Analytical investigation of heat transfer enhancement in a channel partially filled with a porous material under local thermal non-equilibrium condition: Effects of different thermal boundary conditions at the porous-fluid interface

Abstract

Enhancement of forced convective heat transfer is analytically investigated in a channel partially filled with a porous medium under local thermal non-equilibrium (LTNE) condition. Thermally and hydrodynamically fully developed conditions are considered. The flow inside the porous material is modelled by the Darcy–Brinkman–Forchheimer equation. The thermal boundary conditions at the interface between the porous medium and the clear region are described by two different models. For each interface model exact solutions are developed for the solid and fluid temperature fields. The Nusselt number (Nu) associated with each interface model is derived in terms of the porous insert normalised thickness (S) and other pertinent parameters such as thermal conductivity ratio (k), Biot number (Bi), and Darcy number (Da). The differences between the two interface models in predicting the temperature fields of the solid and fluid phases and validity of the Local Thermal Equilibrium (LTE) assumption are examined. Subsequently, for each model the values of S, Bi, k and Da at which LTE holds are determined. Further, the maximum values of S up to that the two models predict LTE condition are found as a function of Bi, k and Da. For each model and for different pertinent parameters the optimum value of S, which maximises the Nu number, is then found. The results show that, in general, the obtained Nu numbers can be strongly dependent upon the applied interface model. For large values of k and Bi, there are significant disparities between the Nu numbers predicted by the two models. Nonetheless, for most values of k and Bi, and under different values of Da numbers both models predict similar trends of variation of Nu number versus S. The Nu number and pressure drop ratio are then used to determine the Heat Transfer Performance (HTP). It is found that for S<0.9, HTP is independent of Da number and the model used at the porous-fluid interface. For S>0.9, reduction of Da results in smaller values of HTP and signifies the difference between the values of HTP predicted by the two interface models.