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分析了平板前表面遭受任意周期热扰动这类非Fourier传热情形下的温度响应.采用双曲型热传导方程描述平板表面温度急速变化时的热传导问题.为求解此类方程,首先利用分离变量法和Duhamel积分原理,得到了平板前表面遭受突变热流和简谐热流两种情况下的解析解.然后,在此基础上应用Fourier级数展开法和叠加原理,获得了平板前表面热流任意周期变化时非Fourier热传导下温度场的解析表达式.利用得到的解析表达式进行数值模拟,分析了不同热松弛时间、不同时刻和不同位置对温度响应的影响,讨论了非Fourier热传导模型所给出的温度响应与Fourier热传导模型的差别.这种方法能够处理许多在生产实际中具有周期边界条件的非Fourier热传导问题.
The temperature response under non-Fourier heat transfer conditions such as any periodic thermal disturbance is analyzed.The hyperbolic heat conduction equation is used to describe the heat conduction problem when the plate surface temperature changes rapidly.In order to solve this kind of equation, And Duhamel integral principle, the analytic solutions are obtained under both the abrupt and simple harmonic heat fluxes on the front surface of the flat plate.And then, based on the Fourier series expansion method and the superposition principle, a periodic change of the heat flux in the front surface of the flat plate is obtained The analytical expression of temperature field under non-Fourier heat conduction is used to simulate the temperature response of different heat-relaxation time, different time and different position. The non-Fourier heat conduction model is given. The difference between the temperature response and the Fourier heat transfer model can deal with many non-Fourier heat conduction problems that have periodic boundary conditions in production practice.