Natural convection in rhombic enclosures with isothermally heated side or bottom wall: Entropy generation analysis

Abstract The energy efficient convection systems can be designed by reducing exergy losses. In this context, the analysis on the entropy generation during natural convection in the fluid-filled (Prandtl number, Pr=0.015-1000) rhombic enclosures with various inclination angles (φ) has been carried out for the efficient thermal processing in various applications such as the chemical reactor modeling, underground coal gasification, and nuclear reactors. The enclosure is subjected to the differential heating (case 1) and Rayleigh-Benard convection (case 2). The conduction based static solution occurs only for φ=90° and it is observed that the conduction based static solution disappears with a slight perturbation of φ at Rayleigh number, Ra≥2×10³ irrespective of Pr in case 2. The active zones of the heat transfer irreversibility (^Sθ) and fluid friction irreversibility (^Sψ) are found to occur near the isothermal walls for all φs irrespective of Pr in both the cases at Ra=10⁵. In addition, the active zones of ^Sψ are also found to occur near the adiabatic walls of the cavity for all φs irrespective of Pr in both the cases at Ra=10⁵. Also, the region between the fluid layers of primary circulation cells acts as the strong active zone of ^Sψ for all φs in case 2 at lower Pr (Pr=0.015) and Ra=10⁵. The total entropy generation (^Stotal) and maximum heat transfer rates (Nu¯) are found to be significantly low for φ=30° in both the cases at Ra=10⁵ irrespective of Pr. Analysis of heating patterns and geometrical orientations relates the exergy to irreversibilities which establishes that the rhombic cavity (φ=30°) with the differential heating pattern may be the optimal design based on the energy efficient perspective.