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 effect of Rayleigh number, Darcy number, and undulations on the left wall is investigated on the heat transfer and fluid flow in a two-dimensional porous right-angled triangular enclosure.
Abstract: Natural convection in a two-dimensional porous right-angled triangular enclosure having undulation on the left wall is analyzed numerically. The bottom wall is having a sinusoidal temperature and other two walls are maintained at isothermal cold temperature. The stream function-vorticity equations are solved using finite-difference technique. The computations are done on a structured non-orthogonal body fitted mesh. Standard QUICK scheme is used for convective term discretization and diffusive term is discretized using central difference scheme. In this study, the effect of Rayleigh number ( Ra = 10 3 − 10 6 ), Darcy number ( Da = 10 −4 − 10 −2 ) and undulations on the left wall is investigated on the heat transfer and fluid flow. It is found that for small Ra , the heat transfer is dominated by conduction across the fluid layers but with the increase of Ra , the process began to be dominated by convection and the undulation on the left wall play an important role in increasing heat transfer. It is also found that heat transfer is also a strong function of Darcy number. As Darcy number increases, heat transfer increases in an appreciable manner.
TL;DR: In this paper, a large-eddy simulation (LES) technique was used for the simulations at two high Rayleigh numbers (Ra =10 6 and 10 8 ) and results were seen to be in agreement with direct numerical simulations (DNS) reported in the literature.
Abstract: This paper discusses flow structures and heat transfer rates generated by Rayleigh–Benard convective motions of a Boussinesq fluid with a Prandtl number of 0.7 in a perfectly conducting cubical cavity. Complete numerical simulations of laminar flows were conducted in the range of Rayleigh numbers 7×10 3 ⩽ Ra ⩽10 5 . The large-eddy simulation (LES) technique was used for the simulations at two high Rayleigh numbers ( Ra =10 6 and 10 8 ). LES were carried out using a second-order accurate finite volume code with a dynamic localized one-equation subgrid-scale (SGS) model with constant SGS Prandtl number. In the laminar regime, two single roll structures and a four-roll structure in which the axis of each roll is perpendicular to one sidewall were found to be stable. LES of Rayleigh–Benard convection in an infinite fluid layer were initially carried out and results were seen to be in agreement with direct numerical simulations (DNS) reported in the literature. At Ra =10 6 and 10 8 , the instantaneous velocity and temperature fields present strong fluctuations with respect to the time-averaged flow field. The confining effect of the conductive lateral walls of the cavity generates, in the unsteady flows at Ra =10 6 and 10 8 , persistent vertical currents near these walls. The recirculation of these ascending and descending flows towards the central region of the cavity produces large-scale organized rolling motions, which imprint the topology of the time-averaged flow field in form of two vortex ring structures located near the horizontal walls.
TL;DR: In this paper, a penalty finite element method with biquadratic elements is used to solve the non-dimensional governing equations for the triangular cavity involving hot inclined walls and cold top wall.
Abstract: In this article, natural convection in a porous triangular cavity has been analyzed. Bejan's heatlines concept has been used for visualization of heat transfer. Penalty finite-element method with biquadratic elements is used to solve the nondimensional governing equations for the triangular cavity involving hot inclined walls and cold top wall. The numerical solutions are studied in terms of isotherms, streamlines, heatlines, and local and average Nusselt numbers for a wide range of parameters Da (10−5–10−3), Pr (0.015–1000), and Ra (Ra = 103–5 × 105). For low Darcy number (Da = 10−5), the heat transfer occurs due to conduction as the heatlines are smooth and orthogonal to the isotherms. As the Rayleigh number increases, conduction dominant mode changes into convection dominant mode for Da = 10−3, and the critical Rayleigh number corresponding to the on-set of convection is obtained. Distribution of heatlines illustrate that most of the heat transport for a low Darcy number (Da = 10−5) occurs from the top...
TL;DR: In this paper, the authors present transient turbulent natural convection with surface thermal radiation in a square differentially heated enclosure using non-primitive variables like stream function and vorticity.
Abstract: Purpose – The purpose of this paper is to present transient turbulent natural convection with surface thermal radiation in a square differentially heated enclosure using non-primitive variables like stream function and vorticity. Design/methodology/approach – The governing equations formulated in dimensionless variables “stream function, vorticity and temperature,” within the Boussinesq approach taking into account the standard two equation k-e turbulence model with physical boundary conditions have been solved using an iterative implicit finite-difference method. Findings – It has been found that using of the presented algebraic transformation of the mesh allows to effectively conduct numerical analysis of turbulent natural convection with thermal surface radiation. It has been shown that the average convective Nusselt number increases with the Rayleigh number and decreases with the surface emissivity, while the average radiative Nusselt number is an increasing function of these key parameters. It has be...
TL;DR: In this paper, a two-dimensional numerical study has been conducted to obtain fluid flow and heat transfer characteristics for Rayleigh-Benard natural convection of non-Newtonian phase-change-material (PCM) slurries in a rectangular enclosure with isothermal horizontal plates and adiabatic lateral walls.
Abstract: A two-dimensional numerical study has been conducted to obtain fluid flow and heat transfer characteristics for Rayleigh–Benard natural convection of non-Newtonian phase-change-material (PCM) slurries in a rectangular enclosure with isothermal horizontal plates and adiabatic lateral walls. Generally, with the melting of PCM, the slurry's density draws down sharply but continuously and the slurry's specific heat capacity shows a peak value. Some PCM slurries such as microemulsions can exhibit pseudoplastic non-Newtonian fluid behavior. This paper deals with the differences in natural convection and flow patterns between Newtonian and non-Newtonian fluids with or without PCM theoretically. Due to the participation of PCM in natural convection, the dependency of Rayleigh number Ra alone cannot reflect its intensity that a modified Stefan number has to be taken into account. A correlation is generalized in the form of Nu=C·Ral·Ste−m which has a mean deviation of 10.4% in agreement with the calculated data. The numerical simulation has been performed with the following parameters: a shear thinning pseudoplastic fluid for pseudoplastic index 0.8⩽n⩽1.0, 6×103⩽Ra⩽2×106, Prandtl number Pr=70–288, and the aspect ratio of the rectangular enclosure from 10:1 to 20:1.