Investigation And Collocation Spectral Methods For Flow And Heat Transfer In The Saturated Porous Media

The fluid flow and heat transfer in porous media is an indispensable research topic in engineering applications of porous media.It is the basis of structure design and optimization of the porous media to ascertain the fluid transmission in porous media.The natural convection heat transfer in saturated porous cavities is a classic problem in the field of porous media transmission.Based on this problem,the accuracy of different numerical methods can be tested,and the basic research on complex fluid and multi-field coupling problems can be investigated.At the present,it is still the hotspot in the research field of natural convection in the saturated porous media to develop the numerical method with high efficiency and high precision,as well as to study the influence of the variable physical properties and the radiation-convection coupled heat transfer on the fluid flow and heat transfer in the porous media.In this paper,the Chebyshev collocation spectral method(CCSM)is used to solve the Darcy natural flow in a saturated porous cavity.The simulation results are compared with the numerical and the experimental results of the literatures to verify the reliability of the numerical method.An exact solution using local thermal equilibrium assumption has been constructed to test the accuracy of the numerical method.The results show that the maximum absolute error between the numerical result and the exact solution is 2.79×10-11 and the maximum E2 error is 2.14×10-12,which proved that the numerical method has a high accuracy.Secondly,considering the effect of variable physical properties on the convective heat transfer in porous media,a fluid flow and heat transfer model in a rectangular porous cavity with a variable thermal diffusivity has been presented.The thermal diffusivity is assumed to vary as a linear function of temperature.The concept of heat function has been adopted,and the governing equation of the heat function and the corresponding boundary conditions with variable thermal diffusivity has been constructed.The governing equations are solved by CCSM.Based on the numerical results,the heatlines,streamlines and isotherms in the rectangular porous cavity are ploted.The influences of the Ra,the thermal diffusivity coefficient and the aspect ratio on the flow field,thermal field and heat transfer rate have been analyzed.The results show that the different distribution of the thermal diffusivity in the cavity will lead to a significant difference in fluid flow and heat transfer.The effect of thermal diffusivity on the fluid flow and heat transfer in porous media can not be ignored.Finally,considering the high temperature applications of porous media,the fluid flow and heat transfer in the porous cavity with thermal radiation of the solid skeletons under the local thermal non-equilibrium is studied.The radiative energy of the solid skeletons is obtained by solving the radiation transfer equation.Based on the numerical results,the effect of the radiative properties(such as the PI,the optical thickness,the scattering albedo and the wall emissivity)and dimensionless parameters(such as the Ra,the interphase heat transfer coefficient,and the interphase thermal conductivity ratio)on the fluid flow and heat transfer are analyzed in detail.The main innovations of this paper are as follows:(1)The CCSM is developed to investigate the problems of fluid flow and heat transfer in porous media for the first time.An exact solution with LTE assumption is constructed to validate the accuracy of the numerical method.(2)The effect of temperature-dependent thermal diffusivity together with the aspect ratio on the free convection in a rectangular porous enclosure is numerically studied.The governing equation and the corresponding boundary conditions for heat function with variable thermal diffusivity has been constructed.(3)Based on the solution of the radiation transfer equation,the influence of the radiative properties and the dimensionless parameters i.e.the Ra,the interphase heat transfer coefficient and the interphase thermal conductivity ratio on the fluid flow and heat transfer in a porous cavity with local thermal non-equilibrium assumption is analyzed.