Mathematical analysis and numerical resolution of a heat transfer problem arising in water recirculation

This work is devoted to the analysis and resolution of a well-posed mathematical model for several processes involved in the artificial circulation of water in a large waterbody. This novel formulation couples the convective heat transfer equation with the modified Navier–Stokes system following a Smagorinsky turbulence model, completed with a suitable set of mixed, nonhomogeneous boundary conditions of diffusive, convective and radiative type. We prove several theoretical results related to existence of solution, and propose a full algorithm for its computation, illustrated with some realistic numerical examples.Ministerio de Economía y Competitividad | Ref. MTM2015-65570-PXunta de Galicia | Ref. ED431D 2017/1

Mathematical analysis and numerical resolution of a heat transfer problem arising in water recirculation

This work is devoted to the analysis and resolution of a well-posed mathematical model for several processes involved in the artificial circulation of water in a large waterbody. This novel formulation couples the convective heat transfer equation with the modified Navier-Stokes system following a Smagorinsky turbulence model, completed with a suitable set of mixed, nonhomogeneous boundary conditions of diffusive, convective and radiative type. We prove several theoretical results related to existence of solution, and propose a full algorithm for its computation, illustrated with some realistic numerical examples

A multi-layer integral model for locally-heated thin film flow

Based on an approach used to model environmental flows such as rivers and estuaries, we develop a new multi-layered model for thin liquid film flow on a locally-heated inclined plane. The film is segmented into layers of equal thickness with the velocity and temperature of each governed by a momentum and energy equation integrated across each layer individually. Matching conditions applied between the layers ensure the continuity of down-plane velocity, temperature, stress and heat flux. Variation in surface tension of the liquid with temperature is considered so that local heating induces a surface shear stress which leads to variation in the film height profile (the Marangoni effect). Moderate inertia and heat convection effects are also included. In the absence of Marangoni effects, when the film height is uniform, we test the accuracy of the model by comparing it against a solution of the full heat equation using finite differences. The multi-layer model offers significant improvements over that of a single layer. Notably, with a sufficient number of layers, the solution does not exhibit local regions of negative temperature often predicted using a single-layer model. With Marangoni effects included the film height varies however we find heat convection can mitigate this variation by reducing the surface temperature gradient and hence the surface shear stress. Numerical results corresponding to the flow of water on a vertical plane show that very thin films are dominated by the Marangoni shear stress which can be sufficiently strong to overcome gravity leading to a recirculation in the velocity field. This effect reduces with increasing film thickness and the recirculation eventually disappears. In this case heating is confined entirely to the interior of the film leading to a uniform height profile

Mixing and Demixing Processes in Multiphase Flows With Application to Propulsion Systems

A workshop on transport processes in multiphase flow was held at the Marshall Space Flight Center on February 25 and 26, 1988. The program, abstracts and text of the presentations at this workshop are presented. The objective of the workshop was to enhance our understanding of mass, momentum, and energy transport processes in laminar and turbulent multiphase shear flows in combustion and propulsion environments

Numerical analysis of heat transfer in the exhaust gas flow in a diesel power generator

This work presents a numerical study of heat transfer in the exhaust duct of a diesel power generator. The analysis was performed using two different approaches: the Finite Difference Method (FDM) and the Finite Volume Method (FVM), this last one by means of a commercial computer software, ANSYS CFX®. In FDM, the energy conservation equation was solved taking into account the estimated velocity profile for fully developed turbulent flow inside a tube and literature correlations for heat transfer. In FVM, the mass conservation, momentum, energy and transport equations were solved for turbulent quantities by the K-ω SST model. In both methods, variable properties were considered for the exhaust gas composed by six species: CO2, H2O, H2, O2, CO and N2. The entry conditions for the numerical simulations were given by experimental data available. The results were evaluated for the engine operating under loads of 0, 10, 20, and 37.5 kW. Test mesh and convergence were performed to determine the numerical error and uncertainty of the simulations. The results showed a trend of increasing temperature gradient with load increase. The general behaviour of the velocity and temperature profiles obtained by the numerical models were similar, with some divergence arising due to the assumptions made for the resolution of the models

Two-Dimensional Mathematical Modelling of a Dam-Break Wave in a Narrow Steep Stream

The paper deals with hydraulic aspects of a wave, emerging as a result of a potential dam break of the upper storage reservoir of the pumpedstorage hydropower plant Kolarjev vrh. A two-dimensional depth-averaged mathematical approach was used. The upper storage reservoir and its dam failure were modelled with the mathematical model PCFLOW2D, which is based on the Cartesian coordinate numerical mesh.\ud The results of PCFLOW2D were used as the upper boundary condition for the mathematical model PCFLOW2D-ORTHOCURVE, based on the orthogonal curvilinear numerical mesh. The model PCFLOW2D-ORTHOCURVE provided a tool for the analysis of flood wave flow in a steep, narrow and geometrically diversified stream channel. The classic Manning’s equation fails to give good results for streams with steep bed\ud slopes and therefore, a different equation should be used. The application of the Rickenmann’s equation was chosen, presented in a form similar to Manning’s equation. For the purpose of the example given here, the equation was somewhat simplified and adapted to the data available. The roughness coefficient used at each calculation cell depended on the slope of that cell. The results of numerical calculations\ud were compared to measurements carried out on a physical model in the scale of 1 : 200. Regarding the complexity of the flow phenomenon a rather good correlation of maximum depth was established: only at one gauge the difference in water depth was up to 27% while at the other four it was 7% of water depth on average