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The present work investigates mass conservation equations in turbulent flow between parallel plates with variable mass diffusivity. Species conservation equations are relative to the average concentration, as well as to the concentration variance. The product of fluctuating mass diffusivity and space gradient of concentration fluctuation is appearing in the equation of mean and concentration variance. A physical interpretation is given to the different terms. The assumption of a relation between mass diffusivity and concentration allows writing expressions for average and fluctuating mass diffusivity, which can be simplified on the basis of theoretical considerations. The new mass flux is expressed as a function of mass diffusivity and a gradient of concentration variance. Further considerations make it possible to model the new terms appearing in the concentration variance equation. The mass conservation equation can be solved when coupled to the equation of concentration variance. The equations are solved numerically for flow between parallel plates in order to evaluate the influence of the new terms. [DOI: 10.1115/1.4002743]

TA study is conducted to examine the thermal conductivity by solving the heat conduction equation with the assumption of parallel isotherms within the cubic space. The results show the agreement is very good at the temperatures in the range (30-50) degree Celsius and acceptable at 70 degree Celsius.

Mass conservation equation is employed to study the time evolution of the mass of oil in a reservoir, according to the actual mass flow rate of extraction. It is also possible to define the critical mass flow rate of extraction, which is the value exhausting the reservoir in an infinite time. The evolution with time of the price of the resources extracted and sold to the market is investigated in case of no-accumulation and no-depletion of the resources, i.e., when the resources are extracted and sold to the market at the same mass flow rate. The total energy conservation equation is transformed into a money or capital per time conservation equation, which allows to study the price evolution with time, which is dependent on the following parameters. The price evolution with time of the extracted resource is dependent on the parameter PIFE, "Price-Increase Factor of Extracted resource," which is the difference between the basic interest rate of the capital, e.g., the inflation rate, and the mass flow rate of extraction. The price evolution with time of the sold resource is dependent on the parameter PIFS, "Price-Increase Factor of Sold resource," which is the difference between the interest rate of the capital, e.g., discount or prime rate, and the mass flow rate of extraction. The parameter CIPS, "Critical Initial Price of Sold resource," depends on the initial price of the extracted resource, on the interest rate of nonextracted resource, and on the difference between PIFS and PIFE. The parameter CIPES, "Critical Initial Price Extreme of Sold resource," depends on the initial price of the extracted resource, on the interest rate of nonextracted resource, and PIFS. The time evolution of the oil price during the 8 months of 2009, when the inflation rate was negative, and following the economic crisis of 2008, is investigated introducing a new category of cases, i.e., the negative inflation rate one. The paper presents and discusses the results of the forecasting for different values of the interest rate of the capital, i.e., prime and discount rate, with the conclusion that the present theory can forecast the evolution of the oil price with a reasonable confidence using the prime and the discount rates as extreme limits. [ABSTRACT FROM AUTHOR]