Convective Heat Transfer Characteristics In The Multilayered-parallel Fractured Porous Channel Under Local Thermal Non-equilibrium Conditions

Fractured porous media is a common geological structure of strata.The existence of cracks in porous media directly affects the motion resistance and heat transfer capacity of the fluid in the formation.The study of fluid flow and heat transfer in fractured porous media provides some theoretical support for geothermal utilization,oil exploitation,carbon dioxide storage and other engineering fields.In this paper,a porous medium channel model with a parallel single fracture layer in the middle region of the channel is firstly constructed.Further,the total height of the single fracture is kept constant,and it is split into multiple fracture layers of the same height,and multiple fracture layers are uniformly inserted into the channel to construct a multilayer parallel fracture type porous medium channel model.Based on the Brinkman-extended-Darcy model and the Local thermal non-equilibrium(LTNE)model of porous media,the flow heat transfer characteristics of the constructed multilayer parallel fracture-type porous media channel are investigated by considering the heat transfer temperature difference between the fluid and solid phases in the porous media.The velocity field distribution in the channel with different number of fracture layers and the temperature field distribution in the channel with different number of fracture layers and different thermal boundary conditions,as well as the exact analytical solution of Nussle number Nu are obtained.The effects of the number of fracture layers n,Darcy number Da,Bi number Bi,thermal conductivity ratio K,interfacial convective heat transfer coefficient Hs,and hollow rate S on the flow heat transfer performance in the channel are analyzed.The results show that when the Darcy number is small,there will be a Darcy velocity that does not change with height in the porous media layer of the channel.This Darcy velocity will increase with the increase of the number of fracture layers,but it is not affected by the change of the position of the porous media layer under each fracture layer.Increasing the number of fracture layers will weaken the influence of the hollow ratio on the pressure drop,so that the fluid pressure drop in the channel will increase,but the degree of increase will gradually decrease with the increase of the number of fracture layers.When the thermal conductivity is small,the heat transfer intensity in the multi-layer fracture channel is not affected by the Biot number,and the heat transfer effect of the multi-fracture layer channel is better than that of the single-fracture layer channel at any hollow ratio.In addition,there is a critical hollow ratio to make the heat transfer intensity under different multi-fracture layers the same.When the ratio of thermal conductivity is large,increasing the number of crack layers under the condition of small Biot number will weaken the influence of Biot number on Nusselt number,so that the heat transfer intensity increases under the condition of small hollow ratio,and the heat transfer intensity tends to be consistent with the increase of hollow ratio.When the ratio of thermal conductivity is large,there is a critical hollow ratio in the case of large Biot number,so that the heat transfer effect in the channel of each crack layer is the same.Only after this critical hollow ratio,the heat transfer effect in the channel of multi-crack layer is better than that in the case of single crack.And increasing the number of crack layers at any hollow ratio in the multi-crack channel has little effect on the heat transfer intensity.In addition,the analytical solutions of the temperature field and Nusselt number of the local thermal equilibrium(LTE)model in the porous medium region are further obtained,and the calculation results of the influence parameters of the LTE model and the LTNE model under different thermal boundary conditions are compared and analyzed.It is concluded that under the LTE model,when the thermal conductivity ratio is small,the heat transfer effect in the multi-layer parallel fracture channel is better than that in the single fracture channel;when the ratio of thermal conductivity is large,there is a critical hollow ratio to make the heat transfer effect in the channel of each crack layer the same,which is the same as the LTNE model in the case of large thermal conductivity and large Biot number.Regardless of single fracture or multiple fractures,when the hollow ratio is large,the Nusselt number curve of the LTE model tends to coincide with the Nusselt number curve under the LTNE model.