Analysis of Entropy Generation due to Natural Convection in Rhombic Enclosures

One way of increasing the energy efficiency in thermal processing of materials is to reduce exergy losses due to irreversibilities, measured as “entropy generation”. In this study, an analysis of entropy generation during natural convection in rhombic enclosures with various inclination angles (φ = 30°, 45°, and 75°) has been carried out for the efficient thermal processing of various fluids (Prandtl numbers of Pr = 0.015, 0.7, 7.2, and 1000) in a range of Rayleigh numbers ( Ra = 10 3 –10 5 ). The enclosure is bounded by an adiabatic top wall, cold side walls, and an isothermally (case 1) and nonisothermally (case 2) heated bottom wall. Isotherms (θ), streamlines (ψ), and entropy generation contours due to heat transfer ( S θ ) and fluid friction irreversibility ( S ψ ) are analyzed for both cases. At low Rayleigh number ( Ra = 10 3 ), the entropy generation in the cavity is dominated by S θ for all φ, irrespective of Pr . As Ra increases to 10 5, the fluid flow intensifies and S ψ also increases for all φ, irrespective of Pr . The total entropy generation ( S total ), average Bejan number ( Be av ), and average heat-transfer rate ( Nu b ) are plotted for Rayleigh number ranges of 10 3 ≤ Ra ≤ 10 5 . The total entropy generation ( S total ) is found to be low for φ = 30° and high for φ = 75° for all Pr values at Ra = 10 5 . Analysis of variations of Be av with Ra for high- Pr fluids indicates that S ψ contributes significantly for increase in S total . It is also found that the largest heat-transfer rate ( Nu b ) corresponds to minimum entropy generation ( S total ) for φ = 30° cavities at Ra = 10 5 with all Pr in case 1. The nonisothermal heating strategy (case 2) is energy efficient, because of its lower S total value, corresponding to low Nu b, which is due to a lesser heating effect than case 1 for all φ. Overall, rhombic cavities with φ = 30° may be the optimal geometrical design for thermal processing of all types of fluids ( Pr = 0.015, 0.7, 7.2, and 1000), irrespective of the heating strategy.