A detailed analysis is carried out on the role of heatlines and energy flux vectors for the heat flow visualization in various enclosures involving natural convection. The three classes of enclosures [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)] have been considered as test cases to study the role of heatlines and energy flux vectors. The bottom wall is maintained as isothermally hot whereas the side and the top walls are isothermally cooled. Heatlines and energy flux vectors do explain adequately the convective heat transfer at the core. The dense energy flux vector may explain the zone of large temperature gradient or the sparse energy flux vectors may explain the low thermal gradient. However, heatlines clearly illustrate the heat flow paths due to conduction and convection. Although, energy flux vectors are simpler to implement compared to heatlines, the thermal management based on heat distribution in various regions of the enclosure can be clearly elaborated via heatlines. © 2019 Elsevier Ltd

Tanmay Basak

Department Of Chemical Engineering

Leo Lukose

Enclosures

Isotherms

Natural convection

thermal gradients

Vectors

BOTTOM WALL

Conduction and convections

Convective heat transfer

ENERGY FLUXES

HEAT DISTRIBUTION

HEAT FLOW PATH

HEATLINES

LOW-THERMAL GRADIENTS

flow visualization

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IIT Madras

International Communications in Heat and Mass Transfer

The role of multiple discrete solar heaters have been studied for energy efficiency in the heating of fluids. Current work involves natural convection studies with the various locations of the double heat sources along each side wall of the triangular-design 1 (regular isosceles triangle), triangular-design 2 (inverted isosceles triangle) and square enclosures for various cases (case 1: larger heater in lower half and smaller heater in central half, case 2: larger heater in central half and smaller heater in lower half, case 3: two heaters of identical lengths are located at the central and lower halves) involving various fluids (Pr=0.015 and 7.2) for various Rayleigh numbers, 103≤Ra≤105. The thermal mixing and energy flow in the cavities are visualized using the mathematical tool of heatlines. Also, the overall rate of heat transfer in conduction and convection dominant regimes is evaluated using Nusselt numbers (average and local). The case 2 discrete heating configuration is inferred as the optimal heating configuration based on the larger zone of uniform temperature and thermal mixing. Also, the thermal management is significantly improved in triangular-design 2 and square cavities. © 2017 Elsevier Ltd

Renewable Energy

Role of multiple solar heaters along the walls for the thermal management during natural convection in square and triangular cavities

Abstract Current work attempts to study the heatline patterns during natural convection for different types of Dirichlet heatfunction boundary conditions. The enclosures with various shapes (square, curved, trapezoidal, tilted square and parallelogrammic) are considered with various thermal boundary conditions such as (a) case 1: hot left wall, cold right wall and adiabatic horizontal walls, (b) case 2: hot bottom wall, cold left and right walls and adiabatic top wall and (c) case 3: hot bottom wall with other cold walls. Traditionally, the reference of heatfunction (Π=0) is assumed at the adiabatic wall and the implementation of reference (Π=0) may be non-trivial for the case with zero or multiple adiabatic wall(s). Various heatfunction boundary conditions have been formulated based on locations of Π=0 for systems with more than one adiabatic walls (case 1) or no adiabatic wall (case 3). As test problems, Π=0 is considered at the junctions of isothermal walls (cases 2 and 3) or on the isothermal wall (case 3). The governing equations are solved via the Galerkin finite element method at various Rayleigh numbers (103 and 105) and Prandtl numbers (Pr=0.015 and 7.2). The magnitudes of the heatfunctions change drastically with the location of the datum of Π (Π=0) whereas, the heat flow patterns remain same irrespective of the heatfunction boundary conditions. The gradients of heatfunctions or the heat flux along the active walls (hot/cold) are invariant of the choice of the reference (Π=0). The local and average Nusselt numbers are also independent of the choice of Π=0 and the Nusselt numbers are found to be identical with heatfunction gradients obtained with various locations of Π=0. Current work may be useful for heat flow visualization in various thermal systems involving complex thermal boundary conditions. © 2015 Elsevier Ltd.

International Journal of Heat and Mass Transfer

Sensitivity of heatfunction boundary conditions on invariance of Bejan's heatlines for natural convection in enclosures with various wall heatings

Numerical simulation for natural convection flow in fluid filled enclosures with curved side walls is carried out for various fluids with several Prandtl numbers (Pr=0.015, 0.7 and 1000) in the range of Rayleigh numbers (Ra=103-106) for various cases based on convexity/concavity of the curved side walls using the Galerkin finite element method. Results show that patterns of streamlines and heatlines are largely influenced by wall curvature in concave cases. At low Ra, the enclosure with highest wall concavity offers largest heat transfer rate. On the other hand, at high Ra, heatline cells are segregated and thus heat transfer rate was observed to be least for highest concavity case. In convex cases, no significant variations in heat and flow distributions are observed with increase in convexity of side walls. At high Ra and Pr, heat transfer rate is observed to be enhanced greatly with increase in wall convexity. Results indicate that enhanced thermal mixing is observed in convex cases compared to concave cases. Comparative study of average Nusselt number of a standard square enclosure with concave and convex cases is also carried out. In conduction dominant regime (low Ra), concave cases exhibit higher heat transfer rates compared to square enclosure. At high Ra, low Pr, concave cases with P1P1'=0.4 is advantageous based on flow separation and enhanced local heat transfer rates. © 2013 Elsevier Ltd.

Energy

Bejan's heatlines and numerical visualization of convective heat flow in differentially heated enclosures with concave/convex side walls

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

A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 103 ≤ Ra ≤ 105 and Prandtl number Pr, 0.7 ≤ Pr ≤ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented. © 2006 Elsevier Ltd. All rights reserved.

Effects of thermal boundary conditions on natural convection flows within a square cavity

Heatlines vs energy flux vectors: Tools for heat flow visualization

Journal	Data powered by TypesetInternational Communications in Heat and Mass Transfer
Publisher	Data powered by TypesetElsevier Ltd
ISSN	07351933
Open Access	No