Role of heatlines on thermal management during Rayleigh-Bénard heating within enclosures with concave/convex horizontal walls
27 Sep 2017-International Journal of Numerical Methods for Heat & Fluid Flow (Emerald Publishing Limited)-Vol. 27, Iss: 9, pp 2070-2104
TL;DR: In this paper, the authors carried out the analysis of Rayleigh-Benard convection within enclosures with curved isothermal walls, with the special implication on the heat flow visualization via the heatline approach.
Abstract: Purpose
This study aims to carry out the analysis of Rayleigh-Benard convection within enclosures with curved isothermal walls, with the special implication on the heat flow visualization via the heatline approach.
Design/methodology/approach
The Galerkin finite element method has been used to obtain the numerical solutions in terms of the streamlines (ψ ), heatlines (Π), isotherms (θ), local and average Nusselt number (Nut¯) for various Rayleigh numbers (103 ≤ Ra ≥ 105), Prandtl numbers (Pr = 0.015 and 7.2) and wall curvatures (concavity/convexity).
Findings
The presence of the larger fluid velocity within the curved cavities resulted in the larger heat transfer rates and thermal mixing compared to the square cavity. Case 3 (high concavity) exhibits the largest Nut¯ at the low Ra for all Pr. At the high Ra, Nut¯ is the largest for Case 3 (high concavity) at Pr = 0.015, whereas at Pr = 7.2, Nut¯ is the largest for Case 1 (high concavity and convexity).
Practical implications
The results may be useful for the material processing applications.
Originality/value
The study of Rayleigh-Benard convection in cavities with the curved isothermal walls is not carried out till date. The heatline approach is used for the heat flow visualization during Rayleigh-Benard convection within the curved walled enclosures for the first time. Also, the existence of the enhanced fluid and heat circulation cells within the curved walled cavities during Rayleigh-Benard heating is illustrated for the first time.
Citations
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TL;DR: A comprehensive review and comparison on heatline concept and field synergy principle have been made based on more than two hundreds of related publications as mentioned in this paper, where the role and function of heat line concept is to visualize the heat transfer path while that of field synergy theory is to reveal the fundamental mechanism of heat transfer enhancement and to guide the development of enhanced structures.
Abstract: A comprehensive review and comparison on heatline concept and field synergy principle have been made based on more than two hundreds of related publications. The major conclusions are as follows. Both heatline concept and field synergy principle are important contributions to the developments of single-phase convective heat transfer theories. The role and function of heat line concept is to visualize the heat transfer path while that of field synergy principle is to reveal the fundamental mechanism of heat transfer enhancement and to guide the development of enhanced structures. None of them can be used to deduce the other, nor none of them can be derived from the other. Hence, there is no problem of mutual remake between them at all. If heatlines are constructed by solving a Poisson equation additional computational work should be done; However, either the synergy number or the synergy angle both can be obtained by using numerical results without additional computational work. Further research needs for both heatline concept and field synergy principle are also provided.
51 citations
TL;DR: In this article, the authors studied thermal convection in nine different containers involving the same area and identical heat input at the bottom wall (isothermal/sinusoidal heating) and solved the governing equations by using the Galerkin finite element method for various processing fluids (Pr = 0.025 and 155) and Rayleigh numbers (103 ≤ ≤ 105).
Abstract: The purpose of this paper is to study thermal (natural) convection in nine different containers involving the same area (area= 1 sq. unit) and identical heat input at the bottom wall (isothermal/sinusoidal heating). Containers are categorized into three classes based on geometric configurations [Class 1 (square, tilted square and parallelogram), Class 2 (trapezoidal type 1, trapezoidal type 2 and triangle) and Class 3 (convex, concave and triangle with curved hypotenuse)].,The governing equations are solved by using the Galerkin finite element method for various processing fluids (Pr = 0.025 and 155) and Rayleigh numbers (103 ≤ Ra ≤ 105) involving nine different containers. Finite element-based heat flow visualization via heatlines has been adopted to study heat distribution at various sections. Average Nusselt number at the bottom wall (
Nub¯) and spatially average temperature (θ^) have also been calculated based on finite element basis functions.,Based on enhanced heating criteria (higher
Nub¯ and higher θ^), the containers are preferred as follows, Class 1: square and parallelogram, Class 2: trapezoidal type 1 and trapezoidal type 2 and Class 3: convex (higher θ^) and concave (higher
Nub¯).,The comparison of heat flow distributions and isotherms in nine containers gives a clear perspective for choosing appropriate containers at various process parameters (Pr and Ra). The results for current work may be useful to obtain enhancement of the thermal processing rate in various process industries.,Heatlines provide a complete understanding of heat flow path and heat distribution within nine containers. Various cold zones and thermal mixing zones have been highlighted and these zones are found to be altered with various shapes of containers. The importance of containers with curved walls for enhanced thermal processing rate is clearly established.
11 citations
References
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TL;DR: In this paper, the Galerkin finite element method was used to simulate convexity/concavity of the curved side walls of a fluid filled enclosing with a curved side wall.
Abstract: Numerical simulation for natural convection flow in fluid filled enclosures with curved side walls is carried out for various fluids with several Prandtl numbers ( Pr = 0.015, 0.7 and 1000) in the range of Rayleigh numbers ( Ra = 10 3 –10 6 ) for various cases based on convexity/concavity of the curved side walls using the Galerkin finite element method. Results show that patterns of streamlines and heatlines are largely influenced by wall curvature in concave cases. At low Ra , the enclosure with highest wall concavity offers largest heat transfer rate. On the other hand, at high Ra , heatline cells are segregated and thus heat transfer rate was observed to be least for highest concavity case. In convex cases, no significant variations in heat and flow distributions are observed with increase in convexity of side walls. At high Ra and Pr , heat transfer rate is observed to be enhanced greatly with increase in wall convexity. Results indicate that enhanced thermal mixing is observed in convex cases compared to concave cases. Comparative study of average Nusselt number of a standard square enclosure with concave and convex cases is also carried out. In conduction dominant regime (low Ra ), concave cases exhibit higher heat transfer rates compared to square enclosure. At high Ra , low Pr , concave cases with P 1 P 1 ′ = 0.4 is advantageous based on flow separation and enhanced local heat transfer rates.
27 citations
TL;DR: In this article, the authors solved the problem of steady, laminar, coupled heat and mass transfer by MHD natural convective boundary layer flow over a permeable truncated cone with variable surface temperature and concentration in the presence of thermal radiation and chemical reaction effects.
Abstract: Purpose – The purpose of this paper is to solve the problem of steady, laminar, coupled heat and mass transfer by MHD natural convective boundary‐layer flow over a permeable truncated cone with variable surface temperature and concentration in the presence of thermal radiation and chemical reaction effects.Design/methodology/approach – The governing equations are derived and transformed into a set of non‐similar equations which are then solved by an adequate implicit finite difference method.Findings – It is found that the presence of thermal radiation, magnetic field and chemical reaction have significant effects on the rates of heat and mass transfer. The variation of the wall temperature and concentration exponent contribute to significant changes in the Nusselt and Sherwood numbers as well.Originality/value – The titled problem with the various considered effects has not been solved before and it is of special importance in various industries. The problem is original.
25 citations
TL;DR: In this paper, the classic Rayleigh-Benard problem is re-examined numerically with the addition of various tilt angles in cubical enclosures of liquid tin (Pr = 0.008).
Abstract: Convection in enclosures heated from below can affect crystals grown from melts. Experiments designed to study such convection can be influenced by small tilts of the experimental system with respect to gravity. Because of the additional body force, tilting can mask flow transition points, making comparisons with stability studies difficult. In this study, the classic Rayleigh–Benard problem is re-examined numerically with the addition of various tilt angles in cubical enclosures of liquid tin (Pr = 0.008). The results presented are applied to experiments which measure both molecular diffusivities as well as convection in the melt.
24 citations
TL;DR: In this paper, the authors used the heatline method to analyze natural convection in porous rhombic enclosures with various inclination angles, φ for differential (case 1) and Rayleigh-Benard heating situations (case 2).
Abstract: 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.
21 citations
TL;DR: In this article, a heat flow visualization method based on heatfunction has been adopted to analyze natural convection via differential heating (case 1) and Rayleigh-Benard convection (case 2) in fluid filled rhombic enclosures with various inclination angles, φ, using the Galerkin finite element method for the range of Rayleigh number, R a = 10 3 -10 5.
Abstract: The heat flow visualization method based on heatfunction has been adopted to analyze natural convection via differential heating (case 1) and Rayleigh–Benard convection (case 2) in fluid filled (Prandtl number, P r = 0.015 – 1000 ) rhombic enclosures with various inclination angles, φ , using the Galerkin finite element method for the range of Rayleigh number, R a = 10 3 – 10 5 . An accurate prediction of the flow structure and heat distribution in such configurations is of great importance due to various engineering applications such as solar energy systems, cooling of electronic devices, combustion, etc. The strength of fluid and heat flow increases with φ and R a due to an enhanced convection effect and the maximum magnitude of streamfunction ( ψ max ) and heatfunction ( Π max ) is observed at φ = 90 ° in both cases. Conduction based static fluid solutions are also found at φ = 90 ° associated with convection based dynamic fluid solutions in case 2 for all P r . Heating strategies are compared via heatlines and also based on local ( N u ) and average Nusselt numbers ( N u ¯ ). It is also shown that φ = 30 ° shows higher N u ¯ in case 2 compared to case 1, whereas φ = 90 ° shows higher N u ¯ in case 1 compared to case 2 for all P r . There exists a critical rhombic angle ( φ = 50 ° ) such that differential heating may be the profound heating situation at φ ≥ 50 ° for materials involving P r = 1000 . Also, the rhombic cavity may be an alternative geometrical design in convective thermal processing of fluids with vertical thermal gradient (case 2) as it establishes only convection based dynamic solutions for all possible angles ( φ 90 ° ).
20 citations