Analysis of natural convection in porous triangles have many important energy related applications in geophysical and solar energy fields. A numerical study on heat distribution and thermal mixing during steady laminar natural convective flow inside a right-angled triangular enclosure filled with porous media subjected to various wall boundary conditions is investigated in this study using Bejan's heatlines approach. Influence of various thermal boundary conditions and inclination angles (φ) on evaluation of complex heat flow patterns are studied as a function of Darcy numbers (Da) for various regimes of Prandtl (Pr) and Rayleigh (Ra) numbers. Studies illustrate that maximum heat transfer occurs at the top vertex for lower top angle (φ=15°) at higher Da (Da=10-3). As φ increases to 45°, the maximum heat flux at the top vertex decreases and thermal mixing increases irrespective of Da and Pr. The enhanced convection at higher Da significantly affects the heat flow distribution, which is clearly depicted by high local Nusselt numbers at Da=10-3. It is also found that isothermal heating of walls enhances the heat distribution and thermal mixing. Overall, it is shown that heatlines provide suitable guideline on thermal management in porous right-angled triangular enclosures with various heating strategies. © 2011 Elsevier Ltd.

Tanmay Basak

Department Of Chemical Engineering

Ram Satish Kaluri

Boundary conditions

Heat flux

heating

Natural convection

Nusselt number

Porous materials

Solar energy

Temperature control

DARCY-FORCHHEIMER MODEL

HEATLINES

LINEAR HEATING

NATURAL CONVECTIVE FLOW

TRIANGULAR ENCLOSURE

Enclosures

BOUNDARY CONDITION

convection

DARCY LAW

Energy efficiency

GEOPHYSICS

Heat flow

Linearity

numerical model

porous medium

Rayleigh number

temperature effect

CALLUNA VULGARIS

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Energy

Efficient visualization techniques are required to understand the flow physics for any numerical simulation. For convective heat transfer problems, most widely used techniques to visualize the fluid flow and heat transfer are streamlines and isotherms respectively. These methods are not sufficient to address the degrees of complexity associated with the complicated convective problems. Thus, different visualization techniques have been developed to represent the results depending on the problem. In this article, an effort has been made to collate visualization techniques in literature for convective heat transfer system like, heatlines, energy streamlines, energy flux vectors, proper orthogonal decomposition (POD), Poincare map etc. The fundamentals of different techniques are briefly discussed, applications of these techniques are shown with proper examples. The usefulness and limitations of these techniques are also discussed. Heatline is found to be the best visualization tool for two dimensional steady situations. However, in 3D and transient scenario Lagrangian approach or POD can be used. © 2017 Elsevier Ltd

International Journal of Heat and Mass Transfer

Heatlines and other visualization techniques for confined heat transfer systems

Natural convection in an enclosure (internal convection) is an important problem due to its significant practical applications. In energy related applications, natural convection plays a dominant role in transport of energy for the proper design of enclosures in order to achieve higher heat transfer rates. This review summarizes the studies on natural convection heat transfer in triangular, trapezoidal, parallelogrammic enclosures and enclosures with curved and wavy walls filled with fluid or porous media. In addition, this review also summarizes the natural convection studies in the nanofluid filled enclosures. Studies have been performed for the enclosures subjected to different thermal boundary conditions. A number of the studies demonstrated that the variation of the aspect ratio and base angle of the triangular and rhombic/parallelogrammic enclosures had a wide influence on the flow distribution pattern. In the trapezoidal enclosure, the aspect ratio of the cavity as well as the presence of the baffles along the walls played a significant role in the temperature and flow distribution. The flow patterns within the complex enclosures were found to be largely dependent on the amplitude-wavelength ratio and number of undulations of the wavy walls. In addition, the researchers have also studied the effect of the various parameters such as the Rayleigh numbers, Prandtl numbers, Darcy numbers, Darcy–Rayleigh number, irreversibility distribution ratios, volume fraction of the nanoparticles, etc. Overall, the current review paper presents an useful insight into the potential strategies for enhancing the convection heat transfer performance. © 2016 Elsevier Ltd

Studies on natural convection within enclosures of various (non-square) shapes – A review

Entropy generation analysis is carried out during natural convection within entrapped porous triangular cavities for two cases based on the heating or cooling of the inclined and horizontal walls (case 1: hot inclined walls with cold horizontal walls and case 2: cold inclined walls with hot horizontal walls). The results are plotted in terms of the isotherms (θ), streamlines (ψ), and entropy generation maps (Sθ and Sψ). The total entropy generation (Stotal), average Bejan number (Beav), and average Nusselt number (or) as a function of Darcy number (Dam) at a high Rayleigh number (Ram = 106) have been studied for both cases 1 and 2 and the optimal case is recommended based on least Stotal and largest or. © 2016 Taylor & Francis Group, LLC.

Numerical Heat Transfer; Part A: Applications

Analysis of entropy generation during natural convection within entrapped porous triangular cavities during hot or cold fluid disposal

The strategic application of entropy generation concept for optimization of the natural convection process has been studied in the present work. The wall, AB is isothermally heated and walls, BC and DA are cooled in presence of adiabatic wall CD. The numerical results are presented in terms of isotherms (θ), streamlines (ψ) and entropy generation maps for heat transfer (S<inf>θ</inf>) and fluid flow (S<inf>ψ</inf>) for various modified Prandtl numbers (Pr<inf>m</inf>=0.015 and 1000), modified Darcy numbers (Da<inf>m</inf>=10-5--10-2) and modified Rayleigh numbers (Ra<inf>m</inf>=103 and 106). The maximum value of the entropy generation due to heat transfer (S<inf>θ, max</inf>) is observed at hot and cold junction points (A and B), due to high temperature gradient, irrespective of Da<inf>m</inf>, Pr<inf>m</inf> and inclination angles (ϕ). The active regions of S<inf>θ</inf> occur at top portion of the walls, BC and DA at high Da<inf>m</inf>(Da<inf>m</inf>=10-2) and high Pr<inf>m</inf>(Pr<inf>m</inf>=1000). The maximum value of entropy generation due to fluid flow (S<inf>ψ, max</inf>) is found at various locations on the walls of the cavity whereas significant S<inf>ψ</inf> is also observed in the interior regions due to the friction between counter rotating circulation cells. The heat transfer rate along the wall AB (Nu<inf>AB</inf>) and the total entropy generation (S<inf>total</inf>) are found to be constant for the conduction dominant regime (10-5≤Da<inf>m</inf>≤10-3) whereas non linear increasing trends are observed for convection dominant regime (10-3≤Da<inf>m</inf>≤10-2). The inclination angle ranges, 30° ≤ ϕ ≤ 50° and 25° ≤ ϕ ≤ 75° are optimal tilt angles for Pr<inf>m</inf>=0.015 and 1000, respectively based on minimum entropy generation and reasonable heat transfer rate at high Da<inf>m</inf>(Da<inf>m</inf>=10-2) with Ra<inf>m</inf>=106. © 2015 Taiwan Institute of Chemical Engineers.

Journal of the Taiwan Institute of Chemical Engineers

Role of entropy generation on thermal management during natural convection in tilted porous square cavities

Heatline concept has been used in order to estimate thermal performance of various energy related systems. Heatlines and streamlines are found to be adequate to visualize and understand heat distribution and thermal mixing occurring inside a inclined porous square cavity. At high Darcy number, Dam (Dam=10-2), heatlines take the shapes of streamlines at the central core of the cavity resulting in enhanced thermal mixing as seen from closed convective heatline cells with high magnitudes. Heat transfer rates are discussed based on local and average Nusselt numbers and further, these are adequately explained based on heatlines. The inclined cavity with higher inclination angle (φ=75°) provides the higher Nu-<inf>BC</inf> whereas higher Nu-<inf>DA</inf> is observed for the small inclination angles (φ=15°) at Dam=10-2. Note that, BC and DA denote the right and left walls, respectively. The larger inclination angle may be optimal for the energy efficient processes involving inclined enclosures due to larger heat flow circulations with enhanced thermal mixing. © 2015 Elsevier Ltd.

Heatlines and thermal management analysis for natural convection within inclined porous square cavities

In this paper, the numerical investigation of natural convection in a porous trapezoidal enclosures has been performed for uniformly or non-uniformly heated bottom wall. Penalty finite element analysis with bi-quadratic elements is used for solving the Navier-Stokes and energy balance equations. The numerical solutions are studied in terms of streamlines, isotherms, heatlines, local and average Nusselt numbers for a wide range of parameters Da(10 -5-10-3), Pr(0.015-1000) and Ra(Ra = 10 3-106). At low Darcy number (Da = 10-5), heat transfer is primarily due to conduction for all 's as seen from the heatlines which are normal to the isotherms. As Da increases to 10-4, convection is initiated and the thermal mixing has been observed at the central regime for all 's. Distribution of heatlines illustrate that most of the heat transport for high Darcy number (Da = 10-3) occurs from hot bottom wall to the top portion of cold side walls. It has been found that secondary circulations appear at the top corners of the cavity for = 45°, 60° and bottom corners of the cavity for = 90° with Pr = 0.015, Da = 10-3 and Ra = 106. The physical interpretation of local and average Nusselt numbers are illustrated using heatlines. For uniformly heated bottom wall with cold side walls, Nub values are maximum near the corners of bottom wall for all 's irrespective to Da and Pr. In contrast, for non-uniformly heated bottom wall, the local Nusselt number (Nub) is found to be minimum near the corners of bottom wall and that is also found to be a sinusoidal variation with distance at high Da for all angles (). The Nu s distribution is similar in both cases along the side wall except near the junction of hot and cold wall for all 's. Overall, heat transfer analysis for bottom and side walls is presented in terms of average Nusselt numbers (Nub,Nus). The critical Ra numbers corresponding to the onset of convection are obtained at Da = 10-3 for Pr(0.015-1000). For Da = 10-3, average Nusselt numbers (Nub and Nus) increase exponentially beyond the critical Ra. Overall, the heat transfer rate is large for square cavity ( = 90°) compared to other angles () irrespective of heating patterns. © 2010 Elsevier Ltd. All rights reserved.

Analysis of heatlines for natural convection within porous trapezoidal enclosures: Effect of uniform and non-uniform heating of bottom wall

Heat flow patterns in the presence of natural convection have been analyzed with Bejan's heatlines concept. Momentum and energy transfer are characterized by streamfunctions and heatfunctions, respectively such that streamfunctions and heatfunctions satisfy the dimensionless forms of momentum and energy balance equations, respectively. Finite element method has been used to solve the velocity and thermal fields and the method has also been found robust to obtain the streamfunction and heatfunction accurately. The unique solution of heatfunctions for situations in differential heating is a strong function of Dirichlet boundary condition which has been obtained from average Nusselt numbers for hot or cold regimes. The physical significance of heatlines have been demonstrated for a comprehensive understanding of energy distribution and optimal thermal management via analyzing three cases. Case 1 involves the uniform and non-uniform heating of bottom wall with cooled side walls. The studies illustrate that the heat flow primarily occurs from the central regime of the bottom wall to a very small regime of the top portion of side walls. A large portion of central regime of cold side walls do not receive significant amount of heat. In order to maximize the thermal energy distribution, the distributed heating at the middle portions of the bottom and side walls have been considered in case 2 and heatlines clearly depict the distributions of heat from the hot walls to the large regimes of the cold wall. Further case 3 illustrates the enhanced heat flows in presence of heated bottom and left side walls. Heatline is found as an effective numerical tool to visualize energy distribution in order to establish a suitable heating strategy. © 2007 Elsevier Ltd. All rights reserved.

Role of 'Bejan's heatlines' in heat flow visualization and optimal thermal mixing for differentially heated square enclosures

Thermal radiation role in conjugate heat transfer across a multiple-cavity building block

Numerical simulation of mass and energy transport phenomena in solid oxide fuel cells

Optimization principles for convective heat transfer

Heatline based thermal management for natural convection within right-angled porous triangular enclosures with various thermal conditions of walls

Journal	Data powered by TypesetEnergy
Publisher	Data powered by TypesetElsevier Ltd
ISSN	03605442
Open Access	No