Timber roof constructions are commonly ventilated through an air cavity beneath the roof sheathing in order to remove heat and moisture from the construction. The driving forces for this ventilation are wind pressure and thermal buoyancy. The wind driven ventilation has been studied extensively, while models for predicting buoyant flow are less developed. In the present study, a novel analytical model is presented to predict the air flow caused by thermal buoyancy in a ventilated roof construction. The model provides means to calculate the cavity Rayleigh number for the roof construction, which is then correlated with the air flow rate. The model predictions are compared to the results of an experimental and a numerical study examining the effect of different cavity designs and inclinations on the air flow rate in a ventilated roof subjected to varying heat loads. Over 80 different test set-ups, the analytical model was found to replicate both experimental and numerical results within an acceptable margin. The effect of an increased total roof height, air cavity height and solar heat load for a given construction is an increased air flow rate through the air cavity. On average, the analytical model predicts a 3% higher air flow rate than found in the numerical study, and a 20% lower air flow rate than found in the experimental study, for comparable test set-ups. The model provided can be used to predict the air flow rate in cavities of varying design, and to quantify the impact of suggested roof design changes. The result can be used as a basis for estimating the moisture safety of a roof construction.

木材屋顶结构通常通过屋顶护套下方的气孔通风，以从结构中去除热量和水分。这种通风的驱动力是风压和热浮力。对风力驱动的通风进行了广泛的研究，而用于预测浮力流量的模型则很少开发。在本研究中，提出了一种新颖的分析模型来预测通风屋顶结构中由热浮力引起的气流。该模型提供了计算屋顶结构的空腔瑞利数的方法，然后将其与空气流速相关联。将模型预测与实验和数值研究的结果进行比较，该研究检查了不同空腔设计和倾角对通风屋顶在不同热负荷下的空气流速的影响。超过80种不同的测试设置，发现分析模型可以在可接受的范围内复制实验和数值结果。对于给定的结构，增加的总屋顶高度，空气腔高度和太阳热负荷的影响是增加了通过空气腔的空气流速。平均而言，对于可比较的测试装置，分析模型预测的空气流量将比数值研究中的空气流量高出3％，比实验研究中的空气流量低20％。提供的模型可用于预测设计变化的型腔中的空气流速，并量化建议的屋顶设计变更的影响。该结果可以用作估计屋顶结构的防潮安全性的基础。