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首页> 外文期刊>Journal of Heat Transfer >Generalized Solution for Two-Dimensional Transient Heat Conduction Problems With Partial Heating Near a Corner
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Generalized Solution for Two-Dimensional Transient Heat Conduction Problems With Partial Heating Near a Corner

机译：二维瞬态导热问题的广义解决方案与拐角附近的部分加热

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摘要

A generalized solution for a two-dimensional (2D) transient heat conduction problem with a partial-heating boundary condition in rectangular coordinates is developed. The solution accommodates three kinds of boundary conditions: prescribed temperature, prescribed heat flux and convective. Also, the possibility of combining prescribed heat flux and convective heating/cooling on the same boundary is addressed. The means of dealing with these conditions involves adjusting the convection coefficient. Large convective coefficients such as 10 10 effectively produce a prescribed-temperature boundary condition and small ones such as 10(-10) produce an insulated boundary condition. This paper also presents three different methods to develop the computationally difficult steady-state component of the solution, as separation of variables (SOV) can be less efficient at the heated surface and another method (non-SOV) is more efficient there. Then, the use of the complementary transient part of the solution at early times is presented as a unique way to compute the steady-state solution. The solution method builds upon previous work done in generating analytical solutions in 2D problems with partial heating. But the generalized solution proposed here contains the possibility of hundreds or even thousands of individual solutions. An indexed numbering system is used in order to highlight these individual solutions. Heating along a variable length on the nonhomogeneous boundary is featured as part of the geometry and examples of the solution output are included in the results.
机译：开发了具有矩形坐标中的部分加热边界条件的二维（2D）瞬态导热问题的一般性解决方案。该解决方案可容纳三种边界条件：规定的温度，规定的热通量和对流。而且，解决了相同边界上结合规定的热通量和对流加热/冷却的可能性。处理这些条件的手段涉及调整对流系数。诸如1010的大型对流系数有效地产生规定温度边界条件，并且诸如10（-10）的小型产生绝缘边界条件。本文还呈现了三种不同的方法来开发解决方案的计算困难稳态分量，因为变量的分离（SOV）在加热的表面上可以较低，另一种方法（非SOV）更有效。然后，在早期使用溶液的互补瞬态部分被呈现为计算稳态解决方案的独特方法。解决方案方法在以前的工作中建立了在局部加热中产生的2D问题中的分析解。但这里提出的广义解决方案包含数百甚至数千个个体解决方案的可能性。使用索引编号系统，以突出显示这些单独的解决方案。沿着非均匀边界上的可变长度进行加热，作为几何形状的一部分，以及解决方案输出的示例包括在结果中。

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