Effects of Thermal Boundary Conditions on Entropy Generation During Natural Convection in a Differentially Heated Square Cavity

2010 ◽  
Author(s):  
Ram Satish Kaluri ◽  
Tanmay Basak ◽  
A. R. Balakrishnan
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Entropy Generation ◽  
Bottom Wall ◽  
Convection Flow ◽  
Uniform Heating ◽  
Square Cavity ◽  
Fluid Friction ◽  
Thermal Boundary Conditions

Natural convection is a widely occurring phenomena which has important applications in material processing, energy storage devices, electronic cooling, building ventilation etc. The concept of ‘entropy generation minimization’, which is a thermodynamic approach for optimization, may be very useful in designing efficient thermal systems. In the current study, entropy generation in steady laminar natural convection flow in a square cavity is studied with following isothermal boundary conditions: (1) Bottom wall is uniformly heated (2) Bottom wall is sinusoidally heated. The side walls are maintained cold and the top wall is maintained adiabatic. The thermal boundary condition in non-uniform heating case (case 2) is such that the dimensionless average temperature of the bottom wall is equal to that of uniform heating case (case 1). The prime objective of this work is to investigate the influence of uniform and non-uniform heating on entropy generation. The governing mass, momentum and energy equations are solved using Galerkin finite element method. Streamlines, isotherms, contour maps of entropy generation due to heat transfer and fluid friction are studied for Pr = 0.01 (molten metals) and 7 (water) in range of Ra = 103–105. Detailed analysis on the effect of uniform and non-uniform thermal boundary conditions on entropy generation due to heat transfer and fluid friction has been presented. Also, the average Bejan’s number which indicates the relative dominance of entropy generation due to heat transfer or fluid friction and the total entropy generation are studied for each case.

Natural Convection Inside a Square Cavity Heated From Below and Symmetrically Cooled at Both Sides: Effects of Various Dirichlet Boundary Conditions at the Bottom Wall

2005 ◽  
Author(s):  
Satyajit Roy ◽  
Tanmay Basak
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Transfer Rate ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Bottom Wall ◽  
Uniform Heating ◽  
Square Cavity ◽  
Rayleigh Numbers

A numerical study is performed 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. 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 the 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 rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained.

Effect of the Temperature Difference Aspect Ratio on Natural Convection in a Square Cavity for Nonuniform Thermal Boundary Conditions

2007 ◽  
Vol 129 (12) ◽  
pp. 1723-1728 ◽  
Author(s):  
M. Sathiyamoorthy ◽  
Tanmay Basak ◽  
S. Roy ◽  
N. C. Mahanti
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Temperature Difference ◽  
Heat Transfer Process ◽  
Bottom Wall ◽  
Maximum Temperature ◽  
Convection Flow ◽  
Square Cavity ◽  
Thermal Boundary Conditions

The present numerical investigation deals with steady natural convection flow in a closed square cavity when the bottom wall is sinusoidal heated and vertical walls are linearly heated, whereas the top wall is well insulated. In the nonuniformly heated bottom wall maximum temperature TH attains at the center of the bottom wall. The sidewalls are linearly heated, maintained at minimum temperature Tc at top edges of the sidewalls and at temperature Th at the bottom edges of the sidewalls, i.e., Tc≤Th≤TH. Nonlinear coupled PDEs governing the flow have been solved by the penalty finite element method with biquadratic rectangular elements. Numerical results are obtained for various values of Prandtl number (Pr)(0.01≤Pr≤10) and temperature difference aspect ratio A=[(Th−Tc)∕(TH−Tc)](0≤A≤1) for higher Raleigh number Ra=105. Results are presented in the form of streamlines, isotherm contours, local Nusselt number, and the average Nusselt number as a function of temperature difference aspect ratio A. The overall heat transfer process is shown to be tuned efficiently with suitable selection of A.

Entropy generation optimization for MHD natural convection of a nanofluid in porous media-filled enclosure with active parts and viscous dissipation

2017 ◽  
Vol 27 (2) ◽  
pp. 379-399 ◽  
Author(s):  
M.A. Mansour ◽  
Sameh Elsayed Ahmed ◽  
Ali J. Chamkha
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Viscous Dissipation ◽  
Entropy Generation ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Convection Flow ◽  
Negative Effects ◽  
Content Type ◽  
Volume Method

Purpose This paper aims to investigate the entropy generation due to magnetohydrodynamic natural convection flow and heat transfer in a porous enclosure filled with Cu-water nanofluid in the presence of viscous dissipation effect. The left and right walls of the cavity are thermally insulated. There are heated and cold parts, and these are placed on the bottom and top wall, respectively, whereas the remaining parts are thermally insulated. Design/methodology/approach The finite volume method is used to solve the dimensionless partial differential equations governing the problem. A comparison with previously published woks is presented and is found to be in an excellent agreement. Findings The minimization of entropy generation and local heat transfer according to different values of the governing parameters are presented in details. It is found that the presence of magnetic field has negative effects on the local entropy generation because of heat transfer and the local total entropy generation. Also, the increase in the heated part length leads to a decrease in the local Nusselt number. Originality/value This problem is original, as it has not been considered previously.

Effects of complex boundary conditions on natural convection of a viscoplastic fluid

2019 ◽  
Vol 29 (8) ◽  
pp. 2792-2808 ◽  
Author(s):  
Behnam Rafiei ◽  
Hamed Masoumi ◽  
Mohammad Saeid Aghighi ◽  
Amine Ammar
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Yield Stress ◽  
Heated Wall ◽  
Uniform Heating ◽  
Content Type ◽  
Yield Stress Fluids ◽  
Complex Boundary

Purpose The purpose of this paper is to analyze the effects of complex boundary conditions on natural convection of a yield stress fluid in a square enclosure heated from below (uniformly and non-uniformly) and symmetrically cooled from the sides. Design/methodology/approach The governing equations are solved numerically subject to continuous and discontinuous Dirichlet boundary conditions by Galerkin’s weighted residuals scheme of finite element method and using a non-uniform unstructured triangular grid. Findings Results show that the overall heat transfer from the heated wall decreases in the case of non-uniform heating for both Newtonian and yield stress fluids. It is found that the effect of yield stress on heat transfer is almost similar in both uniform and non-uniform heating cases. The yield stress has a stabilizing effect, reducing the convection intensity in both cases. Above a certain value of yield number Y, heat transfer is only due to conduction. It is found that a transition of different modes of stability may occur as Rayleigh number changes; this fact gives rise to a discontinuity in the variation of critical yield number. Originality/value Besides the new numerical method based on the finite element and using a non-uniform unstructured grid for analyzing natural convection of viscoplastic materials with complex boundary conditions, the originality of the present work concerns the treatment of the yield stress fluids under the influence of complex boundary conditions.

Natural Convection in a Non-Uniformly Heated Vertical Annular Cavity

2017 ◽  
Vol 377 ◽  
pp. 189-199 ◽  
Author(s):  
M. Sankar ◽  
S. Kiran ◽  
G.K. Ramesh ◽  
Oluwole Daniel Makinde
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Outer Wall ◽  
Uniform Heating ◽  
Cylindrical Wall ◽  
Thermal Boundary Conditions ◽  
Nusselt Numbers ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference ◽  
Model Equations

Natural convection from the linearly heated inner and/or outer walls of a vertical annular cavity has been numerically investigated. The bottom wall is uniformly heated and top cylindrical wall is thermally insulated. In this analysis, we considered two different thermal boundary conditions, namely case (I) and case (II) to understand the effect of non-uniform heating of inner and/or outer walls on the convective flow and subsequently the local and global heat transfer rate. For case (I), the inner and outer walls are heated linearly, while the linearly heated inner wall and cooled outer wall is considered in case (II). An implicit finite difference scheme is applied to solve the model equations of the problem. The numerical simulations in terms of streamlines and isotherms, local and global Nusselt numbers are presented to illustrate the effects of Rayleigh number and non-uniform thermal boundary conditions for a fixed Prandtl number of Pr = 0.7.

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