Evaluation of Nusselt Number for a Flow in a Parallel Plates Using MHD Second Order Slip Model

In this study, two separate boundary condition models, as proposed by Beskok and Karniadakis [1] and Deissler [2], widely preferred for the second order boundary condition, were used. These two proposed boundary condition models were solved in the presence of a magnetic field moving normal to the plate surface in magneto-hydrodynamic (MHD) flow between micro-parallel plates with constant wall heat flux. The energy equation for the second-order temperature jump boundary condition, taking into account the momentum and viscous dissipation, as well as the corresponding Nusselt value were solved analytically in slip flow regime.The flow of an incompressible viscous flow between fixed micro-parallel plates with electrical conductivity is assumed to be constant, laminar, hydrodynamically and thermally developed. The closed form solutions for the temperature field and the fully developed Nusselt number are derived as a function of the Magnetic parameter (MHD), Knudsen number and Brinkman number and shown graphically and in a tabular form. The second order boundary condition model proposed by Deissler [2] predicts the Nusselt number to be at lower values when compared to the first order boundary condition model, and the second order boundary condition model proposed by Beskok and Karniadakis [1] predicts the Nusselt number to be at higher values than that of the first order boundary condition model. Moreover, increasing the magnetic field parameter M, led to higher Nusselt values in the slip flow model proposed by both Deissler [2] and Beskok and Karniadakis [1] compared to that when M = 0.

Effects of Boundary Condition Models on the Seismic Responses of a Container Crane

In recent years, several large earthquakes have caused the collapse of container cranes, which have resulted in halting of freighting, and significantly affected the economy. Some reports are concerned the uplift and derailment events of crane legs, and the collapse of the crane itself. In this study, the effects of different boundary conditions used in the numerical method are investigated for a container crane under seismic excitation. Three different boundary conditions are considered in terms of the connection of the crane’s legs (wheels) and the ground (rails), namely pin support (PIN), gap element (GAP), and Friction contact (FC) elements, by using the SAP2000 program for a typical container crane. Then, time history dynamic analyses are conducted using nine recorded ground motions. Dynamic behaviors of the container crane are studied in terms of the total base shear, portal drift, and relative displacement of legs, by investigating the three types of base boundary conditions. The results of the study show that when the intensity of earthquakes is large enough to create uplift and derailment events, the selection of the boundary condition model considerably affects the dynamic responses of the container crane. In addition, when uplift and derailment of the crane occur, the FC support condition is the most compatible with the real behavior of the crane. On the other hand, under low seismic excitation, there is no significant difference of the crane behavior according to the choice of boundary condition model.

An Outflow Boundary Condition Model for Noninvasive Prediction of Fractional Flow Reserve in Diseased Coronary Arteries

This paper reports on a new boundary condition formulation to model the total coronary myocardial flow and resistance characteristics of the myocardial vascular bed for any specific patient when considered for noninvasive diagnosis of ischemia. The developed boundary condition model gives an implicit representation of the downstream truncated coronary bed. Further, it is based on incorporating patient-specific physiological parameters that can be noninvasively extracted to account for blood flow demand to the myocardium at rest and hyperemic conditions. The model is coupled to a steady three-dimensional (3D) collocated pressure-based finite volume flow solver and used to characterize the “functional significance” of a patient diseased coronary artery segment without the need for predicting the hemodynamics of the entire arterial system. Predictions generated with this boundary condition provide a deep understanding of the inherent challenges behind noninvasive image-based diagnostic techniques when applied to human diseased coronary arteries. The overall numerical method and formulated boundary condition model are validated via two computational-based procedures and benchmarked with available measured data. The newly developed boundary condition is used via a designed computational methodology to (a) confirm the need for incorporating patient-specific physiological parameters when modeling the downstream coronary resistance, (b) explain the discrepancies presented in the literature between measured and computed fractional flow reserve (FFRCT), and (c) discuss the current limitations and future challenges in shifting to noninvasive assessment of ischemia.