No abstract

Analytic time-domain solutions are obtained for the dynamics of a shell-and-tube heat exchanger with finite tube-wall heat capacity and finite shell-side heat transfer resistance. The transient response for step velocity changes is derived for velocity dependent tube-side heat transfer coefficient without the use of perturbation approximations. Solutions are also obtained for the response to disturbances of shell-side and tube-side fluid temperatures. The equations are in terms of tabulated J functions which facilitate the examination of the effects of the parameters and the determination of the range of applicability of the previous "no-wall" solutions. The transient response characteristics are found to be significantly affected by both the ratio of tube-wall and tube-fluid heat capacities and the fractional heat transfer resistance on the shell side. The response for a limiting "no-wall" model including a velocity dependent heat transfer coefficient shows a significant deviation from the exact solution especially for an increase in velocity.

In the clinic, most cases of congenital heart valve defects are thought to arise through errors that occur after the endothelial–mesenchymal transition (EndoMT) stage of valve development. Although mechanical forces caused by heartbeat are essential modulators of cardiovascular development, their role in these later developmental events is poorly understood. To address this question, we used the zebrafish superior atrioventricular valve (AV) as a model. We found that cellularized cushions of the superior atrioventricular canal (AVC) morph into valve leaflets via mesenchymal–endothelial transition (MEndoT) and tissue sheet delamination. Defects in delamination result in thickened, hyperplastic valves, and reduced heart function. Mechanical, chemical, and genetic perturbation of cardiac forces showed that mechanical stimuli are important regulators of valve delamination. Mechanistically, we show that forces modulate Nfatc activity to control delamination. Together, our results establish the cellular and molecular signature of cardiac valve delamination in vivo and demonstrate the continuous regulatory role of mechanical forces and blood flow during valve formation.

The numerical methods developed in Part I are applied to a number of important countercurrent processes. Examples involving simultaneous input disturbances, distributed disturbances, Langmuir isotherms, and nonlinear coupled boundary conditions are tested. These examples, if solved by previous methods, would have required interpolation or iterative procedures, but are solved efficiently and accurately by the explicit algorithms and coding sequence developed in Part I.The solutions for a linear system are in excellent agreement with the analytic solution. Numerical solutions obtained from explicit algorithms based on a nonlinear rate expression also shows very good agreement with the analytic solutions of Thomas (1944) for a fixed bed process. In both cases good accuracy is obtained with as few as sixteen increments. SCOPEThe methods and algorithms developed in Part I are expected to be efficient and accurate because of their noniterative nature and the absence of internal interpolation. Nevertheless, it is desirable to test the accuracy and efficiency of the proposed methods against an analytic solution. The only analytic solution for a countercurrent heat or mass transfer system is that of Jaswon and Smith (1954) for a linear driving force rate equation with a linear isotherm. A countercurrent heat exchanger to which a step input disturbance is applied is used to check the accuracy and efficiency of the basic numerical method. The ease of extending the algorithms for a linear system is illustrated by the use of time dependent input changes, step flow rate changes and the inclusion of a stationary accumulating phase. The flexibility of the basic method is further demonstrated by applying the method of Part I for simultaneous disturbances to a packed column absorber with a linear isotherm.The algorithms developed for a countercurrent system with a Langmuir isotherm are tested for accuracy by comparing a numerical solution to an analytic solution (Thomas, 1944) for a second-order kinetic model for a fixed-bed sorption process.The straightforward extension of the methods of Part I is illustrated by application to a batch distillation with packed column rectification. The application for this system involves the use of the method for a step flow rate (reflux ratio) change together with the application of algorithms derived for Langmuir isotherms. This distillation example also serves to illustrate the simple method of handling coupled boundary conditions that arise because of the reboiler and overhead conditions. The possible errors due to the often used assumption of negligible vapor holdup are examined by comparison to the more accurate model without this assumption. CONCLUSIONS AND SIGNIFICANCEThe proposed noniterative numerical algorithm using a characteristic grid gives results that agree with the analytic solution for a countercurrent heat exchanger to less than 0.1% relative error for an increment size as large as 0.1 of the normalized total length parameter. The computation time required for obtaining this l...