A comprehensive analysis based on the irreversibilities associated with the energy flow and entropy generation is highly essential for the optimization of thermal systems. Entropy generation during mixed convection process has been studied in entrapped triangular cavities for moving horizontal walls involving isothermally hot inclined walls and cold horizontal walls (case 1) or isothermally cold inclined walls and hot horizontal walls (case 2). Overall it is found that, Re = 100 may be preferred over Re → 0, Re = 1 and Re = 10 at Pr = 0.026 and 7.2, Gr = 103 − 105 within the cavities, irrespective of the cases. In addition to Re = 100, Re = 10 may be optimal for the upper cavity with case 1 and lower cavity with case 2 at Gr ≈ 105 (higher Gr regime) and Pr = 7.2 based on moderate heat transfer rates. © 2017 Elsevier Ltd

Satyajit Roy

Department of Mathematics

Tanmay Basak

Department Of Chemical Engineering

Heat transfer

Isotherms

Mixed convection

Nusselt number

Comprehensive analysis

CONVECTION PROCESS

entropy generation

Heat transfer rate

HORIZONTAL WALLS

Thermal efficiency

Thermal systems

TRIANGULAR CAVITIES

entropy

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International Communications in Heat and Mass Transfer

Role of moving horizontal walls on entropy generation during mixed convection within entrapped triangular cavities

Entropy generation during the mixed convection process have been studied in a square enclosure for various moving horizontal (cases 1a-1d) or vertical wall(s) (cases 2a-2c) where the bottom wall of the cavity is isothermally hot, side walls are cold, and the top wall is adiabatic. Simulations have been performed for Prandtl number Pr=0.026 and 7.2, Reynolds number Re=10-100, and Grashof number Gr=103-105. Results show that, in the case of the horizontally moving wall(s) (cases 1a-1d), the overall heat transfer rate Nub- and total entropy generation (Stotal) are identical for cases 1a-1d and the cup-mixing temperature (θcup) is high for case 1b at Pr=0.026, Re=100, and Gr=105. Similarly, in the case of the vertically moving wall(s) (cases 2a-2c), Nub- and Stotal are identical for cases 2a-2c with the maximum θcup occurring for the case 2a. At Pr=7.2, Gr=105, and Re=10, case 1a and case 1c are preferable for horizontally moving wall(s) and either of case 2a-2c is preferable for vertically moving wall(s). At Pr=7.2, Gr=105, and Re=100, case 1d may be preferable for the horizontally moving wall(s) and case 2a may be preferable for the vertically moving wall(s). © 2015 Elsevier Ltd.

Analysis of entropy generation on mixed convection in square enclosures for various horizontal or vertical moving wall(s)

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

Finite element simulations were carried out to analyze entropy generation during mixed convection inside square enclosures with an isothermally hot bottom wall, adiabatic top wall, and isothermally cold side walls (case 1) or linearly heated side walls (case 2), or linearly heated left wall with isothermally cold right wall (case 3) for Pr = 0.015-7.2, Re = 1-100, and Gr = 103-105. Local entropy maps are studied in detail, and the dominance of thermal (Sθ,l) and frictional (Sψ,l) irreversibility is studied using Bejan number maps. In addition, variation in total entropy generation (Stotal), average Bejan number (Beav), and average Nusselt number at the bottom wall with Gr are analyzed to correlate irreversibility and the overall heat transfer rate of the system or process. It is found that, for Pr = 0.015 and 7.2, Re = 100 may be the optimal level for higher convective heat transport with minimum entropy generation in all the cases for Gr = 103-105. Copyright © 2015 Taylor & Francis Group, LLC.

Numerical Heat Transfer; Part A: Applications

Analysis of entropy generation for mixed convection in a square cavity for various thermal boundary conditions

Finite element simulations have been performed to investigate the influence of linearly heated side wall(s) or cooled right wall on mixed convection lid-driven flows in a square cavity. It is interesting to note that multiple circulation cells appear inside the cavity with the increase of Pr for Re = 10 and Gr = 105 in the case of linearly heated side walls. For Pr = 0.015, only two circulation cells are formed inside the cavity. As Pr increases to 0.7, three circulation cells are formed inside the cavity. Further increase in Pr to 10, leads to the formation of four circulation cells inside the cavity. On the other hand, only two circulation cells are formed inside the cavity for the case of cooled right wall. A detailed analysis of flow pattern shows that as the value of Re increases from 1 to 102, there occurs a transition from natural convection to forced convection depending on the value of Gr irrespective of Pr. It is observed that the secondary vortex at the top left corner disappears for Re = 102 and Gr = 105 due to enhanced motion of the upper lid in the case of cooled right wall while a small secondary vortex exist at the bottom right corner in the case of linearly heated side walls. The local Nusselt number (Nub) plot shows that heat transfer rate is equal to 1 at the edges for the case of linearly heated side walls case and that is zero at the left edge and thereafter that increases for the case of cooled right wall. It is interesting to observe that Nub is large within 0.4 ≤ X ≤ 0.6 due to compression of isotherms for Pr = 0.7 and 10 in the case of linearly heated side wall. It is also observed that Nur or Nul exhibits oscillations especially for Pr = 10 at higher Gr due to the presence of multiple circulations. It is also observed that over(Nur, -) or over(Nul, -) vs Gr plots show oscillation for two case studies. Average Nusselt numbers at the bottom and right walls are strong functions of Grashof number at larger Prandtl numbers whereas average Nusselt number at the left wall at a specific Pr is a weaker function of Gr. © 2009 Elsevier Ltd. All rights reserved.

Analysis of mixed convection flows within a square cavity with linearly heated side wall(s)

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