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首页> 外文期刊>International Journal of Heat and Mass Transfer >Sensitivity of heatfunction boundary conditions on invariance of Bejan's heatlines for natural convection in enclosures with various wall heatings
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Sensitivity of heatfunction boundary conditions on invariance of Bejan's heatlines for natural convection in enclosures with various wall heatings

机译：热函数边界条件对Bejan热线不变性的敏感度，用于带有各种壁加热的机柜中的自然对流

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摘要

Current work attempts to study the heatline patterns during natural convection for different types of Dirichlet heatfunction boundary conditions. The enclosures with various shapes (square, curved, trapezoidal, tilted square and parallelogrammic) are considered with various thermal boundary conditions such as (a) case 1: hot left wall, cold right wall and adiabatic horizontal walls, (b) case 2: hot bottom wall, cold left and right walls and adiabatic top wall and (c) case 3: hot bottom wall with other cold walls. Traditionally, the reference of heatfunction (Π = 0) is assumed at the adiabatic wall and the implementation of reference (Π = 0) may be non-trivial for the case with zero or multiple adiabatic wall(s). Various heatfunction boundary conditions have been formulated based on locations of Π = 0 for systems with more than one adiabatic walls (case 1) or no adiabatic wall (case 3). As test problems, Π = 0 is considered at the junctions of isothermal walls (cases 2 and 3) or on the isothermal wall (case 3). The governing equations are solved via the Galerkin finite element method at various Rayleigh numbers (10~3 and 10~5) and Prandtl numbers (Pr = 0.015 and 7.2). The magnitudes of the heatfunctions change drastically with the location of the datum of Π (Π = 0) whereas, the heat flow patterns remain same irrespective of the heatfunction boundary conditions. The gradients of heatfunctions or the heat flux along the active walls (hot/cold) are invariant of the choice of the reference (Π = 0). The local and average Nusselt numbers are also independent of the choice of Π = 0 and the Nusselt numbers are found to be identical with heatfunction gradients obtained with various locations of Π = 0. Current work may be useful for heat flow visualization in various thermal systems involving complex thermal boundary conditions.
机译：当前的工作试图研究自然对流期间不同类型狄利克雷热函数边界条件的热线模式。考虑具有各种形状（正方形，弯曲，梯形，倾斜正方形和平行四边形）的外壳，并具有各种热边界条件，例如（a）情况1：左热壁，右冷壁和绝热水平壁，（b）情况2：热底壁，左，右冷壁和绝热顶壁，以及（c）情况3：热底壁与其他冷壁。传统上，在绝热壁处假设热功能的参考（Π= 0），并且对于零个或多个绝热壁的情况，​​参考（Π= 0）的实现可能并非无关紧要。对于具有不止一个绝热壁（情况1）或不具有绝热壁（情况3）的系统，基于Π= 0的位置，已经制定了各种热函数边界条件。作为测试问题，在等温壁的交界处（情况2和3）或在等温壁（情况3）处考虑Π= 0。通过Galerkin有限元方法在各种瑞利数（10〜3和10〜5）和普朗特数（Pr = 0.015和7.2）下求解控制方程。热函数的大小随（的基准位置（Π= 0）急剧变化，而热流模式保持不变，而与热函数边界条件无关。沿活动壁（热/冷）的热函数或热通量的梯度对于参考的选择是不变的（Π= 0）。局部和平均努塞尔数也与Π= 0的选择无关，并且发现努塞尔数与在Π= 0的各个位置处获得的热函数梯度相同。当前的工作可能对各种热系统中的热流可视化有用涉及复杂的热边界条件。

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