Analysis of thermal efficiency via analysis of heat flow and entropy generation during natural convection within porous trapezoidal cavities

Thermal management via distributions of heatlines and entropy generation for natural convection within trapezoidal cavities in presence of hot left wall, cold right wall and adiabatic horizontal walls has been studied in this article. Heat flow visualization has been carried out via heatline concept. Galerkin finite element method has been used to analyze streamlines, isotherms, heatlines, entropy generation due to fluid friction and heat transfer over wide range of parameters (10-5⩽Da⩽10-3,0.015⩽Pr⩽1000 at Ra=106). At low Darcy number (Da=10-5), conduction dominant heat transfer is found based on low magnitudes of streamlines and heatlines. Heatlines indicate that heat transfer occurs from hot left wall to cold right wall and thermal mixing is found inside the cavity. The thermal mixing is enhanced as Da increases from 10-5 to 10-3. The thermal gradients are high near the lower portion of left wall and near upper portion of right wall for Da⩾10-4 irrespective of φ and Pr and thus, thermal boundary layer thickness is small along those zones. The maximum entropy generation due to fluid friction (Sψ,max) occurs along the left wall for φ=30° and 90° irrespective of Pr whereas that occurs along the right wall for φ=60° at Da=10-3. The maximum entropy generation due to heat transfer (Sθ,max) occurs at the left edge of bottom wall irrespective of Pr and Da for φ=30° and 60° whereas that occurs at the left edge of bottom wall and right edge of top wall for φ=90° with Da=10-5 and 10-4. At φ=90° with Da=10-3,Sθ,max occurs along both side walls for Pr=0.015 whereas that occurs along left wall for Pr=1000. It is found that total entropy generation is high for Pr=1000 compared to that of Pr=0.015 at higher Da. It is also found that the trapezoidal cavities with φ=60° and 90° correspond to less entropy generation with significant heat transfer rates at Da=10-3 for Pr=0.015 and Pr=1000 and thus the trapezoidal cavities with φ⩾60° may be the optimal design for thermal processing of Pr=0.015 and Pr=1000 fluids.