Convective heat transfer in porous channel with multi-layer fractures under Local thermal non-equilibrium condition

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Based on Brinkman-extended-Darcy model and Local thermal non-equilibrium (LTNE) model, analytical solutions of velocity and temperature fields, pressure drop and Nusselt number of porous channels containing different number of fracture layers are obtained. The characteristics of fluid flow and heat transfer in multi-layer parallel fractured channels are further studied. Results show that for a single-layer or multi-layer fractured channel, the pressure drop changes sensitively at small hollow ratio and increases as the number of fracture layers increases with decreasing increase degree, but the pressure drop tends to be consistent regardless of the number of fracture layers when Darcy number is high. For small ratio of effective thermal conductivity, LTE model is valid regardless of Biot number, and the heat transfer intensity in multi-layer fractured channels is always higher than that in single-layer fractured channel at any hollow ratio, but the heat transfer intensity is still low. For large ratio of effective thermal conductivity, increasing Biot number or fracture layer number makes the Nusselt number increase under very small hollow ratio for both single and multiple fracture cases, and when both the ratio of effective thermal conductivity and Biot number are high, there is an intersection point occurs at hollow ratio near 0.1, which makes same heat transfer effect under different fracture numbers.