Study Of The Stability Of Natural Convection In Porous Media Under Local Non-thermal Equilibrium Condition

Natural convection in porous media is common in daily life and industrial and agricultural production, with strong application background. According to local non-thermal equilibrium model and Darcy model, the stability of natural convection in porous media was studied by using Garlerkin approximation and numerical method respectively for three cases that there are temperature gradient and the heat simultaneously; there are concentration gradient and the heat simultaneously; there are temperature gradient, concentration gradient and the heat in the meantime.To the case that there are temperature gradient and the heat simultaneously, the influence of relevant parameters on natural convection in porous media is studied by Garlerkin method. The relational expression of Rayleigh number for the relevant parameters is obtained and we discussed under extreme conditions on some parameters.To the case that there are concentration gradient and the heat simultaneously, the influence of relevant parameters on natural convection in porous media is studied by numerical method and the error of Garlerkin approximate solution is analyzed in the case of the heat source, the concentration gradient and the local non-equilibrium thermal conditions, compared with the exact numerical solution.On the basis of the foregoing, to the case that there are temperature gradient, concentration gradient and the heat simultaneously, some parameters as a function of the Rayleigh number are obtained, such as effective thermal conductivity ratio, heat transfer coefficient, the distribution coefficient of heat source, Lewis number and concentration gradient, temperature gradient.The results showed that: the density difference of the upper and lower portions of fluid, caused by boundary temperature gradient, concentration gradient and the heat source, promotes or inhibits the generation of natural convection. The heat source is always to promote the occurrence of natural convection. The forming region of natural convection mainly located in the upper half of the area when the heat source is positive, while the forming region of natural convection mainly located in the lower half of the area when the heat source is negative. The formed position of natural convection is related to the distribution of internal heat source.When the heat source is in the fluid phase of porous media, the increasing of effective thermal conductivity ratio and heat transfer coefficient promotes the fluid temperature evenly and inhibits natural convection; when the heat source is in the solid phase of porous media, the influence of effective thermal conductivity ratio on natural convection depends on the size of the heat transfer coefficient. Critical wave number decreases with the enhancing of natural convection, regardless of the distribution of the heat source. When the effective thermal conductivity ratio is very large, the critical wave number basically unaffected by the heat transfer coefficient. With the situation of small heat transfer coefficient or large effective thermal conductivity ratio, the formula obtained by Garlerkin approximation can be used directly to analyze the influence of the parameters on the stability of natural convection in porous media and the error of Garlerkin approximate solution is less than 5% compared with the exact solution.