Bio: Pratibha Biswal is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Natural convection & Heat transfer. The author has an hindex of 10, co-authored 29 publications receiving 310 citations. Previous affiliations of Pratibha Biswal include Indian Institute of Petroleum & Shiv Nadar University.
TL;DR: In this paper, a detailed review of works on the entropy generation analysis during natural convection in various enclosures and processes involving different practical applications is presented, where the mathematical formulations of the fundamental governing equations for natural convections followed by the equations of entropy generation are presented.
Abstract: 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.
TL;DR: In this article, the authors studied the heatline patterns during natural convection for different types of Dirichlet heatfunction boundary conditions and showed that the heat flow patterns remain unchanged irrespective of the heat function boundary conditions.
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 ( 10 3 and 10 5 ) 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.
TL;DR: In this article, an analysis of natural convection within inclined porous square cavities for various inclination angles ( φ = 15 °, 30 ° and 60 ° ) is carried out via the heatline and entropy generation approaches.
Abstract: Analysis of natural convection within inclined porous square cavities for various inclination angles ( φ = 15 ° , 30 ° and 60 ° ) is carried out via the heatline and entropy generation approaches. The cases 1 and 2 correspond to the isothermal and non-isothermal heating of the bottom wall, respectively, involving the cold side walls and adiabatic top wall. The governing equations are solved via the Galerkin finite element method to obtain the results in terms the isotherms (θ), streamlines (ψ), heatlines (Π), entropy generation maps ( S θ and S ψ ), total entropy generation (Stotal), average Bejan number (Beav) and average Nusselt number ( Nu ¯ AB ) at various Darcy numbers ( 10 − 5 ≤ Da m ≤ 10 − 2 ) , Prandtl numbers (Prm=0.025 and 998.24) at Rayleigh number, Ra m = 10 6 . The locations of S θ , max and S ψ , max are identified and the magnitudes of S θ , max and S ψ , max are larger for the case 1 compared to those for the case 2 involving all Dam, Prm and φ. Also, the magnitudes of Stotal, Beav and Nu ¯ AB are larger for the case 1 compared to the case 2. The case 2 is the efficient heating strategy with the optimal thermal management compared to the case 1 based on significantly lesser Stotal for all Dam, Prm and φ. The optimal φ involving the lesser Stotal and larger Nu ¯ AB is highly influenced by Dam and Prm. Various ranges of the optimal φ involving the higher thermal efficiency are identified for different Dam and Prm for each of the cases (cases 1 and 2).
TL;DR: In this paper, the Galerkin finite element method was used to simulate convexity/concavity of the curved side walls of a fluid filled enclosing with a curved side wall.
Abstract: 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 = 10 3 –10 6 ) 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 P 1 P 1 ′ = 0.4 is advantageous based on flow separation and enhanced local heat transfer rates.
TL;DR: In this paper, the authors performed an entropy analysis of differentially heated enclosures with curved (concave/convex) side walls via entropy generation analysis and found that the concave cases with high concavity (case 3) may be chosen as the energy efficient case at high Ra and high Pr.
Abstract: Computational study of natural convection within differentially heated enclosures with curved (concave/convex) side walls is carried out via entropy generation analysis. Numerical simulation has been carried out for various Prandtl numbers ( Pr = 0.015 and 1000) and Rayleigh numbers ( 10 3 ⩽ Ra ⩽ 10 5 ) with different wall curvatures. Results are presented in terms of isotherms ( θ ) , streamlines ( ψ ) , entropy generation due to heat transfer ( S θ ) and fluid friction ( S ψ ) . The effects of Rayleigh number on the total entropy generation ( S total ) , average Bejan number ( Be av ) and global heat transfer rate ( Nu ‾ r ) are examined for all the cases. Maximum values of S θ ( S θ , max ) are found at the middle portion of the side walls for concave cases, whereas, S θ , max is observed near the top right and bottom left corner of the cavity for convex cases. On the other hand, S ψ , max is seen near the solid walls of the cavity for all concave and convex cases. At all Ra and low Pr, largest heat transfer rate and lesser entropy generation is found for case 3 (highly concave case). Overall, for convex case, case 1 or case 2 (lesser convex cases) are efficient for all Ra and Pr. On the other hand, case 3 of concave case (highly concave) offers larger heat transfer rate and lesser entropy generation compared to less concave and all convex cases at low Ra and all Pr. At high Ra and low Pr, case 3 (concave) may be the optimal case whereas, at high Ra and high Pr, case 1 (less concave) may be recommended based on higher heat transfer rate. A comparative study of the concave and convex cases also revealed that the concave cases with high concavity (case 3) may be chosen as the energy efficient case at high Ra and high Pr.
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TL;DR: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems and discusses the main points in the application to electromagnetic design, including formulation and implementation.
Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.
TL;DR: In this paper, an entropy generation analysis for the Cu-water nanofluid flow through a wavy channel over heat exchanger plat is investigated, which is expressed as a function of velocity and temperature.
Abstract: An entropy generation analysis for the Cu-water nanofluid flow through a wavy channel over heat exchanger plat is investigated. Entropy generation is expressed as a function of velocity and temperature. Governing equations, containing mass conservation, momentum and energy equations, are solved by a finite volume technique. All simulations are performed with Ansys-Fluent. The effects of physical parameters such as Reynolds number, dimensionless amplitude, nanoparticles volume fraction and wave number on the total, thermal, and viscous entropy generation rates and Bejan number are examined. The obtained results indicate that the thermal entropy generation is main term in most part of the channel, including near the wavy walls. Moreover, the rise in viscous entropy generation with Reynolds number increases with increasing dimensionless amplitude.