The effective thermal conductivity (ETC) of roughened porous media (RPM) is of interest in a number of applications of heat transfer. In this work, a fractal analytical model for the ETC of RPM with microscale effect is proposed. The proposed fractal model is expressed in terms of relative roughness, the molecular mean free path, porosity, fractal dimensions (pore area fractal dimension and tortuosity fractal dimension), maximum pore diameter, capillary straight length, and the thermal conductivity of the solid matrix and gas. It is observed that the dimensionless ETC of RPM decreases with increasing relative roughness, pore area fractal dimension and tortuosity fractal dimension. Besides, it is found that the dimensionless ETC of RPM increases with thermal conductivity ratio of gas phase over solid phase. In addition, it is found that the dimensionless ETC of RPM is slightly dependent on the relative roughness and tortuosity fractal dimension when [Formula: see text]. The determined dimensionless ETC of RPM is in good agreement with experimental data and existing models reported in the literature. With the proposed fractal model, the physical mechanisms of heat transport through RPM with microscale effect are better elucidated. Every parameter in the fractal analytical model has clear physical meaning, with no empirical constant.
The purpose of this paper was to investigate the combined effects of couple stress and surface roughness on lubrication performance and regime transition of misaligned hydrodynamic journals. New lubrication models considering misalignment angle, couple stress, and surface roughness were established. Under the multi-coupled factors, Stribeck curves were exploited to reveal the lubrication regimes of journals. Following Greenwood’s aspect contact theory, force relational equations among external load, asperity support capacity, and oil film bearing capacity have been further discussed. Results showed that the growth of the minimum film thickness, the maximum film pressure, and friction coefficient versus couple stress parameters trended to be opposite to those versus misalignment angle. The speed of the lubrication regime transition and the minimum friction coefficient increased with the enlargement of the misalignment angle but decreased as the couple stress parameter increased. Higher couple stress parameters resulted in an increment of the safety speed of the journal and were conducive to maintaining the hydrodynamic lubrication regime of the misaligned bearing at low speed, which is applicable to such misaligned journal bearings in practical engineering.
The seepage in tree-like bifurcating networks is a very common phenomenon in nature. The research on the transport characteristics of tree-like bifurcating networks has always been a hot topic. In this paper, a novel permeability model for fluid flow in damaged tree-like bifurcating networks is proposed. In the proposed model, the influence of roughness on permeability is considered by means of the fractal method. It is found that the permeability is not only related to the structural parameters of the network but also related to the damaged position and the number of damaged tubes at the damaged position. The effects of these parameters and damaged structure on permeability are discussed separately. The results show that the permeability reduces along with an increase in the roughness level, the length ratio, the number of damaged tubes, and the number of total bifurcating levels. Another major finding is that the permeability increases with an increase in the diameter ratio. Besides, we found that the damaged position and the number of damaged tubes at the damaged position have an important effect on the permeability. Increasing the number of damaged tubes and bringing the damaged position close to the front end of the network will reduce the permeability. Compared with the undamaged network, the permeability of damaged network has a significant decline. The proposed model may provide potential applications for the analysis of fluid flow in damaged tree-like bifurcating network.
Severe vibrations of the marine propulsion shaft can evidently affect the dynamical response of the propulsion system and degrade the performance of a ship. As the vibration forms couples which interact with each other, a better understanding of the coupled vibrations is essential for dynamic prediction to improve the efficiency and reliability of the marine propulsion system. Thus, an investigation of the lumped-mass method for coupled torsional-longitudinal vibrations of the shaft is proposed. First, a theoretical solution for the coupled ordinary differential equations demonstrates the accuracy of the proposed lumped-mass model. This model allows for the bifurcation diagram and the Poincare surface, and transient accelerations of the coupled vibrations are numerically calculated. Furthermore, the impact factors including various length-diameter ratios, coupling stiffness coefficients, and damping coefficients are respectively discussed. These impact factors are found to affect the coupled vibrations to different extents through the comparison of the transient accelerations. Finally, an accurate and applicative lumped-mass method for the coupled torsional-longitudinal vibrations of the marine propulsion shaft has been obtained. An optimal design and vibration reduction of the shaft, considering the above-mentioned impact factors, can be achieved.
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