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, a numerical visualization of mass and heat transport for convective heat transfer by streamlines and heatlines is comprehensively studied and the consistency of the formulations is especially addressed when dealing with conjugate convection/conduction problem.
Abstract: The method of numerical visualization of mass and heat transport for convective heat transfer by streamlines and heatlines are comprehensively studied. Functions are directly defined in terms of dimensionless governing equations or variables. Some basic characteristics of the functions are illustrated in detail, knowledge of which is essential to perceive the results and the philosophy of heat and fluid flow. The consistency of the formulations is especially addressed when dealing with conjugate convection/conduction problem. The functions/lines are unified for both fluid and solid regions, and the diffusion coefficients of the function equations are invariant. The method has been used to visualize the heat and fluid flow structures for natural convection in an air ( Pr =0.71) filled square cavity over a wide range of Ra =10 3 −10 6 , and those for conjugate natural convection/heat conduction problem where the conduction effect of solid body on heat transfer is investigated. As to exhibiting the nature of convective heat transfer, streamlines and heatlines provide a more practical and efficient means to visualize the results than the customary ways.
TL;DR: In this paper, the authors investigated the 2D Rayleigh-Benard convection from the threshold of the primary instability with a theoretical value of critical Rayleigh number Ra c = 1707 to the regime near the flow bifurcation to the secondary instability.
Abstract: Rayleigh–Benard convection is a fundamental phenomenon found in many atmospheric and industrial applications. Many numerical methods have been applied to analyze this problem, including the lattice Boltzmann method (LBM), which has emerged as one of the most powerful computational fluid dynamics (CFD) methods in recent years. Using a simple LB model with the Boussinesq approximation, this study investigates the 2D Rayleigh–Benard problem from the threshold of the primary instability with a theoretical value of critical Rayleigh number Ra c = 1707.76 to the regime near the flow bifurcation to the secondary instability. Since the fluid of LBM is compressible, an appropriate velocity scale for natural convection, i.e. V ≡ β g y Δ TH , is carefully chosen at each value of the Prandtl number to ensure that the simulations satisfy the incompressible condition. The simulation results show that periodic unsteady flows take place at certain Prandtl numbers with an appropriate Rayleigh number. Furthermore, the Nusselt number is found to be relatively insensitive to the Prandtl number in the current simulation ranges of 0.71 ⩽ Pr ⩽ 70 and Ra ⩽ 10 5 . Finally, the relationship between the Nusselt number and the Rayleigh number is also investigated.
TL;DR: The origins and evolution of the heatlines and masslines as visualization and analysis tools, from their first steps to the present are described.
Abstract: Heatlines were proposed in 1983 by Kimura and Bejan (1983) as adequate tools for visualization and analysis of convection heat transfer. The masslines, their equivalent to apply to convection mass transfer, were proposed in 1987 by Trevisan and Bejan. These visualization and analysis tools proved to be useful, and their application in the fields of convective heat and/or mass transfer is still increasing. When the heat function and/or the mass function are made dimensionless in an adequate way, their values are closely related with the Nusselt and/or Sherwood numbers. The basics of the method were established in the 1980(s), and some novelties were subsequently added in order to increase the applicability range and facility of use of such visualization tools. Main steps included their use in unsteady problems, their use in polar cylindrical and spherical coordinate systems, development of similarity expressions for the heat function in laminar convective boundary layers, application of the method to turbulent flow problems, unification of the streamline, heatline, and massline methods (involving isotropic or anisotropic media), and the extension and unification of the method to apply to reacting flows. The method is now well established, and the efforts made towards unification resulted in very useful tools for visualization and analysis, which can be easily included in software packages for numerical heat transfer and fluid flow. This review describes the origins and evolution of the heatlines and masslines as visualization and analysis tools, from their first steps to the present. DOI: 10.1115/1.2177684
TL;DR: In this article, the integral forms of the governing equations are solved numerically using Finite Volume method and computational domains are divided into finite numbers of body fitted control volumes with collocated variable arrangement.
Abstract: In this paper, hydrodynamic and thermal behaviors of fluid inside a wavy walled enclosure are investigated. The enclosure consists of two wavy and two straight walls. The top and the bottom walls are wavy and kept isothermal. Two vertical straight walls (right and left) are considered adiabatic. The integral forms of the governing equations are solved numerically using Finite Volume method. Computational domains are divided into finite numbers of body fitted control volumes with collocated variable arrangement. Results are presented in the form of local and global Nusselt number distributions for a selected range of Grashof number (10 3 –10 7 ). Streamlines and isothermal lines are also presented for four different values (0.0, 0.05, 0.1, 0.15) of amplitude-wavelength ratios (= α / λ ) and for a fluid having Prandtl number 1.0. Throughout this study, aspect ratio (= δ / λ ) is kept equal to 0.40. Calculated results for Nusselt number are compared with the available references.
TL;DR: In this paper, the authors describe a numerical prediction of heat transfer and fluid flow characteristics inside an enclosure bounded by two isothermal wavy walls and two adiabatic straight walls.
Abstract: This paper describes a numerical prediction of heat transfer and fluid flow characteristics inside an enclosure bounded by two isothermal wavy walls and two adiabatic straight walls. Governing equations were discretized using the finite-volume method with collocated variable arrangement. Simulation was carried out for a range of wave ratio λ (defined by amplitude/average width) 0.00–0.4, aspect ratio A (defined by height/average width) 1.0–2.0, Grashof number Gr = 10 0 –10 7 for a fluid having Prandtl number 0.7. Streamlines and isothermal lines are used to present the corresponding flow and thermal field inside the enclosure. Local and global distributions of Nusselt number are presented for the above configuration. Lastly, velocity profiles are presented for some selected locations inside the enclosure for better understanding of the influence of flow field on the thermal field. 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.