It is shown that “fixed” tube sheets may be designed in exactly the same manner as “floating” tube sheets with the same boundary restraint, provided that a fictitious uniform “equivalent design pressure” is used in the calculations instead of the actual hydrostatic pressure. This equivalent pressure is evaluated in terms of tube-side pressure, shell-side pressure, differential thermal expansion, and the condition of boundary restraint. The design factors for all tube sheets presented in an earlier paper are shown to be well represented by very simple expressions when the fundamental design parameter x a becomes large.

In an earlier paper it was indicated that perforated plates of triangular layout, with narrow ligaments, as they occur, for instance, in heat-exchanger tube sheets, can be treated in plane-stress calculations as solid sheets of suitable elastic moduli, provided that the stress distribution does not vary appreciably from hole to hole. This paper completes that study by providing suitable curves (Figs. 4, 8), from which deformations and stresses can be read off in terms of the values calculated for solid sheets, for mechanical, thermal, and gravitational loads.

A semitheoretical method for the design of circular tube sheets is outlined based upon “deflection and ligament efficiencies.” These are roughly known from past experience with other design formulas, but experimental work is advocated for more accurate evaluation. A bayonet or U-tube sheet is considered as a modified solid plate and other types as modified solid plates on elastic foundations (the tubes themselves). Design equations are presented for both types with either simply supported or rigidly clamped boundaries.

The subject matter considered in this paper deals with the mathematical investigation of heat flow in an annular disk of uniform thickness. Originally, the investigation was carried on in connection with the design of fins for increasing the heat transfer in various kinds of heat exchangers and engines. The results of the study, however, might easily be applied to a number of other problems, since by altering the boundary conditions slightly one may use the same basic equations for calculating the temperature distribution and heat transmission in grinding wheels and disk clutches. The study of the problem in connection with fin design has brought forth other solutions for special cases of the general proposition considered here. The particular results obtained by previous investigators can be readily found from the general equations given in this paper. In order to assist in the numerical solution of the somewhat complicated equations a chart for evaluating the mathematical expressions has been included.

A combination of the first and second laws of thermodynamics has been utilized in analyzing the performance of a double pipe heat exchanger with a porous medium attached over the inner pipe. The goal of this work is to find the best conditions that allow the lowest rate of entropy generation due to fluid friction and heat transfer with respect to the considered parameters. Results show that the minimization of the rate of entropy generation depends on the porous layer thickness, its permeability, the inlet temperature difference between the two fluids, and the effective thermal conductivity of the porous substrate. An increase in the effective thermal conductivity of the porous medium seems to be thermodynamically advantageous. Unexpectedly, the fully porous annular gap yields the best results in terms of the rate of total entropy generation.

The fluid-elastic instability of tube arrays in heat exchangers may become chaotic, especially when clearances exist between tubes and supports. When chaotic motion appears in tube arrays, significant sliding between the tubes and supports may be induced. An analytical model, consisting of a row of rigid tubes with three tubes supported by springs, is presented. Bifurcation diagrams, Poincare´ maps, power spectral densities, and tube orbits are used to investigate the conditions under which the unpredictable motion can arise. The emphasis is on fluid-stiffness-controlled instability.

The paper presents an analysis of fixed tube-sheet heat-exchanger stresses and tube-sheet deflections. The tube sheet is considered as a perforated, plate on an elastic foundation, which possesses both a deflection and rotational modulus, with an elastically built-in edge consisting of the shell and the channel head.

Tube sheets of U-tube and bayonet-tube exchangers differ from those of floating-head exchangers in that they receive no external support from the staying or column action of the tubes. The strengthening effect of tube-bending reaction is here investigated, evaluated quantitatively, and presented in the form of simple design factors. These factors are functions of a parameter u a , a measure of the relative “barreling” rigidity of the tube bundle as compared to the flexural rigidity of the tube sheet. With stiff tubes and flexible tube sheets (high u a ) the reinforcement due to tube bending is considerable and, in the central region of the tube sheet, the deflection and curvature are essentially independent of any tube-sheet property. At low u a the benefit gained is negligible.