中文摘要：

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。

英文摘要：

Analytical solutions are important in the study of effect of fire temperature field on components in it.The temperature varies with time on fire,and the temperature of the components boundaries varies too.Duhamel theorem,which can analyze such heat conduction problems that the boundary temperature varies with time and in accordance with certain laws,is applied to deduce the formula of the analytical solutions of the temperature field in the concrete slab on fire.The analytical solutions are calculated through MATLAB programming.By comparing the analytical and the test results obtained,it is shown that both of the temperature distributions are nonlinear,and the distributions have the same trend,that is,the surfaces near the fire have great temperature gradient,the farther the slab near the fire,the smaller the temperature gradient is.Both the temperature distribution curves are convex toward the coordinate axes.So the formula is suitable for solving the temperature field in the concrete slab on fire.Furthermore,if only the solution of the assistant problem is obtained,which belongs to the same heat conduction but the non-homogeneous items are unrelated to the times,the corresponding heat conduction problem can be solved by using Duhamel theorem,thus this method can be extended to obtain the analytical solutions of the temperature field of other construction members on fire.