Fractional Model and Exact Solutions of Convection Flow of an Incompressible Viscous Fluid under the Newtonian Heating and Mass Diffusion

In this paper, we consider a natural convection flow of an incompressible viscous fluid subject to Newtonian heating and constant mass diffusion. The proposed model has been described by the Caputo fractional operator. The used derivative is compatible with physical initial and boundaries conditions. The exact analytical solutions of the proposed model have been provided using the Laplace transform method. The obtained solutions are expressed using some special functions as the Gaussian error function, Mittag–Leffler function, Wright function, and G -function. The influences of the order of the fractional operator, parameters used in modeling the considered fluid, Nusselt number, and Sherwood number have been analyzed and discussed. The physical interpretations of the influences of the parameters of our fluid model have been presented and analyzed as well. We use the graphical representations of the exact solutions of the model to support the findings of the paper.

Investigation of species-mass diffusion in binary-species boundary layers at high pressure using direct numerical simulations

Direct numerical simulations of single-species and binary-species temporal boundary layers at high pressure are performed with special attention to species-mass diffusion. The working fluids are nitrogen or a mixture of nitrogen and methane. Mean profiles and turbulent fluctuations of mass fraction show that their qualitative characteristics are different from those of streamwise velocity and temperature, due to the different boundary conditions. In a wall-parallel plane near the wall, the streamwise velocity and temperature have streaky patterns and the fields are similar. However, the mass fraction field at the same location is different from the streamwise velocity and temperature fields indicating that species-mass diffusion is not similar to the momentum and thermal diffusion. In contrast, at the centre and near the edge of the boundary layer, the mass fraction and temperature fields have almost the same pattern, indicating that the similarity between thermal and species-mass diffusion holds away from the wall. The lack of similarity near the wall is traced to the Soret effect that induces a temperature-gradient-dependent species-mass flux. As a result, a new phenomenon has been identified for a non-isothermal binary-species system – uphill diffusion, which in its classical isothermal definition can only occur for three or more species. A quadrant analysis for the turbulent mass flux reveals that near the wall the Soret effect enhances the negative contributions of the quadrants. Due to the enhancement of the negative contributions, small species-concentration fluid tends to be trapped near the wall.

Recommendation with Diversity: Mass Diffusion Model Based on Trust Network and Object Reputation

The traditional mass diffusion recommendation algorithm only relies on the user’s object collection relationship, resulting in poor recommendation performance for users with small purchases (i.e., small-degree user), and it is difficult to balance the accuracy and diversity of the recommendation system. This paper introduces the trust relationship into the resource allocation process of the traditional mass diffusion algorithm and proposes the Dual Wing Mass Diffusion model (DWMD), which constructs a dual wing graph based on trust relationships and object collection relationships. Implicit trust is mined according to the network structure of the trust relationship and integrated into the resource allocation process, and then merging the positive effects of object reputation on a recommendation through tunable scaling parameters. The user controls the tunable scaling parameter to achieve the best recommendation performance. The experimental results show that the DWMD method significantly improves diversity and novelty while ensuring high accuracy and effectively improves the accuracy and diversity balance. The improved recommendation performance for small-degree users proves that the trust relationship can effectively alleviate the generalized cold start problem of the recommendation algorithm for users who collect a small number of objects.