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A heat-flux based 'building block' approach for solving heat conduction problems

机译：基于热通量的“构件”方法，用于解决热传导问题

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摘要

A numerical approximation of the Green's function equation based on a heat-flux formulation is given. It is derived by assuming as a functional form of the surface heat flux a stepwise variation with space and time. The obtained approximation is very important in investigation of the inverse heat conduction problems (IHCPs) because it gives a convenient expression for the temperature in terms of the heat flux components. Additionally, it is very important for the unsteady surface element (USE) method which is a modern boundary discretization method. Green's function approximate solution equation (GFASE) also creates 'naturally' fixed groups or modules of work elements called "building blocks" that may be added together to obtain space and time values of temperature. In the current case, they are subject to a partial heating by an applied surface heat flux. The "building block" solution can be derived by using the various analytical and numerical approaches available in heat conduction literature though the exact analysis is preferable, as discussed in the text. Poorly-convergent series deriving from Green's functions approach are replaced by closed-form algebraic solutions.
机译：给出了基于热通量公式的格林函数方程的数值近似。它是通过假设随时间和空间的逐步变化作为表面热通量的函数形式而得出的。所获得的近似值在研究逆导热问题（IHCP）方面非常重要，因为它可以根据热通量分量方便地表达温度。此外，对于非稳定表面元素（USE）方法（这是一种现代的边界离散方法）非常重要。格林函数近似解方程（GFASE）还创建了“自然”固定的工作元素组或模块，称为“构件”，可以将这些元素或模块加在一起以获得温度的时空值。在当前情况下，它们通过施加的表面热通量受到部分加热。可以使用热传导文献中可用的各种分析和数值方法来推导“构件”解决方案，尽管如文中所述，最好进行精确分析。格林函数方法派生的收敛性不佳的级数被闭式代数解代替。

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