Analytical And Numerical Analysis Of Heat Transfer In Passages Filled With Porous Media

In recent years, porous media filling for heat transfer enhancement such as design of solar storage, heat exchangers, chemical reaction devices, drying facilities and electronic cooling has attracted more and more attention. Through the combination of theory and numerical methods the circular and annular porous media tubes are analyzed under the local thermal non-equilibrium and constant temperature boundary conditions. The obtained results may be helpful and valuable for both scientific researchers and industries.Firstly, based on the energy equations of tube under local thermal non-equilibrium condition, we derived their dimensionless form without considering the transverse heat condition. The method of separation of variables in mathematical physics is utilized to obtain the analytical solutions for the solid and gas dimensionless temperatures and the Nusselt number( Nu).Then, the analytical dimensionless temperatures and the Nusselt number are validate by COMSOL Multiphysics. A good agreement is found between our analytical solutions and numerical results.Subsequently, parameter analysis is performed for the dimensionless temperatures and the Nusselt number. It is found that solid and gas phase dimensionless temperatures reduce by increasing the axial and increase by the Peclect number. Eventually, the dimensionless temperatures approach zero. The solid dimensionless temperature is lower than gas phase temperature for pertinent parameters. Nusselt number reduces with increasing axial coordinate or increases with increasing the Peclect number, and eventually approaches an asymptotic value at certain position.Finally, the method of separation of variables is extended to the annular porous medium and the corresponding analytical solutions are derived. Under the same conditions, our analytical solutions coincide with COMSOL Multiphysics numerical solutions. It is found that the solid and gas dimensionless temperatures are lower than those for the circular porous medium tube, while the value of Nusselt number at entrance and stable value are higher than those for the circular porous medium tube. Additionally, the variation of the dimensionless temperatures with the dimensionless inner diameter is investigated. It is found that the bigger the inner diameter, the lower the diamensionless temperatures and the higher the Nusselt number.With the help of COMSOL Multiphysics, the corresponding energy governing equations are solved by considering the transverse conduction of gas phrase. The obtained results demonstrated that the dimensionless temperatures and Nusselt number for both circular and annular porous tubes are lower than those without the transverse conduction of fluid phrase but the trend is almost same, this phenomenon can also prove the rationality that we do not considering the liquid phase effect in the transverse direction to some extent.