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首页> 外文期刊>Applied Mathematical Modelling >Numerical Modelling Of Unsteady Convective-diffusive Heat Transfer With A Control Volume Hybrid Method
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Numerical Modelling Of Unsteady Convective-diffusive Heat Transfer With A Control Volume Hybrid Method

机译：非定常对流扩散传热的控制体积混合法数值模拟

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摘要

Presented in this paper is a numerical methodology for the solution of the parabolic governing partial differential equation that describes unsteady advection-diffusion heat transfer. The formulation presented here is shown to be free from the numerical oscillation commonly associated with advection-diffusion heat transfer regardless of the value of the Peclet number. The formulation involves the absorption of the advection term in the unsteady heat equation into the capacitance term. This process is achieved with the use of a control volume methodology applied to each nodal element on a finite-volume mesh. This is shown to ensure that spurious energy losses and gains are avoided and provides for consistency between temperature and energy change. This approach provides unconditional stability and it is shown that good accuracy is achievable with relatively large time-steps.rnIn order to highlight the features of the approach it is compared against those of benchmark numerical schemes. Detailed analysis is performed for the 1D semi-infinite moving solid problem for which an exact solution is available and for a realistic engineering heat transfer problem. Oscillation free results are achieved at good accuracy for a wide range of Peclet numbers and problems considered.
机译：本文提出的是一种求解抛物线控制的偏微分方程的数值方法，该方程描述了不稳定的对流-扩散传热。此处显示的公式表明，与对流扩散热传递无关的数值振荡无视Peclet数的值。该公式包括将非稳态热方程中的对流项吸收到电容项中。该过程是通过将控制体积方法应用于有限体积网格上的每个节点元素来实现的。这样做可以确保避免杂散的能量损失和增益，并确保温度和能量变化之间的一致性。该方法提供了无条件的稳定性，并且证明了在相对较大的时间步长下可以获得良好的准确性。为了突出该方法的功能，将其与基准数值方案进行了比较。对一维半无限移动固体问题进行了详细分析，该问题可以提供精确的解决方案，以及实际的工程传热问题。对于广泛的Peclet数和所考虑的问题，可以很好地获得无振荡的结果。

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