Research On Convective Heat Transfer In Porous Media-free Flow Channel Under Local Thermal Non-equilibrium Conditions

Fluid flow in porous media is widely involved in industrial production and people’s daily life,and has been widely concerned by researchers.Because of the complex internal structure of porous media,there are complex heat and mass exchange behaviors near the interface in the porous-fluid composite channel.Moreover,because the heat transfer model and thermal boundary conditions in the porous media and the interface in the channel are not unified,the research of the model and interfacial conditions in the channel have been place a great valued.In this paper,the heat transfer characteristics of forced flow in the porous-fluid channel are analyzed and studied.Brinkman-extended Darcy model and Brinkman-Forchheimer Extended Darcy model combined with stress jump conditions were used to establish the motion equations,and local non-thermal equilibrium（LTNE）model was used to establish the energy equations.The precise analytical solutions of the temperature distribution of fluid and solid phases in the channel and the Nusselt number,Nu,under three different thermal boundary conditions are obtained.The effects of interfacial stress jump coefficient,β,Darcy number,Da,Biot number,Bi,thermal conductivity ratio,K,interfacial convective heat transfer coefficient,H_s,inertia coefficient,F_f,and hollow ratio,S,on the heat transfer performance of the channel are analyzed.According to the results,under the three thermal boundary conditions,the increase in thermal conductivity ratio and Darcy number,as well as the decrease in hollow ratio and Biot number will increase the temperature difference between fluid phase and solid phase in the porous region.When applying model B,the LTNE model is suitable for almost any condition,but for models A and C,the local thermal equilibrium（LTE）assumption is valid in most cases,only when the hollow ratio and the Biot number are low and the thermal conductivity ratio and Darcy number is large,the LTNE model is applicable.For different thermal conductivity ratios and Biot numbers,the relationship between Nusselt number and hollow ratio under model A can be divided into three types:Nusselt number has a maximum value,Nusselt number has a minimum value,and the Nusselt number decreases monotonously with the increase of hollow heart rate.Under model B,there are only two types of relationship between the Nusselt number and the hollow ratio:the Nusselt number has a minimum value and the Nusselt number decreases monotonously with the increase of the hollow ratio.For model C,the type of Nusselt number curve is related to the interface convection heat transfer coefficient,and the increase of the interface convection heat transfer coefficient will increase the Nusselt number under model C,and make it closer to but not exceeding that of model A;and the Nusselt number of model B is lower than the Nusselt number of model A and model C.In addition,the numerical solution of the temperature and Nu in the partially filled porous media channel under the influence of inertia effect is further obtained,and the influence of various parameters,especially the inertia coefficient,F_f,on the heat transfer is analyzed.The results show that The increase of the inertia coefficient will reduce the temperature difference between the two phases.Increasing the Biot number will weaken the influence of the inertia coefficient on the fluid phase temperature.At the same time,the increase of the thermal conductivity ratio and the Darcy number will enhance the influence of the inertia coefficient on the temperature field and the Nusselt number.When Da<10^-3,the inertia coefficient’s effect on the temperature field and Nusselt number could be neglected.The influence of temperature field and Nusselt number can be ignored.The increase of the Darcy number and the decrease of the inertia coefficient will enhance the comprehensive heat transfer performance of the channel,but the decrease of the Darcy number will weaken the influence of the inertia coefficient on the heat transfer performance.In particular,when F_f=0,the thermal conductivity ratio,Biot number,and Darcy number are all large,there is an optimal hollow ratio so that the comprehensive heat transfer performance is more than twice that of an unfilled porous medium channel.Whether the LTE assumption is considered,the influence of the inertia effect on the heat transfer intensity is similar.