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 effects of sinusoidal gravity modulation fields imposed on two-dimensional Rayleigh-Benard convection flow were studied to understand the effect of periodic source (g•jitter) on fluids system and heat transfer mechanism.
Abstract: Sinusoidal gravity modulation fields imposed on two‐dimensional Rayleigh‐Benard convection flow are studied to understand the effects of periodic source (g‐jitter) on fluids system and heat transfer mechanism. The transient Navier‐Stokes and energy equations are solved by semi‐implicit operator splitting finite element method. Results include two sets. One is considered at normal terrestrial condition and the other one is related to low‐gravity condition. Under low‐gravity condition the research focuses on the effects of modulation frequency and direction in order to find out the critical frequency for heat transfer mechanism transferring from conduction to convection.
TL;DR: In this paper, a temperature-transforming model (TTM) was used to solve solidification of liquid copper saturated in porous structure fabricated by sintered steel particles using a temperature transformer model.
Abstract: Purpose – The purpose of this paper is to solve solidification of liquid copper saturated in porous structure fabricated by sintered steel particles using a temperature‐transforming model (TTM).Design/methodology/approach – The convection in the liquid region is modeled using Navier‐Stokes equation with Darcy's term and Forchheimer's extension. The effect of natural convection is considered using the Boussinesq approximation. For the solid region, the velocity is set to zero by the Ramped Switch‐Off Method (RSOM). The model was validated by comparing the results with existing experimental and numerical results with gallium as phase change material and packed glass beads as porous structure. Solidification of liquid copper saturated in sintered copper particles is then simulated and the effects of various parameters on solidification process were studied.Findings – The results indicate that the stronger convection effects are shown for the cases with high Raleigh number or high Darcy's number. However, whe...
TL;DR: In this paper, the Rayleigh-Benard-Marangoni problem for natural convection in a rectangular cavity with thermocapillary forces on a free surface is investigated using a stream function-vorticity formulation.
Abstract: The Rayleigh‐Benard‐Marangoni problem for natural convection in a rectangular cavity with thermocapillary forces on a free surface is investigated using a stream function‐vorticity formulation. The nonlinear system is iteratively decoupled and high‐degree p finite elements are used for the discretization of the physical domain. The linear systems arising from the discretization at each iteration are solved using a spectral multilevel scheme, which is a natural preconditioner for high‐p (spectral) elements. The spectral multilevel solver lends itself to parallelization in an element‐by‐element (EBE) framework. Simulation results are presented and compared to previously published results. The multilevel efficiency is compared to previous results for the driven cavity problem. Parallel performance studies are presented for the Cray T3E distributed memory architecture.
TL;DR: In this paper, a nonlinear spectral-amplausitude-perturbation approach was proposed to solve the post-critical convective state for Rayleigh-Benard (RB) convection.
Abstract: Purpose – The post-critical convective state for Rayleigh-Benard (RB) convection is studied using a nonlinear spectral-amplitude-perturbation approach in a fluid layer heated from below. The paper aims to discuss these issues. Design/methodology/approach – In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A combined amplitude-perturbation approach is developed to solve the nonlinear spectral system in the post-critical range, even far from the linear stability threshold. Also, to leading order, the Lorenz model is recovered. Findings – It is found that very small Prandtl numbers (Pr < 0.1) can change the Nusselt number, when terms to O(e5/2) and higher are considered. However, to lower orders the Prandtl number does not affect the results. Variation of the Nusselt number to different orders is found to be highly consistent. Comparison with experimental results is made and a very good qualit...