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Openings, also called Nozzles, in Pressure Vessels are provided to attach piping and other instruments. Piping attached, exerts external forces on openings which create local stresses on the Nozzle-to-Shell junction. Determination of failure stresses is necessary for both safety and economics. Currently WRC 107 (also WRC 537) is the most popular and acceptable bulletin for calculation of local stresses. The bulletin is based on P.P. Bijilaard's experimental work and aimed at providing methods for determining the stresses in pressure vessel-nozzle connections subjected to various forms of external loadings. This bulletin has advantage over other methods for its safety and provides results in very short span of time but geometrical limitations of this bulletin leads to non-conservative results, especially for large openings. Finite Element Method can be used to overcome the geometric limitation problem. For this purpose, this paper is produced to provide finite element procedure for pad reinforced nozzles and also a comparison is made with WRC method.

Heat transfer in Nano fluid from a stretching (shrinking) and porous sheet of variable thickness is investigated in this paper. A set of unseen transformations is generated and the new variables are consequently used for the solution of partial differential equations under consideration. The classical models of heat transfer in Nano fluids from rigid/porous and stretching/shrinking sheets with Brownian motion and thermophoresis effects will be the special case of current study. The set of generalized similarity variables is introduced into the systems of boundary layer equations and boundary conditions and a system of coupled and non-linear ODE’s is formed. The final ODE’s are characterized by several dimensionless parameters and their effects are examined on field quantities. The governing parameters are: suction (injection), stretching (shrinking) parameters, Brownian motion number ( Nb), Thermophoresis number ( Nt) and Lewis number ( Le). The numerical observations are shown in different graphs and tables, whereas, effects of physical parameters are seen on the rate of heat transfer [Formula: see text] and mass transfer [Formula: see text], defined at the surface of the sheet. Moreover, the new results are presented in the respective sections. The remarkable aspects of the present simulations are scrutinized, however, special cases of current simulations give the previous problems, which are highlighted in the consequent sections.

In this paper, we have studied the transport of heat and mass in viscous fluid flow over a disk, rotating with variable angular velocity, whereas, both the nonuniform injection and suction velocities can take place through its porous surface. Moreover, the disk is stretched (shrunk) with variable velocity in its own plane. Besides that the temperature and concentration functions, defined at the surface of disk, are assumed nonuniform and nonlinear, whereas, their nonlinear nature can be expressed in the form of algebraic and non-algebraic functions, however, the uniform and linearly variable temperature and concentration functions at the surface of the disk are easily obtained by fixing the exponents of these functions either zero or one. Diffusion of these two quantities in flows over such disk are the fundamental objective of current investigations. Six PDE’s control the fluid motion along with the diffusion of heat and mass in flow over the rotating disk of such special characteristics. The system of PDE’s is transformed into a set of ODE’s, which is solved numerically with the help of bvp4c package of MATLAB. The present simulation and its solution are exactly matched with the solution of classical problems of rotating disk flows with the additional characteristic of diffusion of heat and mass in flows. Therefore, we have seen the individual and combined effects of all physical parameters on field variables under consideration. The higher order governing equations are nonlinear PDE’s, which are converted into the system of ODE’s in view of proper similarity transformations. Moreover, the tangential and radial shears, shaft torque, rates of the diffusion are evaluated at the surface of the disk, whereas, they are graphed against different parameters and interesting results have been presented. It is found that the nonlinear nature of surface temperature and concentration reduced the thermal and concentration boundary layers, however, the large negative values of power index parameters give rise to an overshoot in temperature and concentration profiles.

In determining the punching shear capacity of flat slabs, current codes of practice usually do not consider the effect of boundary restraint against rotation. The contribution of flexural steel reinforcement is ignored by some of the code provisions. Present paper is comprised of the test results of 15 model slabs in an effort to ascertain the influence of boundary restraint, the influence of flexural reinforcement and effect of thickness of the slabs on their structural behavior and punching load-carrying capacity. Cracking pattern and load-deflection behavior of the slabs tested have also been monitored closely. Significant effect of edge restraint on the punching failure load, resulting in an enhancing of the ultimate punching strength, and effect of flexural reinforcement on the punching failure load have been noticed. The code-specified strength of the specimens was calculated in accordance with the American, British, Canadian, European, and Australian codes. It has been understood that punching shear is not effectively estimated in some codes. Thus, inclusion of the findings of the study in the design codes is expected to result in a rational design of structural systems where punching phenomenon plays a vital role.