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In the current study, a combined conduction-convection model is developed to analyze the effect of natural convection inside the Phase Change Material (PCM) during melting and solidification processes of a cascade Latent Heat Thermal Energy Storage System (LHTESS) and it is compared with pure conduction model. Effective heat capacity method is employed to simulate the phase change phenomena in both combined model and pure conduction models. Boussinesq approximation is used to predict the effect of natural convection inside the PCM in the combined model. The governing equations involved in the model are solved using finite element based simulation software, COMSOL Multiphysics 4.3a. Parametric study is conducted on charging and discharging processes of cascade LHTESS using both the models. The comparative study between combined model and pure conduction model demonstrated that the pure conduction model under predicts the rate of heat transfer between HTF and PCM at lower inlet velocity of HTF, where natural convection plays a significant role in the phase change phenomena. The deviation between the models decreases with increase in the inlet velocity of HTF for both charging and discharging processes. The simulation results indicated that the heat transfer phenomena inside the PCM become more conduction dominant at higher inlet velocity of HTF. The results also revealed that the inlet temperature of HTF plays a major role in decreasing the charging/ discharging time.

The performance of an extruded finned plate air heating solar collector is studied theoretically for paddy drying applications. Climatic conditions and solar radiation data are accounted based on Guwahati region (26.11˚N, 91.72˚E). Outlet air temperature and pressure drop are considered as controlling parameters to find optimum number of fins, fin height and fin thickness. Outlet air temperature increases and then decreases with number of fins whereas pressure drop increases with number of fins. The analysis showed that finned plate air heating solar collector with 80 fins, 0.6 Height (H) to-Duct length (D) ratio and 2 mm fin thickness yield best results for paddy drying applications at Guwahati weather conditions.

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.

Analysis of natural convection in porous right angled triangular enclosures with a concave/ convex hypotenuse has been carried out using the Bejan's heatlines approach. A generalized non-Darcy model without Forchheimer term is employed for fluid flow in a porous matrix and the governing equations are solved by the Galerkin finite element method. The cavity is subjected to a thermal boundary condition of an isothermal cold left wall, isothermal hot curved right wall, and adiabatic bottom wall. Due to intense closed loop heatlines, thermal mixing is higher in convex cases compared to the concave case for all parameters. Average heat transfer rate is found to be largest in the concave hypotenuse case. Copyright � Taylor & Francis Group, LLC.

Analysis of ‘entropy generation’ is an important strategy to build, optimize and operate the heat exchange systems within their maximum operating efficiency. Porous rhombic cavities with various inclination angles, φ and various thermal aspect ratios, A, have been considered for the numerical investigation of thermal processing of various fluids (Prandtl number, Pr = 0.015 and 1000) in the range of Darcy number (Da = 10−3–10) due to its extensive energy related applications. The effect of A and φ for various governing parameters during convection are discussed in detail via heat transfer irreversibility (Sθ) and fluid friction irreversibility, Sψ. At lower A, the entropy generation in the cavity is dominated by both Sθ and Sψ for all φs irrespective of Da and Pr. As A increases, Sθ as well as Sψ decreases for all φs which in turn decreases Stotal with A irrespective of Da and Pr. The total entropy generation (Stotal) is found to be lower for φ = 30° and higher for φ = 75° for all Pr and Da. Analysis of variations of Beav with A for higher Da (Da = 10) indicates that, entropy generation is highly fluid friction dominant irrespective of φ and A. Lesser entropy generation (Stotal) with larger heat transfer rate ( Nu b ¯ ) and reasonable heat transfer rate ( Nu b ¯ ) occurs for Pr = 0.015 and Pr = 1000, respectively at φ = 30° cavities with all A irrespective of Da. Current work attempts to analyze energy efficient thermal convection strategies and role of thermal aspect ratio within porous rhombic enclosures based on entropy generation minimization vs heat transfer rates for various fluids.

Natural convection in isosceles triangular enclosures with various configurations (case 1 — inverted, case 2 — straight and case 3 — tilted) is studied via heatline analysis for linear heating of inclined walls. Detailed analysis and comparison for various base angles (φ = 45°, 60°) of triangular enclosures have been carried out for a range of fluids (Pr = 0.015 − 1000) within Ra = 103 − 105 using Galerkin finite element method. The heat flow distributions indicate conduction dominant heat transfer at low Ra (Ra = 103) for case 1 and case 2 whereas in case 3, convective heat flow is observed due to high buoyancy force. As Ra increases, enhanced thermal mixing is observed at the core of the cavity. Wall to wall heat transfer occurs at walls AB and AC due to linear heating boundary condition in all the cases. Although the distributions of fluid flow and heat flow are qualitatively similar for φ = 45° and 60°, the intensity of fluid flow and heat flow decreases as φ increases. Strength of fluid flow and heat flow circulation cells is found to be higher in case 3 for identical parameters. Results show that upper side wall (AC) for case 3 exhibits higher heat transfer rates whereas heat transfer rates for walls AB and AC are the same for case 1 and case 2. Also NuAB is higher for case 2 followed by case 1 and case 3 at the middle portion of wall AB. Thus to achieve high heat transfer from fluid to wall at the central region, case 2 and case 3 configurations may be recommended at high Ra (Ra = 105) and Pr, irrespective of φ.

Entropy generation analysis has been introduced to investigate the effectiveness in heat transfer during natural convection within porous rhombic enclosures of various inclination angles ? for differential (case 1) and Rayleigh Benard (case 2), heating situations. The results are presented in terms of streamlines (?), isotherms (?), and entropy generation maps (S? and S?). Entropy production on the basis of various heating patterns and geometrical orientations have been reported based on the relation between total entropy generation (Stotal) and average Nusselt number (Nul or Nub) via Bejan Number, which relates the available thermal energy to irreversibilities. � 2013 Copyright Taylor and Francis Group, LLC.

Thermal energy conservation is at the heart of energy efficiency in process industries. This allows researchers to go for advances in CFD methods to track the requirement of thermal energy for various thermal processing applications. CFD models need to be incorporated into optimization principles to achieve efficient industrial process designs. In this study, entropy generation due to natural convection in right-angled triangular enclosures (cases 1-4) has been studied numerically for energy efficient processing of various fluids (Pr=0.025, 7 and 1000). It is found that maximum value of entropy generation due to heat transfer (S ?,max) occurs near the vertex of the enclosures for cases 1 and 3, near corner between left wall and bottom wall for case 2 and near lower portion of the right wall for case 4. On the other hand, maximum value of entropy generation due to fluid flow (S ?,max) is observed near middle portions of the side walls for all cases and the location of S ?,max mainly depends on the presence of high velocity gradients. The entropy generation rates and heat transfer rates were also shown for various angles. Triangular cavities with specific angles are recommended for various processing fluids. � 2012 The Institution of Chemical Engineers.

Analysis of ‘entropy generation’ is an important strategy to optimize the natural convection process in order to achieve efficient heat transfer within the system. Rhombic enclosures of various inclination angles ( φ = 30 ° , 45° and 75°) filled with porous media and bounded by adiabatic top wall, cold side walls, isothermally (case 1) and non-isothermally (case 2) heated bottom wall have been considered for the analysis of thermal processing of various fluids ( Pr =0.015, 0.7, 7.2 and 1000) in the range of Darcy number ( Da =10 −5 – 10 −3 ). At Da =10 −5 , the total entropy generation, S total , is found to be significantly high for φ = 30 ° and low for φ = 75 ° and is dominated by heat transfer irreversibility ( S θ ) for all Pr in case 1 whereas the distributions of S total for φ = 45 ° , 75° and 90° closely follow the distributions of φ = 30 ° for all Pr in case 2. Cup mixing temperature ( Θ cup ) is higher for φ = 75 ° and 90° whereas overall heat transfer rate, Nu ¯ , is higher for φ = 30 ° compared to other φ s in both heating cases except at high Pr ( 0.7 − 1000 ) fluids at Da =10 −5 . On increase of Da to 10 − 3 , fluid friction irreversibility, S ψ also increases for all φ s irrespective of Pr in both cases. Increase in S total with Da is small for lower φ ( φ = 30 ° ) due to insignificant S ψ of S total and large for higher φ ( φ = 75 ° ) due to significant S ψ of S total at Da ≥ 10 − 4 irrespective of Pr in both cases. Also, Θ cup slightly decreases at Da ≥ 10 − 4 and further, that reaches a constant value at higher Da as well as S total in both cases irrespective of φ for all Pr except Pr =0.015. Maximum Nu ¯ occurs for φ = 30 ° cavities at Da =10 −3 for all Pr in case 1 due to less available energy loss corresponding to less S ψ . Current work attempts to analyze energy efficient thermal convection strategies within porous rhombic enclosures based on entropy generation minimization vs enhanced thermal mixing or heat transfer rates for various fluids in porous media.

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.

A comprehensive understanding of energy flow and entropy generation is needed for an optimal process design via reducing irreversibilities in terms of 'entropy generation'. In this study, analysis on entropy generation during natural convection in a trapezoidal cavity with various inclination angles (phiv, =45�, 60� and 90�) have been carried out for an efficient thermal processing of various fluids of industrial importance (Pr=0.015, 0.7 and 1000) in the range of Rayleigh number (10 3-10 5). The total entropy generation (S total), average Bejan number (Be av) and average heat transfer rate (NubOverBar, and NulOverBar, ) have been computed. The comparison of magnitudes of S ? and S ? indicates that maximum entropy generation due to heat transfer (S ?, max) is identical for both Ra=10 3 and Ra=10 5 whereas maximum entropy generation due to fluid friction (S ?, max) is lower for Ra=10 3 and that is higher for Ra=10 5 due to enhanced fluid flow at higher Ra irrespective of phiv, and Pr. The total entropy generation (S total) is found to increase with Pr due to increase in S ? with Pr. The non-isothermal heating strategy (case 2) is found to be an energy efficient due to less total entropy generation (S total) values despite its lower heat transfer rate (NubOverBar, ) based on lesser heating effect than isothermal heating (case 1) for all phiv, s. � 2011 Elsevier Ltd.

Analysis has been carried out for the energy distribution and thermal mixing in steady laminar natural convective flow through the rhombic enclosures with various inclination angles, φ for various industrial applications. Simulations are carried out for various regimes of Prandtl ( Pr ) and Rayleigh ( Ra ) numbers. Dimensionless streamfunctions and heatfunctions are used to visualize the flow and energy distribution, respectively. Multiple flow circulations are observed at Pr = 0.015 and 0.7 for all φ s at Ra = 10 5 . On the other hand, two asymmetric flow circulation cells are found to occupy the entire cavity for φ = 75° at higher Pr ( Pr = 7.2 and 1000) and Ra ( Ra = 10 5 ). Heatlines are found to be parallel circular arcs connecting the cold and hot walls for the conduction dominant heat transfer at Ra = 10 3 . The enhanced convective heat transfer is explained with dense heatlines and convective loop of heatlines at Ra = 10 5 . Heatlines clearly demonstrate that the left wall receives heat from the bottom wall as heatlines directly connect both the walls whereas the convective heat circulation cells play lead role to distribute the heat along the right wall, especially for smaller φ s. On the other hand, the heat flow is evenly distributed to both side walls at higher φ s via convection as well as direct conductive transport. Significant convective heat transfer from the bottom hot wall to the left cold wall occurs for φ = 30° cavity whereas the heat transfer to the right cold wall is maximum for φ = 75° irrespective of Pr . Average Nusselt number studies also show that φ = 30° cavity gives maximum heat transfer rate from the bottom to left wall irrespective of Pr in isothermal heating case. On the other hand, enhanced thermal mixing occurs at φ = 75° for both isothermal and non-isothermal heating strategies except at Pr = 0.015 in isothermal heating case.

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.

Natural convection in right-angled triangular enclosures with various top angles ( φ =15°, 30°, 45°) is studied in detail via heat flow analysis for various uniform isothermal and linear isothermal heating thermal boundary conditions. Detailed analysis on the effects of aspect-ratio and thermal boundary conditions on the fluid and heat flow inside the triangular enclosures have been carried out for a range of fluids ( Pr = 7.2, 1000, 0.015) within Ra = 10 3 –10 5 . Interesting features of heat flow patterns under various thermal boundary conditions are ‘visualized’ by heatlines. The effect of increase in φ of triangular enclosures is such that the maximum heat flux at the top vertex decreases and the thermal mixing in cavity increases with the increase in φ . It is found that, the fluid in the lower corners is adequately heated in presence of hot right wall compared to that in left wall heating cases. Further, the heat transfer characteristics, in terms of local and average Nusselt numbers, indicate that isothermal heating cases exhibit exponential decrease in Nu l whereas linear heating cases interestingly show local intermediate maxima. Also, various qualitative and quantitative features of Nu and N u ¯ are adequately explained based on heatlines. Finally, the correlations for N u l ¯ and Ra are obtained for various fluid with all heating situations.

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, P r = 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 = 9 0 ∘ and it is observed that the conduction based static solution disappears with a slight perturbation of φ at Rayleigh number, R a ≥ 2 × 10 3 irrespective of P r in case 2. The active zones of the heat transfer irreversibility ( S θ ) and fluid friction irreversibility ( S ψ ) are found to occur near the isothermal walls for all φ s irrespective of P r in both the cases at R a = 10 5 . In addition, the active zones of S ψ are also found to occur near the adiabatic walls of the cavity for all φ s irrespective of P r in both the cases at R a = 10 5 . Also, the region between the fluid layers of primary circulation cells acts as the strong active zone of S ψ for all φ s in case 2 at lower P r ( P r = 0.015 ) and R a = 10 5 . The total entropy generation ( S t o t a l ) and maximum heat transfer rates ( N u ¯ ) are found to be significantly low for φ = 3 0 ∘ in both the cases at R a = 10 5 irrespective of P r . Analysis of heating patterns and geometrical orientations relates the exergy to irreversibilities which establishes that the rhombic cavity ( φ = 3 0 ∘ ) with the differential heating pattern may be the optimal design based on the energy efficient perspective.

One of the important objectives in thermal systems engineering is to analyze utilization of thermal energy in an efficient manner. Analysis based on second law of thermodynamics may give an insight about efficient usage of thermal energy in various industrial systems. In this regard, entropy generation analysis during conjugate natural convection within a differentially heated square cavity enclosed by vertical conducting walls of different thicknesses (t1 and t2) has been carried out for various thermal systems. Finite element based numerical simulations are carried out for various location of vertical wall thicknesses (cases 1, 2, and 3) in the range of parameters, Ra (103 ? Ra ? 105), Pr (Pr = 0.015-1000), wall thicknesses (t = 0.2 and 0.8), and conductivity ratios (K = 0.1,1 10 and ?). Maximum entropy generation due to heat transfer (S ?,max) occurs near the solid-fluid interface region due to high temperature gradient whereas maximum magnitude of the entropy generation due to fluid friction (S?,max) occurs near the cavity walls due to friction between the circulation cells and cavity walls. Larger heat transfer and high intensity fluid flow lead to larger S?,max and S ?,max for K = 10 compared to that of K = 0.1 and K = 1 irrespective of Pr and location of solid wall thickness. Qualitative features of ?, ?, S? and S? for t1 + t2 = 0.8 are identical with t1 + t2 = 0.2. However, the magnitude of S?,max and S?,max is less for t1 + t2 = 0.8 compared to t1 + t 2 = 0.2. Based on detailed discussion of average Nusselt number (Nul), average Bejan number (Beavg) and total entropy generation (Stotal) vs various governing parameters (Ra, Pr and t), it may be concluded that thermal processing is invariant of K in conduction dominant region (103 ? Ra ? 104) irrespective of Pr and t. On the other hand, K ? 1 with t1 + t2 ? 0.8 may be optimal for thermal processing within the convection dominant region (104 ? Ra ? 105) due to less entropy generation and reasonable heat transfer rate, irrespective of Pr. � 2014 American Chemical Society.

An accurate prediction of the flow structure and heat distribution in rhombic configurations are of greater importance due to its significant engineering i.e. cooling of electronics devices as well as natural applications i.e. geothermal extraction. Heatline method is used to analyze natural convection in porous rhombic enclosures with various inclination angles, φ for differential (case 1) and Rayleigh–Benard heating situations (case 2). Increase in φ(φ = 90°) results in pure conduction dominant heat transfer with stagnant fluid condition for φ = 90° at Da = 10−5 and a slight perturbation of φ at higher Da (Da ⩾ 4 × 10−5) leads to convection based dynamic solution for φ = 90° in case 2 irrespective of Pr. At Da = 10−3, strength of fluid and heat flow increase with φ due to enhanced convection effect and φ = 90° shows maximum magnitude of streamfunction (ψmax) and heatfunction (Πmax) values in both cases except convection based solution at φ = 90° for Pr = 7.2. Both cases are compared based on local (Nu) and average Nusselt numbers ( Nu ¯ ) and those are adequately explained based on heatlines. Also, Nu ¯ increases with Da in both cases except convection based solution at φ = 90° for Pr = 7.2. Overall, Nu ¯ is higher for case 2 at φ ⩽ 45° whereas case 1 shows larger Nu ¯ for φ ⩾ 45° irrespective of Pr at Da = 10−3. Hence, φ = 45° is the critical rhombic angle which demarcates the heating strategies of case 1 and case 2 to achieve higher heat transfer rates ( Nu ¯ ) in various applications.

Conjugate natural convection finds various thermal applications in chemical industries, where the heat transfer is controlled by the presence of solid walls such as heat exchanger, nuclear reactors, fin type cooling and solar storage systems. Heat flow distribution within square cavity enclosed by vertical conducting walls of definite thickness ( t 1 and t 2 ) is analyzed for various fluids (Pr) in this study based on the location of the wall thickness [left wall (case 1)/ right wall (case 2)/ both side walls (case 3)] and conductivity ratios between solid and fluid regions ( K ). At Ra = 10 5 , circular heatlines are observed near core of the cavity at K =0.1 whereas they are distorted and pushed towards the hot wall at K =10 with low Pr ( Pr =0.015). On the other hand, heatlines are horizontally stretched at core of the cavity for higher Pr ( Pr =0.7 and 1000) at K =10. End to end heatlines are highly compressed near top portion of the cavity at K =10 irrespective of Pr. Closed loop heatlines are absent for case 2 at Ra = 10 3 whereas closed loop heatlines with lesser magnitude than cases 1 and 3 are observed for case 2 at Ra = 10 5 due to less heat transfer from the hot solid wall irrespective of Pr at K =0.1 and 1. The heat transfer rate can be maintained constant at low thermal conductivity ratio ( K ) even for the high convective regime ( Ra = 10 5 ) irrespective of wall thickness ( t 1 and t 2 ). Average Nusselt number shows overall larger heat transfer rate for higher K ( K =10), which is almost identical with classical natural convection (zero wall thickness) compared to lower K ( K =0.1 and 1) irrespective of location of wall thickness (cases 1–3). In order to achieve almost invariant or lower fluid temperature at Ra = 10 5 for t 1 + t 2 = 0.2 and 0.8, solid wall at hot side (case 2) may be useful. This heating strategy may be viewed for high temperature shielding or minimization of thermal runaway for temperature sensitive applications, such as environmental control system, chemical storage reservoirs, etc., where heat flow is controlled by solid wall resistance.

Entropy generation due to natural convection in right-angled triangular enclosures filled with porous media with top angles 15° and 45° for various thermal boundary conditions (cases 1–4) has been studied numerically using Galerkin finite element method. Simulations are carried out for Pr = 0.025 and 1000 in the range of Darcy numbers 10−5–10−3. Note that, Sθ,max is observed at vertex of the cavity for cases 1 and 3, near corner between left wall and bottom wall for case 2 and near lower portion of the right wall for case 4. It is found that, Sψ,max is observed near middle portions of the side walls for all cases and the location of Sψ,max mainly depends on the presence of high velocity gradients. The total entropy generation, Stotal, is found to be an increasing function of Da. It is observed that decrease in Beav with Da for both φs is due to increase in fluid friction irreversibility. Analysis of the variation of Beav with Da for various fluids indicates that, higher Beav values are observed for Pr = 0.025 due to low frictional irreversibility. It is observed that Θcup decreases with Da for all Pr due to decrease in thermal mixing. It is found that, the maximum heat transfer rate ( Nu l ¯ or Nu r ¯ ) occurs for φ = 15° cavities compared to φ = 45° cavities at Da = 10−3 in both isothermal and linear heating cases for all Pr due to larger thermal gradients at φ = 15°. Overall, triangular cavities with φ = 15° may be the optimal top angle for right angled triangular enclosure for thermal processing of all types of fluids (Pr = 0.025 and 1000) due to its high heat transfer rate ( Nu l ¯ or Nu r ¯ ), high thermal mixing (high Θcup) and less total entropy generation (Stotal) for all heating strategies (cases 1–4) especially at Da = 10−4.

The phenomena of natural convection within a rhombic enclosure filled with air (Pr = 0.71) for (a) isothermally (case 1) and (b) non-isothermally (case 2) heated bottom walls with various aspect-ratios has been studied numerically. In all the cases, top horizontal wall is maintained adiabatic and side walls are maintained cold. Galerkin finite element method with penalty parameter is used to solve non-linear coupled partial differential equations for flow and temperature fields. Poisson equation of streamfunction and heatfunction is also solved using Galerkin method. Simulations are carried out over a range of Rayleigh numbers and numerical results are presented in terms of streamfunction, heatfunction and temperature contours. Streamlines are useful to visualize the fluid flow whereas heatlines are used to study the heat energy distribution within the rhombic cavity. Heatlines are further used to visualize the trajectories of heat flow and zones of high thermal mixing. At lower Ra, heatlines are smooth circular arcs with low magnitude streamfunctions and heatfunctions and thus the heat transfer is conduction dominant. Asymmetric flow is observed for all the cases due to geometrical asymmetry. As Ra increases, buoyant force starts dominating and the magnitudes of streamfunctions and heatfunctions are found to be greater due to enhanced convection effect. Heatlines are distorted greatly showing complex heat distribution inside the cavity. It is observed that primary heat circulation cell is larger for greater tilt angles and thus thermal mixing is high. Heat transfer rates are also studied via local and average Nusselt numbers as functions of Ra and Pr on bottom, left and right walls. Various quantitative and qualitative features of Nusselt numbers have also been explained based on heatlines.