A penalty finite-element-based study has been carried out for natural-convection flow in a trapezoidal cavity with uniformly heated bottom wall and linearly heated and/or cooled vertical wall(s) in the presence of an insulated top wall. For linearly heated side walls, symmetry in flow patterns is observed, whereas secondary circulation is observed for the linearly heated left wall and cooled right wall. The local Nusselt number indicates reversal of heat flow at the side walls or the left wall. The average Nusselt number versus Rayleigh number illustrates that the overall heat transfer rate at the bottom wall is larger for the linearly heated left wall and cooled right wall.

Satyajit Roy

Department of Mathematics

Tanmay Basak

Department Of Chemical Engineering

E. Natarajan

Flow patterns

Natural convection

Nusselt number

Heat transfer rates

Rayleigh number

Trapezoidal cavity

Boundary conditions

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IIT Madras

Effect of Various Thermal Boundary Conditions on Natural Convection in a Trapezoidal Cavity with Linearly Heated Side Wall(s)

Numerical Heat Transfer, Part B: Fundamentals

Entropy generation during natural convection in trapezoidal enclosures with various inclination angles (φ), φ = 45°, 60°, and 90° for uniformly heated bottom wall and insulated top wall with linearly heated side walls (case 1) or linearly heated left wall with cold right wall (case 2) have been investigated numerically using penalty finite element method. Parametric studies for the wide range of Rayleigh numbers (Ra = 10 3-10 5) and Prandtl numbers (Pr = 0.015-1000) have been performed. Symmetry in flow pattern is observed for case 1. During the conduction regime at low Ra (Ra = 10 3), the entropy generation in the cavity is dominated by heat transfer irreversibility for all Pr. The strength of fluid flow increases with Ra and that leads to an increase in thermal energy transport due to enhanced convection at Ra = 10 5. Consequently, the entropy generation due to heat transfer (S θ) and fluid friction (S ψ) also increases with Ra for all Pr. The comparison of magnitudes of S θ and S ψ indicates that maximum entropy generation due to heat transfer (S θ,max) and fluid friction (S ψ,max) is lower for case 1 and higher for case 2. It is found that S θ,max occurs at the top portion of side walls in case 1, whereas S θ,max occurs at a hot-cold junction due to a high thermal gradient in case 2. The total entropy generation, S total is found to be smaller in case 1 and larger in case 2 for all Pr at Ra = 10 5. It is observed that S ψ,max occurs at the top wall in both heating situations for Pr = 0.015 and Ra = 10 5. It is also found that, S ψ,max is observed near side walls in case 1, whereas that is observed near the right cold wall in case 2 for Pr = 0.7 and 1000 at Ra = 10 5. The total entropy generation (S total) is larger for φ = 45° in both heating cases at high Pr (Pr = 1000). The total entropy generation (S total) also increases with Pr due to an increase in S ψ with Pr. It is found that, high heat transfer rate (Nu b) and minimum entropy generation (S total) occur for square cavities at Ra = 10 5 for all Pr in case 1. It is observed that S total is smaller for case 1 compared to case 2, even though high Nu b is observed at case 2 for all φs. The inclination angle (φ) has almost identical effect on entropy production rate for 45° ≤ φ ≤ 60° within the entire range of Pr at all Ra. © 2012 American Chemical Society.

Industrial and Engineering Chemistry Research

Analysis of entropy generation minimization during natural convection in trapezoidal enclosures of various angles with linearly heated side wall(S)

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.

International Journal of Heat and Mass Transfer

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

A penalty finite element analysis with bi-quadratic rectangular elements is performed to investigate the influence of uniform and non-uniform heating of wall(s) on natural convection flows in a square cavity. In the present investigation, one vertical wall and the bottom wall are uniformly and non-uniformly heated while the other vertical wall is maintained at constant cold temperature and the top wall is well insulated. Parametric study for a wide range of Rayleigh number (Ra), 103 ≤ Ra ≤ 106 and Prandtl number (Pr), 0.2 ≤ Pr ≤ 100 shows consistent performance of the present numerical approach to obtain the solutions as stream functions and temperature profiles. Heat transfer rates at the heated walls are presented in terms of local Nusselt number. © 2005 Elsevier Ltd. All rights reserved.

International Journal of Engineering Science

Finite element analysis of natural convection flows in a square cavity with non-uniformly heated wall(s)

Numerical Heat Transfer, Part A: Applications

THERMOSOLUTAL TRANSFER WITHIN TRAPEZOIDAL CAVITY

International Journal of Thermal Sciences

Effects of the thermal boundary conditions at the sidewalls upon natural convection in rectangular enclosures heated from below and cooled from above

Journal of Heat Transfer

Buoyancy-Driven Flow Transitions in Deep Cavities Heated From Below

Effect of various thermal boundary conditions on natural convection in a trapezoidal cavity with linearly heated side wall(s)

Journal	Numerical Heat Transfer, Part B: Fundamentals
ISSN	10407790
Open Access	No