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.
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.
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.
TL;DR: In this article, the authors focus on the advanced solution of the parametric non-linear model related to the Rayleigh-Benard laminar flow involved in the modeling of natural thermal convection.
Abstract: Purpose – The purpose of this paper is to focus on the advanced solution of the parametric non-linear model related to the Rayleigh-Benard laminar flow involved in the modeling of natural thermal convection. This flow is fully determined by the dimensionless Prandtl and Rayleigh numbers. Thus, if one could precompute (off-line) the model solution for any possible choice of these two parameters the analysis of many possible scenarios could be performed on-line and in real time. Design/methodology/approach – In this paper both parameters are introduced as model extracoordinates, and then the resulting multidimensional problem solved thanks to the space-parameters separated representation involved in the proper generalized decomposition (PGD) that allows circumventing the curse of dimensionality. Thus the parametric solution will be available fast and easily. Findings – Such parametric solution could be viewed as a sort of abacus, but despite its inherent interest such calculation is at present unaffordable for nowadays computing availabilities because one must solve too many problems and of course store all the solutions related to each choice of both parameters. Originality/value – Parametric solution of coupled models by using the PGD. Model reduction of complex coupled flow models. Analysis of Rayleigh-Bernard flows involving nanofluids.
TL;DR: In this article, a 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.
Abstract: 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.
TL;DR: In this article, a numerical model for the Benard-type flow was proposed based on the network simulation method, and the Nusselt-Rayleigh correlation was determined for a broad range of Rayleigh, the dimensionless number that influences the solution.
Abstract: Purpose – Natural convection with heat transfer in porous media has been subject of extensive study in engineering due to its numerous applications. A case of particular interest is the Benard-type flow.The paper aims to discuss this issue. Design/methodology/approach – Based on the network simulation method in order to solve this problem, a numerical model is proposed. Findings – Nusselt-Rayleigh correlation is determined for a broad range of Rayleigh, the dimensionless number that influences the solution, above and below the threshold which separates the conduction and convection pure mechanisms. Originality/value – Based on the network simulation method.
TL;DR: In this paper, the Forchheimer-Brinkman-extended Darcy momentum model with the Local Thermal Non-Equilibrium energy model is used in the mathematical formulation for the porous layer, and the results show that the porous medium can play the role of insulator or enhancer of heat transfer from the heat source.
Abstract: Benard convection around a circular heated cylinder embedded in a packed bed of spheres is studied numerically. The Forchheimer–Brinkman–extended Darcy momentum model with the Local Thermal Non-Equilibrium energy model is used in the mathematical formulation for the porous layer. The governing parameters considered are the Rayleigh number (103 ≤ Ra ≤ 5 × 107) and the thermal conductivity ratio (0.1 ≤ kr ≤ 10,000). The structural properties of the packed bed are kept constant as: cylinder-to-particle diameter ratio D/d = 20 and porosity e = 0.5, while the Prandtl number is fixed at Pr = 0.71. It is found that the presence of the porous medium suppresses significantly the strong free convection produced in the empty enclosure, and reduces considerably the high intensity of the pair of vortices generated behind the cylinder. Also, the results show that the porous medium can play the role of insulator or enhancer of heat transfer from the heat source, depending mainly on their thermal conductivities regardless of the Rayleigh number.
TL;DR: In this paper, two-dimensional micro-scale Rayleigh-Benard flows are investigated numerically using direct simulation Monte Carlo method and an enclosure of length-to-height aspect ratio of AS ǫ = 4 is taken to explore the influence of initial setting of simulated molecules.
Abstract: Two-dimensional micro-scale Rayleigh–Benard flows are investigated numerically using direct simulation Monte Carlo method. An enclosure of length-to-height aspect ratio of AS = 4 is taken to explore the influence of initial setting of simulated molecules. The simulation domain is divided into 81 × 21 sampling cells and the range of Rayleigh number from 3000 to 10 000 corresponds to the convection state. Cases of 8, 10, 12, 14, 16 and 24 simulated particles in each collision cell are examined. It is shown that flow patterns with three-, four- or five-roll modes may appear depending on the number of simulated particles.