Variable viscosity condition in the modeling of a slider bearing

To reduce tear and wear of machinery lubrication is essential. Lubricants form a layer between two surfaces preventing direct contact and reduce friction between moving parts and hence reduce wear. In this short letter the lubrication of two slider bearings with parallel and nonparallel is studied. First, we show that bearings with parallel plates cannot support any load. For bearings with nonparallel plates we are interested on how constant and temperature dependent viscosity affects the properties of the bearings. Also, a critical temperature for which the bearings would fail due to excess in temperature is found for both latter cases. If the viscosity is constant, the critical temperature is given by an explicit formula, while for the non-constant viscosity the critical temperature can be always found from a closed form formula involving Weber functionsComment: 8 pages, 3 figure

A Mathematical Model for Transport and Growth of Microbes in Unsaturated Porous Soil

In this work, we develop a mathematical model for transport and growth of microbes by natural (rain) water infiltration and flow through unsaturated porous soil along the vertical direction under gravity and capillarity by coupling a system of advection diffusion equations (for concentration of microbes and their growth-limiting substrate) with the Richards equation. (e model takes into consideration several major physical, chemical, and biological mechanisms. (e resulting coupled system of PDEs together with their boundary conditions is highly nonlinear and complicated to solve analytically. We present both a partial analytic approach towards solving the nonlinear system and finding the main type of dynamics of microbes, and a full-scale numerical simulation. Following the auxiliary equation method for nonlinear reaction-diffusion equations, we obtain a closed form traveling wave solution for the Richards equation. Using the propagating front solution for the pressure head, we reduce the transport equation to an ODE along the moving frame and obtain an analytic solution for the history of bacteria concentration for a specific test case. To solve the system numerically, we employ upwind finite volume method for the transport equations and stabilized explicit Runge–Kutta–Legendre super-time-stepping scheme for the Richards equation. Finally, some numerical simulation results of an infiltration experiment are presented, providing a validation and backup to the analytic partial solutions for the transport and growth of bacteria in the soil, stressing the occurrence of front moving solitons in the nonlinear dynamics

A Numerical Solution of Water Flow in Unsaturated Soil with Evapotraspiration

Flow movement in unsaturated soil can be expressed by Richards equation. This equation can be obtained by applying the mass conversation law and the Darcy law. In this work, we solve one-dimensional Kirchhoff transformed Richards equation with loss of water due to the evaporation of unsaturated porous media (soils) and transpiration of plants numerically using Crank-Nicolson method. The result has compared with evapotranspiration function and without it in the governing equation. It has found that an additional work in time and flow movement is needs to reach the given boundary condition for the model without evapotranspiration

An Explicit Stabilized Runge–Kutta–Legendre Super Time-Stepping Scheme for the Richards Equation

We solve one-dimensional Kirchhof transformed Richards equation numerically using finite difference method with various time-stepping schemes, forward in time central in space (FTCS), backward in time central in space (BTCS), Crank–Nicolson (CN), and a stabilized Runge–Kutta–Legendre super time-stepping (RKL), and compare their performances

Bioheat Transfer Equation with Protective Layer

The human thermal comfort is the state of mind, which is affected not only by the physical and body’s internal physiological phenomena but also by the clothing properties such as thermal resistance of clothing, clothing insulation, clothing area factor, air insulation, and relative humidity. In this work, we extend the one-dimensional Pennes’ bioheat transfer equation by adding the protective clothing layer. The transient temperature profile with the clothing layer at the different time steps has been carried out using a fully implicit Finite Difference (FD) Scheme with interface condition between body and clothes. Numerically computed results are bound to agree that the clothing insulation and air insulation provide better comfort and keep the body at the thermal equilibrium position. The graphical representation of the results also verifies the effectiveness and utility of the proposed model

Numerical Modeling of Indoor Air Pollutant Distribution Using Navier-Stokes Equation

The dissertation presents the development of the mass balance model for the distribution of the indoor air pollutants using box method for one and two compartments. The concentration of the pollutants is observed in a compartment with the variation of flow rate and volume taking other parameters like initial concentration, concentration of incoming air, volumetric flow rates, concentration of the outgoing air, source emitting the pollution constant. The result is also compared with the existing data. Discussions are made on the solution of the mass balance equation representing the distribution of the pollutants in two chambers using analytical method. The model has assumptions that all emissions entering the compartment are well-mixed. The model is used to describe the data of TSP in ICS and TCS by Reid (1986) that showed that the air flow rate should be increased through the use of ventilation

Numerical Modeling of Indoor Air Pollutant Distribution Using Navier-Stokes Equation

Most of the rural people in developing countries depend on the biomass energy for cooking and heating purposes. Women in developing country spent their time in the kitchen for cooking the food and suffer from the contaminants emitted from the biomass cook stoves. The study is focused on the numerical modeling of indoor air pollutant originated from a biomass source in a rural kitchen solving the Navier-Stokes equation and mass-energy-species conservation equations to assess its ventilation effectiveness. Turbulence is modeled by the standard k-e model. The velocity profile and temperature distribution in the kitchen are modeled in the present study. Velocity profile and temperature distribution throughout different sections of the kitchen are depicted to explain the primary and secondary pollutant paths. The study suggests proper positioning of the ventilation which will be analyzed to minimize the effect of the pollutant to the person working in the kitchen. Keywords: Numerical modeling, Navier-Stokes equation, Pollutants, Ventilation