本文主要是研究北方居民住宅屋顶的保温层厚度问题。根据物理学定律:厚度为的均匀介质,两侧温度差为,则单位时间有高温的一侧型向温度低的一侧通过单位面积的热量Q与△T成正比,与成反比,即:Q=k(△T)/d(k为热传导系数)建立了最优的保温层模型。并采用了等效替代、最优化思想求解,同时借助MATLAB软件绘图对模型的解进行分,得保温层在40mm-50mm之间最好。最后,我们再换用其它的保温材料,利用上述方法进行求解,得到其它保温材料的最优厚度。我们采用挤塑聚苯板其厚度为25mm-35mm。 This paper is mainly to study the insulation layer thickness of residential buildings in northern China. According to the laws of physics: the uniform thickness of the medium, the temperature difference between the two sides, then the high temperature per unit of time to the side of the low temperature through the unit area of ​​the heat Q and △ T is proportional to inversely proportional to, namely: Q = k (△ T) / d (k is the thermal conductivity) to establish the best model of insulation layer. And the use of equivalent replacement, the optimization of ideas to solve, at the same time with MATLAB software drawing on the solution of the model points, the insulation layer in the 40mm-50mm between the best. Finally, we use another thermal insulation material, using the above method to solve, get the optimal thickness of other thermal insulation material. We use extruded polystyrene board thickness of 25mm-35mm.