Analysis of Entropy Generation Minimization during Natural Convection in Trapezoidal Enclosures of Various Angles with Linearly Heated Side Wall(s)

Abstract

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 = 103–105) 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 = 103), 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 = 105. Consequently, the entropy generation due to heat transfer (Sθ) and fluid friction (Sψ) also increases with Ra for all Pr. The comparison of magnitudes of Sθ and Sψ indicates that maximum entropy generation due to heat transfer (Sθ,max) and fluid friction (Sψ,max) is lower for case 1 and higher for case 2. It is found that Sθ,max occurs at the top portion of side walls in case 1, whereas Sθ,max occurs at a hot–cold junction due to a high thermal gradient in case 2. The total entropy generation, Stotal is found to be smaller in case 1 and larger in case 2 for all Pr at Ra = 105. It is observed that Sψ,max occurs at the top wall in both heating situations for Pr = 0.015 and Ra = 105. It is also found that, Sψ,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 = 105. The total entropy generation (Stotal) is larger for φ = 45° in both heating cases at high Pr (Pr = 1000). The total entropy generation (Stotal) also increases with Pr due to an increase in Sψ with Pr. It is found that, high heat transfer rate (Nub) and minimum entropy generation (Stotal) occur for square cavities at Ra = 105 for all Pr in case 1. It is observed that Stotal is smaller for case 1 compared to case 2, even though high Nub 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.