有内热源的多孔层中自然对流的稳定性分析

采用局部非热平衡模型, 通过数值法和Garlerkin近似法, 分析存在均匀内热源和边界浓度梯度时, 有效热导率比、流体和固相间的传热系数、浓度梯度的大小以及内热源在流体与固相内的分布情况对水平多孔层中临界内热源Rayleigh数的影响, 来研究相关参数对自然对流的稳定性的影响, 并得到临界内热源Rayleigh数的表达式。结果表明, 浓度Rayleigh数的增加可以促进自然对流的形成;内热源为正时, 自然对流的形成区域主要位于上半区域;内热源为负时, 自然对流的形成区域位于下半区域, 内热源总是促进自然对流的发生;有效热导率比、流体和固相间的内部传热系数、内热源在流体与固相内的分布情况相互耦合, 影响自然对流的稳定性, 这种影响取决于各参数的范围。

Stability analysis of natural convection in porous channel with heat generation

The stability of natural convection in a horizontal porous channel with uniform heat generation and concentration gradients was considered by using numerical method and Garlerkin methods. Attention is focused on cases where the fluid and solid phases are not in local thermal equilibrium, and standard linearized stability theory is used to analysis how the criterion for the onset of convection varies with the inter-phase heat transfer coefficient, H, the porosity-modified thermal conductivity ratio, g, the size of the temperature gradient in the vertical direction of the porous layer, and the distribution of heat source in the fluid phase and solid phase. We also get the expressions of the critical Rayleigh number of heat source. The results show that, the forming region of natural convection mainly located in the upper half of the area when the heat source is positive from the distribution of the velocity field, while the forming region of natural convection mainly located in the lower half of the area when the heat source is negative. The heat source is always to promote the occurrence of natural convection. Effective thermal conductivity ratio, internal heat transfer coefficient of fluid and solid phases and the distribution of heat source in the fluid and solid phase, mutual coupling, affects the stability of natural convection.