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To increase the efficiency of any heat transfer processes which involves heat recovery from hot fluid or removal of excess heat via processing of cold fluid, the loss in available energy due to various irreversibilities must be analyzed in terms of entropy generation. In the present study, hot or cold fluid is passed through the inclined tubes with a square cross section, and the entropy generation characteristics within the entrapped fluid in triangular space during natural convection is the subject of investigation. The tubes are surrounded by cold fluid while hot fluid is passed through the tubes and vice versa. Thus, hot inclined walls with cold horizontal walls (case 1) and cold inclined walls with hot horizontal walls (case 2) are considered as boundary conditions during convection (Ra = 103 to 105) for various fluids (Pr = 0.015, 0.7, and 1000) within/surrounded by the tubes. Entropy generation maps (S? and S?) with heat transfer characteristics (? and ?) are analyzed for both the cases. Minimum spatial active zones of S? and S? are found in the lower and upper triangles with case 1 and case 2, respectively. On the other hand, maximum spatial active zones of S? and S? are observed inside the upper and lower triangles with case 1 and case 2, respectively. High Stotal and low Beav are observed inside the upper and lower triangles for case 1 and case 2, respectively, for all Pr at Ra = 105. On the other hand, heat transfer rate and fluid flow are independent of Ra and Pr within the upper triangular cavity for case 2 and lower triangular cavity for case 1. Overall, high Pr fluids may be used inside the upper triangle with case 1 and lower triangle with case 2 within 7 � 103 ? Ra ? 5 � 104, whereas low Pr fluids may be used for upper triangle with case 2 and lower triangle with case 1 boundary conditions in the range of 104 ? Ra ? 9 � 104 for large heat transfer rates with less entropy generation. � 2013 American Chemical Society.

Entropy generation during natural convection in trapezoidal enclosures with various inclination angles (?), ? = 45�, 60�, and 90� for uniformly heated bottom wall and insulated top wall with linearly heated side walls (case 1) or linearly heated left wall with cold right wall (case 2) have been investigated numerically using penalty finite element method. Parametric studies for the wide range of Rayleigh numbers (Ra = 10 3-10 5) and Prandtl numbers (Pr = 0.015-1000) have been performed. Symmetry in flow pattern is observed for case 1. During the conduction regime at low Ra (Ra = 10 3), the entropy generation in the cavity is dominated by heat transfer irreversibility for all Pr. The strength of fluid flow increases with Ra and that leads to an increase in thermal energy transport due to enhanced convection at Ra = 10 5. Consequently, the entropy generation due to heat transfer (S ?) and fluid friction (S ?) also increases with Ra for all Pr. The comparison of magnitudes of S ? and S ? indicates that maximum entropy generation due to heat transfer (S ?,max) and fluid friction (S ?,max) is lower for case 1 and higher for case 2. It is found that S ?,max occurs at the top portion of side walls in case 1, whereas S ?,max occurs at a hot-cold junction due to a high thermal gradient in case 2. The total entropy generation, S total is found to be smaller in case 1 and larger in case 2 for all Pr at Ra = 10 5. It is observed that S ?,max occurs at the top wall in both heating situations for Pr = 0.015 and Ra = 10 5. It is also found that, S ?,max is observed near side walls in case 1, whereas that is observed near the right cold wall in case 2 for Pr = 0.7 and 1000 at Ra = 10 5. The total entropy generation (S total) is larger for ? = 45� in both heating cases at high Pr (Pr = 1000). The total entropy generation (S total) also increases with Pr due to an increase in S ? with Pr. It is found that, high heat transfer rate (Nu b) and minimum entropy generation (S total) occur for square cavities at Ra = 10 5 for all Pr in case 1. It is observed that S total is smaller for case 1 compared to case 2, even though high Nu b is observed at case 2 for all ?s. The inclination angle (?) has almost identical effect on entropy production rate for 45� ? ? ? 60� within the entire range of Pr at all Ra. � 2012 American Chemical Society.

Analysis has been carried out for energy distribution and thermal mixing in steady laminar natural convective flow through the porous rhombic cavities with inclination angle ? for various applications such as geothermal, grain storage, electronic cooling, etc. A generalized non-Darcy model without the Forchheimer inertia term is used to predict the flow in porous media. The effect of the Darcy number (Da) and the role of ? on the energy distribution and thermal mixing within porous rhombic cavities with isothermal (case 1) and nonisothermal (case 2) hot bottom walls are illustrated via " heatlines". Heat transfer is found to be primarily conduction dominant at Da = 10 -5 even at a higher Rayleigh number (Ra = 10 6). The onset of convection occurs at Da = 10 -4, and the distorted heatlines from the hot bottom wall take a longer path to reach the cold side walls of the cavity. Larger heat transfer and thermal mixing occurs for Da = 10 -3 at Ra = 10 6 irrespective of ? and Pr. Multiple flow/convective circulations are observed at Pr = 0.015 for all ? values at Da = 10 -3. On the other hand, two asymmetric flow circulation cells are found to occupy the entire cavity at Pr = 0.7, 7.2, and 1000 for ? = 75� at Da = 10 -3. The cavity with inclination angle ? = 30� enhances the convective heat transfer from the hot wall to the cold wall, and the heat transfer to the right cold wall is a maximum for ? = 75�, as depicted by "heatlines" irrespective of Pr at Da = 10 -3. Average Nusselt number studies based on heatfunction gradients also show that the cavity with ? = 30� gives a maximum heat-transfer rate from the bottom to the left wall irrespective of Pr in case 1 at Da = 10 -3. The cup mixing temperature (? cup) is higher for case 1 compared to case 2, and it is almost invariant with ? for higher Pr (Pr = 7.2 and 1000) in case 1 at Da = 10 -3. � 2011 American Chemical Society.

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 (? = 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 = 103-105). 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 (?), streamlines (?), and entropy generation contours due to heat transfer (S?) and fluid friction irreversibility (S ?) are analyzed for both cases. At low Rayleigh number (Ra = 103), the entropy generation in the cavity is dominated by S ? for all ?, irrespective of Pr. As Ra increases to 10 5, the fluid flow intensifies and S? also increases for all ?, irrespective of Pr. The total entropy generation (S total), average Bejan number (Beav), and average heat-transfer rate (Nub) are plotted for Rayleigh number ranges of 103 ? Ra ? 105. The total entropy generation (S total) is found to be low for ? = 30� and high for ? = 75� for all Pr values at Ra = 105. Analysis of variations of Beav with Ra for high-Pr fluids indicates that S? contributes significantly for increase in Stotal. It is also found that the largest heat-transfer rate (Nub) corresponds to minimum entropy generation (Stotal) for ? = 30� cavities at Ra = 105 with all Pr in case 1. The nonisothermal heating strategy (case 2) is energy efficient, because of its lower Stotal value, corresponding to low Nub, which is due to a lesser heating effect than case 1 for all ?. Overall, rhombic cavities with ? = 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. � 2011 American Chemical Society.