No abstract

As the environment for the oil and gas industry has become increasingly demanding, so has the need for reliable sealing solutions and related standards. Traditionally, metal seals and gaskets had been considered of interest because of their high temperature resistance and mechanical properties. However, their obvious downside of limited ductility and elasticity, compared to non-metallic materials, remained difficult to overcome. Soft, compressible elastomers provide good sealing performance, but are porous and cannot reliably withstand temperatures in excess of 482°F (250°C). They also become hard and brittle in cryogenic service. Metal seals have much greater temperature capabilities, high mechanical properties, lack of porosity and long shelf life, but as mentioned, ductility and elasticity have always been the limiting factor. Understanding application requirements and design criteria is critical to selecting the proper sealing solution in challenging applications such as subsea oil & gas production.

This paper gives a theoretical idea for extracting the underground fluids through peristalsis. Due to the similarity in aforesaid problem, peristaltic transportation of a viscous Newtonian fluid over a vertical porous conduit is studied by considering the impact of heat transfer. Presuming the long-wavelength approximation, explicit solutions are found as asymptotic expansions with reference to free convection and porosity parameters. Mathematical expressions for coefficient of heat transfer, temperature and mean flux are derived. It is experiential that for few precise values of dissimilar parameters under contemplation, the coefficient of heat transfer increases significantly as Grashof number and Eckert number increases. This narrates to optimization of heat transfer in some processes. Further, it has been observed that mean flow enhances with amplitude ratio, porosity in addition to pressure drop. This authorizes auxiliary research on the impacts of peristalsis on the flow features in vertical channels.

An effective method of solving a 6th order nonlinear BVP based on the numerical differentiation is presented in this article. The Uniqueness and existence properties of the solution are established. A more accurate and reliable process is derived to know the solution of 6th order BVPs. The procedure is verified on nonlinear problem. The solutions are matched with exact solutions and absolute errors obtained in this method are compared with that of Galerkin method.

In the present study, we have investigated the differential equations of order four to evolve the methods to achieve the solution for differential equations. Absolute Stability Region (ASR) of the differential equations has been examined. Numerical Differentiation (ND) and Differential Transform Method (DTM) which are suggested and derived in this article are much suitable to understand the solutions of differential equations of fourth order. Both the methods are applied to some differential equations, numerical examples and results are presented to outline the capability and robustness of our strategies and compared them with that of exact solution.