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 article, the mean Nusselt number Nu ¯ is found to increase with increasing values of Rayleigh number for both Newtonian and Bingham fluids, but weaker convective transport in Bingham fluid leads to smaller values of Nu ¯ than that obtained in the case of Newtonian fluids with the same nominal value of Ra and Pr in the differentially heated vertical sidewall configuration.
Abstract: In this study, two-dimensional steady-state simulations of laminar natural convection in square enclosures with differentially heated horizontal walls with the bottom wall at higher temperature have been conducted for yield-stress fluids obeying the Bingham model. Heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 103–105 and a Prandtl number (Pr) range of 0.1–100. The mean Nusselt number Nu ¯ is found to increase with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, weaker convective transport in Bingham fluids leads to smaller values of Nu ¯ than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra. The mean Nusselt number Nu ¯ decreases with increasing Bingham number in the case of yield stress fluids, and, for large values of Bingham number Bn, the value rapidly approaches to unity ( Nu ¯ = 1.0 ) as thermal conduction dominates the heat transfer. However, this variation in the present configuration is found to be markedly different from the corresponding variation of Nu ¯ with Bn for the same nominal values of Ra and Pr in the differentially-heated vertical sidewall configuration. The effects of Prandtl number have also been investigated in detail and physical explanations are provided for the observed behaviour. Guided by a detailed scaling analysis, new correlations are proposed for the mean Nusselt number Nu ¯ for both Newtonian and Bingham fluids which are demonstrated to satisfactorily capture the correct qualitative and quantitative behaviours of Nu ¯ for the range of Ra, Pr and Bn considered in this analysis.
80 citations
TL;DR: In this article, the integral forms of the governing equations are solved numerically using finite-volume method in non-orthogonal body-fitted coordinate system and SIMPLE algorithm with higher-order upwinding scheme are used.
Abstract: In this paper, natural convection inside a two-dimensional cavity with a wavy right vertical wall has been carried out. The bottom wall is heated by a spatially varying temperature and other three walls are kept at constant lower temperature. The integral forms of the governing equations are solved numerically using finite-volume method in non-orthogonal body-fitted coordinate system. SIMPLE algorithm with higher-order upwinding scheme are used. The method of numerical visualization of heat transport for convective heat transfer by heatlines is studied. The heatfunction equation in the transformed plane is solved in terms of dimensionless variables. Results are presented in the form of streamlines, isotherms, heatlines, local and average Nusselt number distribution for a selected range of Rayleigh number (100–106). The results are presented for three different undulations (1–3) with different wave amplitude (0.00–0.10) and a fluid having Prandtl number 0.71.
78 citations
TL;DR: In this paper, a three-dimensional numerical study of the natural convection in a cubical cavity heated from below is reported at moderate Rayleigh numbers for three Prandtl numbers Pr = 0.71, 10 and 130.
Abstract: A three-dimensional numerical study of the natural convection in a cubical cavity heated from below is reported at moderate Rayleigh numbers for three Prandtl numbers Pr = 0.71, 10 and 130. The six walls are considered rigid and immobile, with isothermal horizontal plates and adiabatic lateral walls. The Boussinesq approximation for the variation of physical properties is assumed. Seven different structures, four single roll-type, two four roll-type and a toroidal roll, and several flow transitions have been identified in the steady and laminar regime for Ra ⩽ 6×10 4 and Pr ⩽ 130. Both, the dynamic and heat transfer characteristics of these seven structures are discussed. The effects of slightly changing the aspect ratio or tilting the cavity on the stability of the different structures are also analyzed. There is general agreement between the predicted average Nusselt number and available correlations for Rayleigh–Benard convection in rectangular enclosures and between two horizontal plates.
66 citations
TL;DR: In this paper, 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.
Abstract: 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.
50 citations
TL;DR: A picture is worth a thousand words as mentioned in this paper, and it has become a lot easier to take an existing idea change some key words and drawings and publish the old idea as new.
Abstract: A picture is worth a thousand words. This article is about a picture known as “heatlines” since 1983, and “synergy” since 1998. Both concepts, heatlines and synergy, are about visualizing the physics of convection, which is the combination (superposition) of heat conduction lines and enthalpy flow lines over a material in motion. Heatlines and synergy are reviewed here comparatively. This comparison reveals that synergy is a remake of heatlines, and that synergy has no physical connection with heat transfer enhancement. At bottom, it has become a lot easier to take an existing idea change some key words and drawings and publish the old idea as new.
50 citations