containers with curved walls for enhanced thermal processing rate is clearly established.

Details

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

Keywords

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Article

Debayan Das, Leo Lukose and Tanmay Basak

The purpose of the paper is to study natural convection within porous square and triangular geometries (design 1: regular isosceles triangle, design 2: inverted isosceles…

Abstract

Purpose

The purpose of the paper is to study natural convection within porous square and triangular geometries (design 1: regular isosceles triangle, design 2: inverted isosceles triangle) subjected to discrete heating with various locations of double heaters along the vertical (square) or inclined (triangular) arms.

Design/methodology/approach

Galerkin finite element method is used to solve the governing equations for a wide range of modified Darcy number, Dam = 10−5–10−2 with various fluid saturated porous media, Prm = 0.015 and 7.2 at a modified Rayleigh number, Ram = 106 involving the strategic placement of double heaters along the vertical or inclined arms (types 1-3). Adaptive mesh refinement is implemented based on the lengths of discrete heaters. Finite element based heat flow visualization via heatlines has been adopted to study heat distribution at various portions.

Findings

The strategic positioning of the double heaters (types 1-3) and the convective heatline vortices depict significant overall temperature elevation at both Dam = 10−4 and 10−2 compared to type 0 (single heater at each vertical or inclined arm). Types 2 and 3 are found to promote higher temperature uniformity and greater overall temperature elevation at Dam = 10−2. Overall, the triangular design 2 geometry is also found to be optimal in achieving greater temperature elevation for the porous media saturated with various fluids (Prm).

Practical implications

Multiple heaters (at each side [left or right] wall) result in enhanced temperature elevation compared to the single heater (at each side [left or right] wall). The results of the current work may be useful for the material processing, thermal storage and solar heating applications.

Originality/value

The heatline approach is used to visualize the heat flow involving double heaters along the side (left or right) arms (square and triangular geometries) during natural convection involving porous media. The heatlines depict the trajectories of heat flow that are essential for thermal management involving larger thermal elevation. The mixing cup or bulk average temperature values are obtained for all types of heating (types 0-3) involving all geometries, and overall temperature elevation is examined based on higher mixing cup temperature values.

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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Article

Pratibha Biswal and Tanmay Basak

This paper is aimed to study natural convection in enclosures with curved (concave and convex) side walls for porous media via the heatline-based heat flow visualization approach.

Abstract

Purpose

This paper is aimed to study natural convection in enclosures with curved (concave and convex) side walls for porous media via the heatline-based heat flow visualization approach.

Design/methodology/approach

The numerical scheme involving the Galerkin finite element method is used to solve the governing equations for several Prandtl numbers (Prm) and Darcy numbers (Dam) at Rayleigh number, Ram = 106, involving various wall curvatures. Finite element method is advantageous for curved domain, as the biquadratic basis functions can be used for adaptive automated mesh generation.

Findings

Smooth end-to-end heatlines are seen at the low Dam involving all the cases. At the high Dam, the intense heatline cells are seen for the Cases 1-2 (concave) and Cases 1-3 (convex). Overall, the Case 1 (concave) offers the largest average Nusselt number ( Nur¯) at the low Dam for all Prm. At the high Dam, Nur¯ for the Case 1 (concave) is the largest involving the low Prm, whereas Nur¯ is the largest for Case 1 (convex) involving the high Prm.

Practical implications

Thermal management for flow systems involving curved surfaces which are encountered in various practical applications may be complicated. The results of the current work may be useful for the material processing, thermal storage and solar heating applications

Originality/value

The heatline approach accompanied by energy flux vectors is used for the first time for the efficient heat flow visualization during natural convection involving porous media in the curved walled enclosures involving various wall curvatures.

Details

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

Keywords

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Article

Pratibha Biswal and Tanmay Basak

This study aims to carry out the analysis of Rayleigh-Bénard convection within enclosures with curved isothermal walls, with the special implication on the heat flow…

Abstract

Purpose

This study aims to carry out the analysis of Rayleigh-Bénard convection within enclosures with curved isothermal walls, with the special implication on the heat flow visualization via the heatline approach.

Design/methodology/approach

The Galerkin finite element method has been used to obtain the numerical solutions in terms of the streamlines (ψ ), heatlines (Π), isotherms (θ), local and average Nusselt number ( Nut¯) for various Rayleigh numbers (103Ra ≥ 105), Prandtl numbers (Pr = 0.015 and 7.2) and wall curvatures (concavity/convexity).

Findings

The presence of the larger fluid velocity within the curved cavities resulted in the larger heat transfer rates and thermal mixing compared to the square cavity. Case 3 (high concavity) exhibits the largest Nut¯ at the low Ra for all Pr. At the high Ra, Nut¯ is the largest for Case 3 (high concavity) at Pr = 0.015, whereas at Pr = 7.2, Nut¯ is the largest for Case 1 (high concavity and convexity).

Practical implications

The results may be useful for the material processing applications.

Originality/value

The study of Rayleigh-Bénard convection in cavities with the curved isothermal walls is not carried out till date. The heatline approach is used for the heat flow visualization during Rayleigh-Benard convection within the curved walled enclosures for the first time. Also, the existence of the enhanced fluid and heat circulation cells within the curved walled cavities during Rayleigh-Benard heating is illustrated for the first time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Mokhtar Ferhi and Ridha Djebali

This paper aims to perform the lattice Boltzmann simulation of conjugate natural convection heat transfer, heat flow visualization via heatlines approach and entropy…

Abstract

Purpose

This paper aims to perform the lattice Boltzmann simulation of conjugate natural convection heat transfer, heat flow visualization via heatlines approach and entropy generation in a partitioned medium filled with Ag-MgO (15-85%)/water.

Design/methodology/approach

The lattice Boltzmann method (LBM) is used to predict the dynamic and thermal behaviors. Experimental correlations for dynamic viscosity and thermal conductivity versus solid volume fraction are used. The study is conducted for the ranges of Rayleigh number 103 ≤ Ra ≤ 106, the partitioner thickness 0.01 ≤ δ ≤ 0.9, its position 0.15 ≤ Xs ≤ 0.85 and the hybrid nano-suspensions volume fraction 0% ≤ ϕ ≤ 2%.

Findings

The effects of varying of controlling parameters on the convective flow patterns, temperature contours, heat transfers, the heatlines and the entropy generation are presented. It has been found that the maximum rate of heat transfer enhancement occurs for low Ra numbers (103) and is close to 13.52%. The solid thickness d and its horizontal position Xs have a substantial influence on the heat transfer rate, flow structure, heatline, total entropy generation and Bejan number. Besides, the maximum heat transfer is detected for high Ra and δ ≈ 1 and the percentage of augmentation is equal to 65.55% for ϕ = 2%. According to the horizontal position, the heat transfer remains invariant for Ra = 103 and takes a maximum value near the active walls for Ra ≥ 104. The total entropy generation increases with Ra and decreases with ϕ for Ra = 106. The increase of ϕ from 0 to 2% leads to a reduction in close to 40.76%. For this value of Ra, the entropy is the maximum for δ = 0.4 and Xs = 0.35 and Xs = 0.65%. Moreover, as the Ra increases the Bejan number undergoes a decrease. The Bejan number is the maximum for Ra = 103 independently to δ and Xs. The superior thermal performance manifests at low Ra and high value of δ independently to the positions of the conducting body.

Originality/value

The originality of this paper is to analyze the hybrid nano-additive effects on the two-dimensional conjugate natural convection in a partitioned medium using the LBM. The experimental correlations used for the effective thermal conductivity and dynamic viscosity give credibility to our study. Different approaches such as heatlines and entropy generation are used.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Kamel Hooman

The aim of this paper is to introduce a new technique for convection visualization. This is similar to Bejan's heatlines and is even an exact match to Landau and…

Abstract

Purpose

The aim of this paper is to introduce a new technique for convection visualization. This is similar to Bejan's heatlines and is even an exact match to Landau and Lifshitz's energy streamlines for two‐dimensional geometries.

Design/methodology/approach

The work benefits from a combination of numerical and analytical tools to show that, in two‐dimensional space, heatlines and energy streamlines are effectively the same. More importantly, the energy flux vectors are tracing both of them accurately; as verified for some cases of free and forced convection problems in this paper.

Findings

The new technique is easier to implement compared to the existing counterparts which are available in the literature. More specifically, the advantage of this new technique is that, contrary to heatlines and energy streamlines, it does not require further numerical analysis in addition to solving momentum and energy equations.

Originality/value

Energy flux vectors offer higher resolution compared to existing visualization tools.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Alireza Rahimi, Abbas Kasaeipoor, Emad Hasani Malekshah and Lioua Kolsi

This paper aims to perform the lattice Boltzmann simulation of natural convection heat transfer in cavities included with active hot and cold walls at the side walls and…

Abstract

Purpose

This paper aims to perform the lattice Boltzmann simulation of natural convection heat transfer in cavities included with active hot and cold walls at the side walls and internal hot and cold obstacles.

Design/methodology/approach

The cavity is filled with double wall carbon nanotubes (DWCNTs)-water nanofluid. Different approaches such as local and total entropy generation, local and average Nusselt number and heatline visualization are used to analyze the natural convection heat transfer. The cavity is filled with DWCNTs-water nanofluid and the thermal conductivity and dynamic viscosity are measured experimentally at different solid volume fractions of 0.01 per cent, 0.02 per cent, 0.05 per cent, 0.1 per cent, 0.2 per cent and 0.5 per cent and at a temperature range of 300 to 340 (K).

Findings

Two sets of correlations for these parameters based on temperature and solid volume fraction are developed and used in the numerical simulations. The influences of different governing parameters such as Rayleigh number, solid volume fraction and different arrangements of active walls on the fluid flow, heat transfer and entropy generation are presented, comprehensively. It is found that the different arrangements of active walls have pronounced influence on the flow structure and heat transfer performance. Furthermore, the Nusselt number has direct relationship with Rayleigh number and solid volume fraction. On the other hand, the total entropy generation has direct and reverse relationship with Rayleigh number and solid volume fraction, respectively.

Originality/value

The originality of this work is to analyze the two-dimensional natural convection using lattice Boltzmann method and different approaches such as entropy generation and heatline visualization.

Details

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

Keywords

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Article

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

Keywords

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Article

HamidReza KhakRah, Mehdi Mohammaei, Payam Hooshmand, Navid Bagheri and Emad Hasani Malekshah

The nanofluid flow and heat transfer within a heat exchanger, with different thermal arrangements of internal active bodies, are investigated.

Abstract

Purpose

The nanofluid flow and heat transfer within a heat exchanger, with different thermal arrangements of internal active bodies, are investigated.

Design/methodology/approach

For the numerical simulations, the lattice Boltzmann method is utilized. The KKL model is used to predict the dynamic viscosity of CuO-water nanofluid. Furthermore, the Brownian method is taken account using this model. The influence of shapes of nanoparticles on the heat transfer performance is considered.

Findings

The results show that the platelet nanoparticles render higher average Nusselt number showing better heat transfer performance. In order to perform comprehensive analysis, the heatline visualization, local and total entropy generation, local and average Nusselt variation are employed.

Originality/value

The originality of this work is carrying out a comprehensive investigation of nanofluid flow and heat transfer during natural convection using lattice Boltzmann method and employing second law analysis and heatline visualization.

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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Article

Sukanta K. Dash

The concept of a heat function is introduced to visualize the path ofheat flow in a buoyancy‐driven turbulent flow heated vertical flat plate. Thevelocities and the…

Abstract

The concept of a heat function is introduced to visualize the path of heat flow in a buoyancy‐driven turbulent flow heated vertical flat plate. The velocities and the temperature field near the vertical plate are predicted numerically, using an algebraic flux model of turbulent heat transport. As an accurate prediction of the turbulent heat flux is required in order to predict the heat function in the flow field, the use of an algebraic flux model for the turbulent heat transport θui, is made as compared with a simple eddy diffusivity hypothesis. The algebraic flux expression was closed with a low‐Re‐number‐k‐ε — θ2θ model. The solution ofthe 4 equation low‐Re‐number‐k‐ε — θ2 — εθ model predicts very well the local Nusselt number along the plate height as well as the velocity and the temperature field near the wall when compared with the experiments. Then the partial differential equation for the heat function is numerically solved to show the true path of heat flow in the buoyancy‐driven turbulent flow field near a heated vertical plate.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

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