Purpose

This paper aims to investigate the role of shapes of containers (nine different containers) on entropy generation minimization involving identical cross-sectional area (1 sq. unit) in the presence of identical heating (isothermal). The nine containers are categorized into three classes based on their geometric similarities (Class 1: square, tilted square and parallelogram; Class 2: trapezoidal type 1, trapezoidal type 2 and triangular; Class 3: convex, concave and curved triangular).

Design/methodology/approach

Galerkin finite element method is used to solve the governing equations for a representative fluid (engine oil: Pr = 155) at Ra = 10³–10⁵. In addition, finite element method is used to solve the streamfunction equation and evaluate the entropy generation terms (S_ψ and S_θ). Average Nusselt number ( Nub¯) and average dimensionless spatial temperature ( θ^) are also evaluated via the finite element basis sets.

Findings

Based on larger Nub¯, larger θ^ and optimal S_total values, containers from each class are preferred as follows: Class 1: parallelogrammic and square, Class 2: trapezoidal type 1 and Class 3: convex (larger θ^, optimum S_total) and concave (larger Nub¯). Containers with curved walls lead to enhance the thermal performance or efficiency of convection processes.

Practical implications

Comparison of entropy generation, intensity of thermal mixing ( θ^) and average heat transfer rate give a clear picture for choosing the appropriate containers for processing of fluids at various ranges of Ra. The results based on this study may be useful to select a container (belonging to a specific class or containers with curved or plane walls), which can give optimal thermal performance from the given heat input, thereby leading to energy savings.

Originality/value

This study depicts that entropy generation associated with the convection process can be reduced via altering the shapes of containers to improve the thermal performance or efficiency for processing of identical mass with identical heat input. The comparative study of nine containers elucidates that the values of local maxima of S_ψ (S_ψ,max), S_θ (S_θ,max) and magnitude of S_total vary with change in shapes of the containers (Classes 1–3) at fixed Pr and Ra. Such a comparative study based on entropy generation minimization on optimal heating during convection of fluid is yet to appear in the literature. The outcome of this study depicts that containers with curved walls are instrumental to optimize entropy generation with reasonable thermal processing rates.

中文翻译：

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形状会影响在相同加热条件下相同流体质量的热对流的熵产生吗？有限元内省

目的

本文旨在研究在相同加热（等温）的情况下，容器形状（九个不同的容器）在涉及相同横截面积（1平方单位）的熵产生最小化中的作用。九个容器根据它们的几何相似性分为三类（第1类：正方形，倾斜的正方形和平行四边形；第2类：梯形1，梯形2和三角形；第3类：凸，凹和弯曲三角形）。

设计/方法/方法

Galerkin有限元方法用于求解Ra = 10 ³ –10 ^5时代表流体（发动机机油：Pr = 155）的控制方程。此外，使用有限元法来解决流函数方程，并评估熵代术语（小号_ψ和小号_θ）。平均努塞尔特数（ ñüb¯）和平均无量纲空间温度（ θ^也可以通过有限元基集进行评估。

发现

基于较大 ñüb¯，更大 θ^和最佳S_总值，每个类别的容器都优选如下：第1类：平行四边形和正方形，第2类：梯形类型1和第3类：凸形（较大 θ^，最佳S _total）和凹面（更大 ñüb¯）。具有弯曲壁的容器可提高对流过程的热性能或效率。

实际影响

熵产生，热混合强度的比较（ θ^）和平均传热速率为选择合适的容器在Ra的各种范围内处理流体提供了清晰的画面。基于这项研究的结果可能对选择一个容器（属于特定类别或具有弯曲或平面壁的容器）有用，该容器可以从给定的热量输入中获得最佳的热性能，从而节省能源。

创意/价值

这项研究表明，可以通过改变容器的形状来减少与对流过程相关的熵产生，从而提高热性能或效率，以处理具有相同热量输入的相同质量的物质。九个容器阐明了比较研究，的局部极大值的值小号_ψ（小号_ψ，最大），小号_θ（小号_{θ，最大值}）和大小小号_总在固定的Pr和Ra下，随容器形状的变化（1-3级）而变化。这种基于熵产生最小化的比较研究尚未在文献中出现，该熵产生最小化是在流体对流期间的最佳加热。这项研究的结果表明，具有弧形壁的容器有助于以合理的热处理速率优化熵的产生。