I. Pop

Visualization of Heat Transport during Natural Convection Within Porous Triangular Cavities via Heatline Approach

In this article, natural convection in a porous triangular cavity has been analyzed. Bejans heatlines concept has been used for visualization of heat transfer. Penalty finite-element method with biquadratic elements is used to solve the nondimensional governing equations for the triangular cavity involving hot inclined walls and cold top wall. The numerical solutions are studied in terms of isotherms, streamlines, heatlines, and local and average Nusselt numbers for a wide range of parameters Da (10−5–10−3), Pr (0.015–1000), and Ra (Ra = 103–5 × 105). For low Darcy number (Da = 10−5), the heat transfer occurs due to conduction as the heatlines are smooth and orthogonal to the isotherms. As the Rayleigh number increases, conduction dominant mode changes into convection dominant mode for Da = 10−3, and the critical Rayleigh number corresponding to the on-set of convection is obtained. Distribution of heatlines illustrate that most of the heat transport for a low Darcy number (Da = 10−5) occurs from the top region of hot inclined walls to the cold top wall, whereas heat transfer is more from the bottom region of hot inclined walls to the cold top wall for a high Darcy number (Da = 10−3). Interesting features of streamlines and heatlines are discussed for lower and higher Prandtl numbers. Heat transfer analysis is obtained in terms of local and average Nusselt numbers (Nu l , Nu t ) and the local and average Nusselt numbers are found to be correlated with heatline patterns within the cavity.

Analysis of Entropy Generation for Mixed Convection in a Square Cavity for Various Thermal Boundary Conditions

Finite element simulations were carried out to analyze entropy generation during mixed convection inside square enclosures with an isothermally hot bottom wall, adiabatic top wall, and isothermally cold side walls (case 1) or linearly heated side walls (case 2), or linearly heated left wall with isothermally cold right wall (case 3) for Pr = 0.015–7.2, Re = 1–100, and Gr = 103–105. Local entropy maps are studied in detail, and the dominance of thermal (Sθ,l) and frictional (Sψ,l) irreversibility is studied using Bejan number maps. In addition, variation in total entropy generation (Stotal), average Bejan number (Beav), and average Nusselt number at the bottom wall with Gr are analyzed to correlate irreversibility and the overall heat transfer rate of the system or process. It is found that, for Pr = 0.015 and 7.2, Re = 100 may be the optimal level for higher convective heat transport with minimum entropy generation in all the cases for Gr = 103–105.