基于Monte-Carlo随机有限元方法的随机边界条件下自然对流换热不确定性研究

Abstract

In order to study the effects of stochastic boundary conditions on natural convection heat transfer in square cavities, a Monte-Carlo stochastic finite element method was developed to solve uncertainty propagation of natural convection heat transfer under stochastic boundary condition. The input random parameters were expanded through the Karhunen-Loeve expansion and the random samples of boundary condition were generated with the Latin sampling method. The flow field and temperature field in the square cavity for different random samples of boundary condition were calculated numerically. The mathematical expectations and variances of stochastic output fields were calculated with the sampling statistical method. The stochastic finite element program with the MATLAB language was coded to solve the uncertainty propagation of natural convection heat transfer in cavity under stochastic boundary condition based on the computational framework. The effects of the correlation length and the variance of stochastic boundary condition on natural convection uncertainty were analyzed. The results show that the mean temperature field and flow field are basically the same as the deterministic temperature field and flow field, respectively. The probability distribution of the Nusselt number under stochastic boundary condition is a normal distribution. The mean Nusselt number increases with the correlation length and the variance, the variance has a greater influence on natural convection heat transfer than the correlation length.