Nonlinear mathematical and numerical modeling of the effect of temperature on membrane pore size
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Due to the growth of the global population, water stress has risen sharply. However, water stress in high latitudes is not only due to population growth but also to low local temperatures. Numerous studies have shown that temperature affects the pore size of membranes, becoming larger at higher temperatures and smaller at lower temperatures. Since the average low temperature at high latitudes is usually below 10°C, the effect of low temperature on the membrane can reduce water flow and thus reduce the effectiveness of the membrane. In this paper, the effect of temperature change on the membrane is mainly studied using the nonlinear thermoelastic model. In the model, an axisymmetric large mechanical deformation as well a large temperature change is considered. Traction-free mechanical boundary conditions and convective thermal boundary conditions were used in the study. The finite difference method is used to solve the nonlinear system of equations. The proposed model is validated by comparison with limited published experimental results. Differences between the model and the published results were analyzed by comparing the MATLAB and experimental results. The effects of the mechanical and thermal properties of the material on the membrane under increasing temperature changes were investigated. The modeling results are in reasonably good agreement with the experimental results.