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.

Tanmay Basak

Department Of Chemical Engineering

Pratibha Biswal

Natural convection

Bejan number

entropy generation

ENTROPY GENERATION ANALYSIS

HORIZONTAL WALLS

INCLINED WALLS

Rayleigh number

TOTAL ENTROPY

TRIANGULAR CAVITIES

entropy

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

Numerical Heat Transfer; Part A: Applications

Comparative study based on the entropy generation analysis has been carried out within porous square and triangular (design 1 and 2) enclosures subjected to discrete heating involving double heaters (cases 1–3) and single heater (case 0) along each side wall during natural convection for Da m = 10 -5 - 10 -2 involving Pr m = 0.015 and 7.2 at Ra m = 10 6 . Galerkin finite element method is implemented for the accurate evaluation of the entropy generation terms involving thermal and velocity gradients based on elemental basis set. Cases 1–3 are found to correspond lower values of the entropy generation compared to case 0 especially at higher values of Da m . © 2018, © 2018 Taylor & Francis Group, LLC.

Role of multiple discrete heaters on the entropy generation during natural convection in porous square and triangular enclosures

The aim of the present investigation is to analyze the effect of the motion of horizontal walls on the entropy generation and heat transfer rates in an entrapped triangular porous cavity during mixed convection. Two different thermal boundary conditions are considered as follows: (i) hot inclined walls and cold horizontal walls and (ii) cold inclined walls and hot horizontal walls. Overall, Re = 100 may be recommended at Prm = 0.026, 7.2, Gr = 105, and Dam = 10−4 to 10−2 within the upper and lower cavities for cases 1 and 2. © 2017 Taylor & Francis.

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

The entropy generation minimization (EGM) technique is an important tool for the optimization of the thermal systems via the analysis of the associated irreversibilities measured by the entropy generation. This article presents a detailed review of works on the entropy generation analysis during natural convection in various enclosures and processes involving different practical applications. The mathematical formulations of the fundamental governing equations for natural convection followed by the equations of the entropy generation are presented. The calculation procedure of the entropy generation for various test cases is reported briefly with the finite difference and finite volume techniques for some test cases and the detailed discussion of the evaluation of the entropy generation via the finite element method is addressed. Further, the problem formulation and results in terms of the entropy generation are discussed for natural convection in enclosures of various shapes (square/rectangular, trapezoidal, triangular, parallellogrammic/rhombic, curved/wavy). The brief discussion on the entropy generation analysis during various practical applications is also addressed. Overall, the minimum entropy generation vs enhanced heat transfer rate is the main issue in all the case studies with various enclosures involving a number of practical applications to achieve the optimal configuration with the high energy efficiency. The need of the renewable energy is increasing day by day. Thus, the conversion of the renewable energy to a useful form is one of the most challenging processes and natural convection plays an important role in the conversion. The loss of the available energy via the entropy production during natural convection is highly important for the design of suitable energy systems. This review article further provides basis for future research on the entropy generation analysis during natural convection in order to improve the energy efficiency which may be applicable for various renewable energy systems. © 2017 Elsevier Ltd

Renewable and Sustainable Energy Reviews

Entropy generation vs energy efficiency for natural convection based energy flow in enclosures and various applications: A review

A detailed study on natural convection heat transfer within porous trapezoidal enclosures has been carried out for two different cases. The effect of linearly heated side walls on flow pattern is investigated in case 1; whereas, the effect of linearly heated left wall and cold right wall is studied in case 2. In both cases, the bottom wall of the cavity is uniformly heated and the upper wall is adiabatic. The results are analyzed for a wide range of parameters such as Rayleigh number, Ra(103Ra106), Prandtl number, Pr(0.015 Pr988.24), and Darcy number, Da(105Da10 3). © 2013 Taylor and Francis Group, LLC.

Heatlines for visualization of heat transport for natural convection within porous trapezoidal enclosures with various wall heating

Analysis of natural convection in porous right angled triangular enclosures with a concave/ convex hypotenuse has been carried out using the Bejan's heatlines approach. A generalized non-Darcy model without Forchheimer term is employed for fluid flow in a porous matrix and the governing equations are solved by the Galerkin finite element method. The cavity is subjected to a thermal boundary condition of an isothermal cold left wall, isothermal hot curved right wall, and adiabatic bottom wall. Due to intense closed loop heatlines, thermal mixing is higher in convex cases compared to the concave case for all parameters. Average heat transfer rate is found to be largest in the concave hypotenuse case. Copyright © Taylor & Francis Group, LLC.

Analysis of convective heat flow visualization within porous right angled triangular enclosures with a concave/convex hypotenuse

Natural convection in isosceles triangular enclosures with various configurations (case 1 - inverted, case 2 - straight and case 3 - tilted) is studied via heatline analysis for linear heating of inclined walls. Detailed analysis and comparison for various base angles (φ=45°, 60°) of triangular enclosures have been carried out for a range of fluids (Pr=0.015-1000) within Ra=103-105 using Galerkin finite element method. The heat flow distributions indicate conduction dominant heat transfer at low Ra (Ra=103) for case 1 and case 2 whereas in case 3, convective heat flow is observed due to high buoyancy force. As Ra increases, enhanced thermal mixing is observed at the core of the cavity. Wall to wall heat transfer occurs at walls AB and AC due to linear heating boundary condition in all the cases. Although the distributions of fluid flow and heat flow are qualitatively similar for φ=45° and 60°, the intensity of fluid flow and heat flow decreases as φ increases. Strength of fluid flow and heat flow circulation cells is found to be higher in case 3 for identical parameters. Results show that upper side wall (AC) for case 3 exhibits higher heat transfer rates whereas heat transfer rates for walls AB and AC are the same for case 1 and case 2. Also NuAB is higher for case 2 followed by case 1 and case 3 at the middle portion of wall AB. Thus to achieve high heat transfer from fluid to wall at the central region, case 2 and case 3 configurations may be recommended at high Ra (Ra=105) and Pr, irrespective of φ. © 2013 Elsevier Ltd.

International Communications in Heat and Mass Transfer

Heatlines based natural convection analysis in tilted isosceles triangular enclosures with linearly heated inclined walls: Effect of various orientations

Analysis has been carried out for energy distribution and thermal mixing in steady laminar natural convective flow through the porous rhombic cavities with inclination angle φ for various applications such as geothermal, grain storage, electronic cooling, etc. A generalized non-Darcy model without the Forchheimer inertia term is used to predict the flow in porous media. The effect of the Darcy number (Da) and the role of φ on the energy distribution and thermal mixing within porous rhombic cavities with isothermal (case 1) and nonisothermal (case 2) hot bottom walls are illustrated via " heatlines". Heat transfer is found to be primarily conduction dominant at Da = 10 -5 even at a higher Rayleigh number (Ra = 10 6). The onset of convection occurs at Da = 10 -4, and the distorted heatlines from the hot bottom wall take a longer path to reach the cold side walls of the cavity. Larger heat transfer and thermal mixing occurs for Da = 10 -3 at Ra = 10 6 irrespective of φ and Pr. Multiple flow/convective circulations are observed at Pr = 0.015 for all φ values at Da = 10 -3. On the other hand, two asymmetric flow circulation cells are found to occupy the entire cavity at Pr = 0.7, 7.2, and 1000 for φ = 75° at Da = 10 -3. The cavity with inclination angle φ = 30° enhances the convective heat transfer from the hot wall to the cold wall, and the heat transfer to the right cold wall is a maximum for φ = 75°, as depicted by "heatlines" irrespective of Pr at Da = 10 -3. Average Nusselt number studies based on heatfunction gradients also show that the cavity with φ = 30° gives a maximum heat-transfer rate from the bottom to the left wall irrespective of Pr in case 1 at Da = 10 -3. The cup mixing temperature (θ cup) is higher for case 1 compared to case 2, and it is almost invariant with φ for higher Pr (Pr = 7.2 and 1000) in case 1 at Da = 10 -3. © 2011 American Chemical Society.

Industrial and Engineering Chemistry Research

Heatline analysis for natural convection within porous rhombic cavities with isothermal/nonisothermal hot bottom wall

Entropy generation due to natural convection in right-angled triangular enclosures filled with porous media with top angles 15° and 45° for various thermal boundary conditions (cases 1-4) has been studied numerically using Galerkin finite element method. Simulations are carried out for Pr = 0.025 and 1000 in the range of Darcy numbers 10 -5-10 -3. Note that, S θ,max is observed at vertex of the cavity for cases 1 and 3, near corner between left wall and bottom wall for case 2 and near lower portion of the right wall for case 4. It is found that, S ψ,max is observed near middle portions of the side walls for all cases and the location of S ψ,max mainly depends on the presence of high velocity gradients. The total entropy generation, S total, is found to be an increasing function of Da. It is observed that decrease in Be av with Da for both s is due to increase in fluid friction irreversibility. Analysis of the variation of Be av with Da for various fluids indicates that, higher Be av values are observed for Pr = 0.025 due to low frictional irreversibility. It is observed that Θ cup decreases with Da for all Pr due to decrease in thermal mixing. It is found that, the maximum heat transfer rate ( Nul or Nur) occurs for = 15° cavities compared to = 45° cavities at Da = 10 -3 in both isothermal and linear heating cases for all Pr due to larger thermal gradients at = 15°. Overall, triangular cavities with = 15° may be the optimal top angle for right angled triangular enclosure for thermal processing of all types of fluids (Pr = 0.025 and 1000) due to its high heat transfer rate ( Nul or Nur), high thermal mixing (high Θ cup) and less total entropy generation (S total) for all heating strategies (cases 1-4) especially at Da = 10 -4. © 2012 Elsevier Ltd. All rights reserved.

Journal	Data powered by TypesetNumerical Heat Transfer; Part A: Applications
Publisher	Data powered by TypesetTaylor and Francis Ltd.
ISSN	10407782
Open Access	No