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首页> 外文期刊>International Journal of Heat and Mass Transfer >A general exact analytical solution for anisotropic non-axisymmetric heat conduction in composite cylindrical shells
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A general exact analytical solution for anisotropic non-axisymmetric heat conduction in composite cylindrical shells

机译：复合圆柱壳中各向异性非轴对称导热的一般精确解析解

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摘要

In this study, a solution for anisotropic conductive heat transfer in a composite cylindrical shell is computed by an exact analytical method. The fibers are considered to be winded around the cylinder at any arbitrary angle. A general linear boundary condition is applied on both circular bases of the cylindrical shell to account for various combinations of thermal conditions. The solution considers the effects of convection of the ambient flow motion and various external radiative heat fluxes. The analytical solution describes the temperature distribution in the axial and circumferential directions. In principle, the heat conduction equation should involve a dual second-order derivation, which precludes solving the equation by the direct application of common exact methods. Therefore, an appropriate canonical mapping is selected as a solution to cancel the dual derivation of temperature in the mapped equations. The separation of variables method is then applied to the mapped equations, which are conducted to obtain an exact form of the solution. Finally, an analytical technique based on the Fourier series concept is proposed to determine unknown coefficients in the final solution. The obtained analytical results correspond well with the solved numerical results. The capability of the current solution is examined by application to a few relevant industrial cases.
机译：在这项研究中，通过精确的分析方法计算了复合圆柱壳中各向异性导热的解决方案。认为纤维以任意角度缠绕在圆柱体上。将一般的线性边界条件应用于圆柱壳的两个圆形基部，以考虑热条件的各种组合。该解决方案考虑了环境流动对流和各种外部辐射热通量的影响。解析解描述了轴向和圆周方向的温度分布。原则上，热传导方程应该包含一个二阶二阶导数，这排除了直接应用常见精确方法来求解方程的可能性。因此，选择适当的规范映射作为解决方案，以消除映射方程式中温度的双导数。然后将变量分离方法应用于映射方程，进行求解以获得精确形式的解。最后，提出了一种基于傅立叶级数概念的分析技术来确定最终解中的未知系数。所获得的分析结果与求解的数值结果非常吻合。通过将其应用于一些相关的工业案例来检验当前解决方案的功能。

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