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针对火灾情况下火场温度和构件边界的温度均随时间不断变化的问题,应用杜哈美尔定理分析了边界温度按一定规律随时间变化的热传导问题。推导得到了火灾情况下混凝土板温度场的解析解公式,并应用MATLAB编程计算得到了解析解结果。比较解析解的计算结果和试验结果发现:两者得到的截面温度场都呈非线性分布;两者的变化趋势一致,即近火面的温度梯度很大,距受火面越远,温度梯度越小;温度曲线都是凸向坐标轴。因此,推导得到的解析解公式适合于求解火灾时混凝土板横截面的温度场。同时,只要能够求出非齐次项与时间无关时的辅助问题的解,便可应用杜哈美尔定理求解该热传导问题的温度场,因此该方法可推广应用于火灾情况下其它构件温度场解析解的计算。
Aiming at the problem that the temperature of the fire field and the boundary of the component all change with time under the condition of fire, the problem of heat conduction with time varying of the boundary temperature is analyzed by using the Duhamel principle. The analytical solution of the temperature field of concrete slab under fire condition is deduced and the analytic solution is obtained by MATLAB programming. Comparing the results of calculation and experimental results, it is found that the temperature field of the two sections are non-linearly distributed. The trend of the two is consistent, that is, the temperature gradient of the near-fire surface is large, The smaller the temperature curve is convex to the axis. Therefore, the analytic solution deduced is suitable for solving the temperature field of concrete slab cross-section in fire. At the same time, Duhamel’s theorem can be used to solve the temperature field of the heat conduction problem, so long as the solution to the auxiliary problem can be obtained when the nonhomogeneous term is independent of time. Therefore, this method can be widely applied to the temperature field of other components under fire Analytic solution calculation.