An entropy generation analysis of horizontal convection under the centrifugal buoyancy approximation

Abstract

An entropy generation analysis is conducted for horizontal convection under the centrifugal buoyancy and the Boussinesq approximations in a relatively shallow enclosure at a fixed Prandtl number of unity to characterise irreversible losses across the conduction and convection-dominated regimes using the Bejan number (Be). A variable irreversibility distribution factor is expressed for the entropy generation analysis as a ratio of the Brinkman number (Br) and the Gay-Lussac (Ga) parameter for the first time. Governing equations are solved numerically using a high-order nodal spectral-element method. Calculations are performed at a fixed Br = 2 × 10−5 over the physical range of the Gay-Lussac parameter 0 ≤ Ga ≤ 2 up to Ra = 5 × 108. As expected, increasing the Rayleigh number shifts the flow toward a convection-dominated regime; however it is found that increasing the Gay-Lussac parameter draws the heat transfer mechanism back to a conduction-dominated state. In other words, advection related buoyancy effects act to keep the buoyancy-driven flow in conduction-dominated regime. The entropy generation analysis indicates that at Ga ≳ 0.5 conduction and convection are in balance at Ra ≈ 6 × 105, while under the conventional Boussinesq approximation (Ga = 0), heat transfer is convection-dominated. The transition of the average Bejan number from conduction to convection-dominated regime follows closely to a reciprocal scaling against Rayleigh number Beave~Ra−1 when Ga = 0 but the same process scales with Beave~Ra−0.5 relation at Ga = 2.