Analysis Of Film Condensation And Film Boiling On A Vertical Plate Imbedded In Porous Media

Film condensation and film boiling are widely used in heat exchanger design,heat pipe system,chemical system,geothermal system and energy storage system,etc.The liquid film or gas film covering the heat transfer surface seriously reduces the heat transfer efficiency.The thermal conductivity and specific surface area of metal foam are very high,which makes it have the potential to strengthen film condensation and film boiling heat transfer.Presently,the study of film condensation and film boiling heat transfer on vertical surfaces in porous media is mainly carried out by numerical simulation method,and there is a lack of theoretical research.In this thesis,film condensation and film boiling heat transfer on vertical surfaces in porous media are studied by theoretical derivation.The main research contents and conclusions are as follows:Film condensation and film boiling on a vertical plate imbedded in porous media under the local thermal equilibrium(LTE)or local thermal non-equilibrium(LTNE)condition is analyzed.Darcy-Brinkman model and LTE or LTNE model are introduced to establish the mathematical formulation.For LTE model,the temperature of phase change interface is equal to temperature outside the phase transition interface.For LTNE model,a parameter describing the heat flow distribution at the phase transition interface is introduced and the boundary condition in the form of heat flow distribution is adopted.Through analytically solving the mathematical model,the temperature distribution,velocity distribution,film thickness and local heat transfer coefficient are obtained.The approximate analytical solution of film thickness with better accuracy can be obtained under certain circumstances.In the study of film condensation,the problem is solved in the boundary layer approximation.The shear stress at the liquid-vapor interface is assumed to be negligible.The wall temperature remains constant.Two of the most fundamental models are established to describe the condensation heat flux distribution between the fluid and solid phases at the liquid-vapor interface.When the ratio of liquid film thickness to Darcy number is much less than 1,an approximate analytical solution to LTE model is obtained,and the approximate analytical solutions of the LTNE model are obtained respectively under the two cases where the ratio of gas film thickness to Darcy number is much less than 1 and Biot number is much less than or greater than 1.Those approximate solutions are proved to have better accuracy.In the study of film condensation,the effects of Biot number and Darcy number on liquid film thickness,temperature and velocity distribution and local Nu number are investigated.For Model A,the increases of Biot number and Darcy number have positive effects on the increase of local Nu number.As Biot number increases and Darcy number decreases,the liquid film thickness increases.At the end of the vertical wall,the liquid-vapor interface velocity reaches the balance velocity,and the liquid film thickness increases linearly.Furthermore,the local thermal equilibrium condition is always achieved for Model B,which is independent of the Biot number.In the study of film boiling,in addition to boundary conditions of film condensation study,the constant heat flux on the wall and a stationary liquid at the outer boundary of the vapor film commonly used in practical engineering applications are also considered.The approximate analytical solutions satisfying certain conditions under various combinations of boundary conditions are obtained.When the ratio of vapor film thickness to Darcy number is much less than 1,an approximate analytical solution to LTE model is obtained,and the approximate analytical solutions of the LTNE model are obtained respectively under the two cases where the ratio of vapor film thickness to Darcy number is much less than 1 and Biot number is much less than or greater than 1.Those approximate solutions are proved to have better accuracy.In the study of film boiling,the balance velocity also appears in the vapor film.For the moving liquid,the balance velocity first appears at the phase change interface.For stationary liquid,the equilibrium velocity first appears in the middle of the vapor film.The increases of Biot number and Darcy number have positive effects on the increase of local Nu number.As Biot number increases and Darcy number decreases,the liquid film thickness increases.