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This paper is concerned with the analysis of a single-server batch arrival retrial queue with starting failures in discrete time in which all the arriving customers need essential service (ES) necessarily whereas only some may require the optional service (OS) after ES. The customers are assumed to arrive at the system according to a geometric process during the consecutive slots. The service times and retrial times are generally distributed. The generating functions of the number of customers in the retrial group and in the system are obtained along with the marginal distributions of the number of customers in the retrial group when the server is idle, busy (in providing ES or OS) or broken down. The explicit formulae for the stationary distribution and other performance measures at equilibrium are obtained. Some special cases are deduced by setting appropriate parameters. The stochastic decomposition property has also been discussed. The numerical examples are facilitated to explore the effect of different parameters on various performance measures.

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An important parameter required for computing heat loss through buried submarine pipelines transporting crude oil is the thermal conductivity of soils. This paper describes an apparatus designed for determination of the thermal conductivity of soils at the desired moisture/ density condition in the laboratory under steady-state conditions. Experimental results on the three soils studied show that thermal conductivity increases as dry density increases at a constant moisture content and that it increases as water content increases at constant dry density. These results confirm the trends isolated earlier by Kersten. The experimental results are compared with the available empirical relationships. Kersten's relation is observed to predict the thermal conductivity of these soils reasonably. The predictions from Makowski and Mochlinski's relation (quoted by Szilas) are not good but improve if the sum of silt and clay fractions is treated as a clay fraction in the computation. Introduction Submarine pipelines are used extensively for transporting crude oil from offshore to other pipelines offshore or onshore. These pipelines usually are steel pipes covered with a coating of concrete. They often are buried some depth below the mudline. The rheological properties of different crude oils vary, and their viscosities increase with a decrease in temperature. Below some temperature, the liquid oil tends to gel. Therefore, for efficient transportation, the crude must be at a relatively high temperature so that it has a low viscosity. The temperature of the soil/water system surrounding a submarine pipeline is usually lower than that of oil. This temperature difference induces heat to flow from the oil to the environment, and the temperature of the oil decreases as it travels along the length of the pipeline. One must ensure that this temperature reduction does not exceed desirable limits dictated by the rheological properties of oil and by the imperatives of efficient economic properties of oil and by the imperatives of efficient economic transportation. Thus the analytical problem is to predict the temperature of crude in the pipeline some distance away from the input station. To do so, knowledge of the overall heat transfer coefficient for the pipeline is required, for which, in turn, it is necessary to know the thermal conductivities of the oil, the pipeline materials and its coating, and the soil. This paper presents thermal conductivities of soils determined in the laboratory under steady-state conditions and also presents a comparison of the test results of three soils with values determined from existing empirical relationships. Literature Review Heat moves spontaneously from higher to lower temperatures. In a completely dry porous body, transmission of heat can take place not only by conduction through the solid framework of the body and the air in the pores but also by convection and radiation between the walls of a pore and by macro- and microdistillation. In soils, however, it can be ascribed essentially to conduction, a molecular phenomenon that can be expressed in terms of experimentally determined coefficients of conductivity or resistivity, although these actually may include microdistillation and other mechanisms. SPEJ p. 558

Density, viscosity and sound velocity of six binary liquid mixtures of methanol, ethanol, propanol, butanol, hexanol and octanol with 1,4-dioxane have been measured over the entire range of composition at temperature 303.15K. From the experimental densities, viscosities and sound velocity, the excess molar volume (V E ), deviation in viscosity (Δη) and deviation in isentropic compressibility (ΔK S ) have been calculated. The results have been used to discuss the nature and strength of intermolecular interactions in these mixtures.