Finite elements with continuous stress fields in calculation of folded prismatic thin-walled rods and shells

The article deals with methods of creating a rectangular wall-beam finite element with eight degrees of freedom per node and continuous stress fields along the boundaries. This effect is achieved by specifying displacement fields in the plane of the element in forms similar to those in finite elements of Bogner, Fox, and Schmitt plate. The article provides algebraic expressions for displacement forms; methods of forming reaction and stress matrices are also considered. Test calculations carried out with the help of “Computational mechanics” FEM complex have proved high efficiency of the finite element analysis performed. A rectangular shell finite element with twelve degrees of freedom per node was developed as a combination of membrane finite element and Bogner, Fox and Schmitt plate element.

Novel Heat Exchanger Design With Rectangular Shell Geometry

Shell and Tube Heat Exchangers (STHE) are the most versatile type of heat exchangers used in industrial applications. The shape of Shell side of the traditional STHE’s is cylindrical for industrial applications. On one hand, STHE have some good features but on the other hand, it has some limitations due to the cylindrical geometry of the shell side. Some of these limitations are maximum two shell pass is possible as per TEMA layout, complete counter flow cannot be achieved, possibility of reverse heat transfer when number of tube passes are more, tubes are always laid parallel to shell and mounting over the entire length of shell is not possible when impingement plate provided etc. The objective of this study is to design a novel heat exchanger to overcome the limitations of traditional STHE. An experimental setup has been designed with rectangular shell side for STHE. The novel heat exchanger provides the flexibility to increase the number of shell pass and complete counter flow can be achieved due to rectangular geometry of shell side. For the same heat transfer rates, the proposed novel heat exchanger design provides better Effective Mean Temperature Difference (EMTD) and hence less surface area for heat transfer in comparison with traditional STHE. The experiments have been conducted on novel heat exchangers under different operation conditions of hot and cold fluids. The experiment results are compared with theoretical estimations of overall heat transfer coefficient and Log Mean Temperature Difference (LMTD) for traditional shell and tube heat exchangers for the same operation conditions. The results show that under the same operation conditions, the performance of novel heat exchanger is much better than traditional STHE.

Temperature Field Prediction of Rectangular Shell-and-Tube Heat Exchanger

Shell-and-tube heat exchangers are the most common type of heat exchangers in oil refineries and other large chemical processes. In this manuscript, we demonstrate that the shell-side flow in a cylindrical shell was not as homogeneous as that in a rectangular shell. According to the periodic flow field and the arrangement of tubes in the rectangular shell, the solid-fluid coupling heat transfer model consisting of a single tube section and the outer and inner fluids was developed to represent the whole heat exchanger. Using this model, the relationship among four temperatures, namely the inlet and outlet temperatures of tube-side fluid and the upstream and downstream temperatures of shell-side fluid, was established. By dividing each tube into several tube sections at the sites of baffles, a method for predicting the temperature field of the rectangular shell-and-tube heat exchanger was proposed. Based on the node temperature correlation, all the node temperatures were obtained by iterative computation using the established relationship between the four temperatures and the operating conditions. It was found that the temperature distribution of the fluid in tube was approximately linear along axial direction, but the temperature of tube showed nonlinear regularity. The axial deformation compatibility condition for the tube bundle and shell was considered when resolving the stresses in tubes. For the model established in this paper, the mean temperature of the tube at lower position was found to be larger than that at higher position; hence the thermal expansion of the tube at the lower end is larger. In the case the tube-side fluid was heated, all tubes were pulled because of the larger axial thermal expansion of shell, and the stress in the tube with higher temperature is smaller because of the smaller strain.