21 research outputs found

    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

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    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

    Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition: an exact solution

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    This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers

    Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition: an exact solution

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    This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers

    Mechanism of the onset of detonation in blast initiation

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    The problem of blast initiation of gaseous detonation has been studied by focusing on the onset of detonation, i.e. the development of a pressure pulse during the quasi-steady period which leads to an abrupt acceleration to form a self-sustained detonation. This study has been carried out by numerical simulation of the one-dimensional Euler equations in a planar geometry. For the chemical kinetics model, a single-step Arrhenius law was assumed. It was found that for the critical energy required to initiate a detonation, the onset starts with the development of a pressure pulse between the reaction front and the shock front. The formation of the pressure pulse was attributed to the rapid energy release in the long induction length during the quasi-steady period. It was observed that within the framework of the present analytical model of a single-step Arrhenius rate law without losses, it is difficult to define a precise value for the critical initiation energy. However, the abrupt increase in the run up distance when the initiation energy reaches some critical range can be used to define the critical initiation energy. The present results show that initiation process has the same mechanism for both stable and unstable detonations. However, for unstable detonations when the activation energy is very high, no unique value can be defined for the critical initiation energy. It was found that analytical models based on the Zeldovich criterion cannot predict the critical initiation energy over the full range of activation energies considered in this study. This is because the Zeldovich criterion does not consider any dynamic effects during the quasi-steady period. Comparing previous research on initiation which used other initial conditions and the "blast initiation" which was studied in the present work, it was concluded that the onset of detonation during the quasi-steady period has the same mechanism for "deflagration to detonation transition" and "direct initiatio
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