Sharif Digital Repository

A mathematical model has been proposed for evaluation of velocity and temperature fields in hot forging operations for axisymmetric parts. The model can be applied to determine forging load, strain rate, strain and temperature distributions. In addition, the effects of temperature and strain rate on metal flow have been considered through simultaneous modelling of dynamic phase transformation within the deforming metal. Hot forging experiments have been carried out under different working conditions and the results have been compared with the predictions. A good agreement between the simulated and experimental results was found. © 2004 Elsevier Ltd. All rights reserved  

A mathematical model based on the finite element method and additivity rule has been developed to predict temperature history and microstructural changes during cooling of steel. The utilized model considers the effects of various factors including initial austenite grain size and its role on the kinetics of pearlite and ferrite transformations, amount of residual strain within the cooling material, heat of transformation and variation of thermo-physical properties of the steel during cooling. The model can be employed as a guideline to design new cooling programs for achieving the desired microstructure and mechanical properties. To verify the results of the modelling, time-temperature... 

Consider a number of parallel queues, each having unlimited capacity and multiple identical exponential servers. The service discipline in each queue is first-come-first-served (FCFS). Customers arrive according to a state-dependent Poisson process with an arrival rate which is a function of the total number of customers in the system. Upon arrival, a customer joins a queue according to a state-dependent stationary policy, where the state of the system is taken to be the number of customers in each queue. No jockeying among queues is allowed. Each arriving customer has a generally distributed deadline until the beginning of its service, after which it must depart the system immediately. An... 

pH control is known to be a challenging problem due to its highly nonlinear nature. Several control strategies are proposed for controlling pH processes among which is the strong acid equivalent scheme. Although this technique is robust to modeling error, the controller performance is degraded if the titration curve undergoes large changes. To overcome this problem, two control schemes that are based on the strong acid equivalent strategy and that use the multiple models, switching, and tuning approach are proposed in this work. For modeling, both fixed and adaptive models are considered. An experimental setup is used to evaluate the performance of the proposed scheme. The effectiveness of... 

Splashing in the Peirce Smith copper converter was investigated using the Smoothed Particle Hydrodynamics (SPH) method. A model 50 cm in diameter (one eighth of the actual convertor) was made to verify results. The ffect of air flow rate and the distance of air blowers from the surface were identified as two major contributors to splashing and their effect on splashing was investigated. Using C++ based on SPH method, a model, geometrically identical to the physical model, was designed for simulation and verification of results. It was found that splashing may be reduced by as much as 85% by controlling the air flow rate into the convertor  

In tissue engineering, the development of a tissue essentially depends on supply of an adequate amount of nutrients and the design of a proper biophysical micro-environment for cells. The limitation of the available initial number of cells, expensive substances and time consuming experiments are the main bottlenecks in this type of processes. In this regard, mathematical modelling and computational fluid dynamics simulation (CFD) are powerful tools to identify an efficient and optimized design by providing reliable insights of the process. This study presents a mathematical model and CFD simulation of cartilage cell culture under a perfusion flow, which allows not only to characterize the... 

On-chip phase separation of multiphase microflows at the divergence point of Y-shaped microfluidic junctions is an effective way for integrating continuous microstructured devices. In this study, flow pattern maps of various solvent pairs based on the volumetric flow rates of both phases have been drawn experimentally and compared with numerical prediction to investigate the effective domain for which complete phase separation occurred. Furthermore, sufficient separation of aqueous and organic phases at the end of the microchannel was achieved by controlling the pressure difference at the liquid-liquid interface via loading back-pressure on the organic phase. A mathematical model based on... 

In this paper, we introduce and analyze a mathematical model of a viral infection with explicit age-since infection structure for infected cells. We extend previous age-structured within-host virus models by including logistic growth of target cells and allowing for absorption of multiple virus particles by infected cells. The persistence of the virus is shown to depend on the basic reproduction number R0. In particular, when R0 ≤ 1, the infection free equilibrium is globally asymptotically stable, and conversely if R0 > 1, then the infection free equilibrium is unstable, the system is uniformly persistent and there exists a unique positive equilibrium. We show that our system undergoes a... 

Due to the importance of environmental protection and the need to use new energy and alternative to conventional fuels, renewable energy has received much attention. Due to this necessity, a discontinuous bioreactor producing methane gas from animal waste has been modeled and simulated in this research. Monod kinetics was used to express the relationship between the growth rate of microorganisms and substrate concentration. The fourth-order Rong Kuta numerical method solved the substrate consumption and production of microorganisms and methane gas. The effect of the initial concentration of microorganisms on methane production has also been investigated. The initial concentrations of... 

In this paper, heat and mass transfer phenomena occurring simultaneously in falling film generator of absorption chillers have been studied. The analysis is based on the laminar flow of an Li/Br solution over a horizontal single tube and tube bundle having a constant tube wall temperature. The effect of boiling has been ignored. An extensive numerical code is provided to calculate the heat transfer coefficient and the rate of evaporation. A parametric study is performed on the coefficient of heat transfer and the evaporation flux of the refrigerant. Dimensionless correlations are obtained to calculate the heat transfer coefficient on the horizontal tube and tube bundle. The comparison... 

In this work, a model based on the finite element method and assumption of second order phase transformation has been developed to predict temperature history and austenite decomposition kinetics during continuous cooling of a low carbon steel. In order to accurately assess the temperature field and transformation rate the effects of various factors such as work hardening role on the kinetics of transformation, interconnection between austenite phase change and thermo-physical properties of the steel, and initial austenite grain size have been considered in the model. To verify the results of the modelling, time-temperature histories during cooling of a low carbon steel has been determined... 

A mathematical model is proposed for evaluating flow behaviour under hot deformation conditions. The effects of dynamic recovery and recrystallisation as well as temperature and strain rate variations are considered in the model by means of Bergstrom's approach and the additivity rule for strain. To verify the model, hot compression tests for three grades of steel together with upsetting experiments are carried out. Comparison between experimental and theoretical results confirms the reliability of the model. © 2003 IoM Communications Ltd. Published by Maney for the Institute of Materials, Minerals and Mining  

Using a model reduction method, a formula for the ideality factor of a pn junction as a function of the diffusion and generation terms of its reverse current is derived. Using this formula a method for separate computation of these two currents for a pn junction is presented. The validity of the method is investigated using computer simulations for an assumed diode with known ideality factor and total leakage current. Experimental results for two commercially available diodes validate the proposed technique  

In this paper a mathematical model based on the finite element method and the Scheil additivity rule is presented for predicting the temperature distribution and phase transformation behavior on the run-out table during the hot strip rolling of a low carbon steel. The model considers the austenite to ferrite and pearlite transformations, the temperature-dependent material properties of the cooling austenite as well as the austenite work hardening effect on the kinetics of austenite transformation. To determine the validity of the model predictions, the time-temperature histories of a low carbon steel rod in different cooling media were measured and also hot rolling experiments were... 

We investigate the effect of directed short- and long-range connections in a simple model of a small-world network. Our model is one in which we can determine many quantities of interest by an exact analytical method. We calculate the function [formula presented] defined as the number of sites affected up to time T when a naive spreading process starts in the network. As opposed to shortcuts, the presence of unfavorable bonds has a negative effect on this quantity. Hence, the spreading process may not be able to affect all of the network. We define and calculate a quantity identified as the average size of the accessible world in our model. The interplay of shortcuts and unfavorable bonds on... 

This paper presents a mathematical model for predicting the temperature distribution and austenite microstructural changes during hot rolling of steel bars and rod. The model is based on the finite element method for evaluating the temperature distribution and Wusatowski approach to determine the strain field within the deformation zone. Also, by employing double and single hit hot compression experiments, the kinetics of dynamic and static recrystallization of a low carbon steel are determined to predict the flow stress as well as the phase changes in austenite range during and after the hot rolling process. To deal with the correlation between the metal flow and thermal behaviour and... 

A unidirectional two-lane road is approximated by a set of two parallel closed one-dimensional chains. Two types of cars, i.e., slow and fast ones are considered in the system. Based on the Nagel-Schreckenberg model of traffic flow [K. Nagel and M. Schreckenberg, J. Phys. 2, 2221 (1992)], a set of reaction-diffusion processes is introduced to simulate the behavior of the cars. Fast cars can pass the slow ones using the passing lane. We write and solve the mean-field rate equations for the density of slow and fast cars, respectively. We also investigate the properties of the model through computer simulations and obtain the fundamental diagrams. A comparison between our results and the... 

Though wound healing process is well-researched, this area is poorly known. One reason is that all interactions have not been discovered, the main reason, though, is that the involved processes interact in a very complicated manner with nonlinear feedback. Such complex feedback mechanisms can be easily addressed by mathematical modeling. This paper contains a review of the mathematical modeling of cell interaction with extracellular matrix components during the process of dermal wound healing with focusing on remodeling phase. The models are of partial differential equation type and solved by numerical method  

Though wound healing process is well-researched, this area is poorly known. One reason is that all interactions have not been discovered, the main reason, though, is that the involved processes interact in a very complicated manner with nonlinear feedback. Such complex feedback mechanisms can be easily addressed by mathematical modeling. This paper contains a review of the mathematical modeling of cell interaction with extracellular matrix components during the process of dermal wound healing with focusing on remodeling phase. The models are of partial differential equation type and solved by finite element method  

A two-dimensional non-isothermal mathematical model has been developed for the ethane dehydrogenation reaction in a fixed-bed catalytic membrane reactor. Since ethane dehydrogenation is an equilibrium reaction, removal of produced hydrogen by the membrane shifts the thermodynamic equilibrium to ethylene production. For further displacement of the dehydrogenation reaction, oxidative dehydrogenation method has been used. Since ethane dehydrogenation is an endothermic reaction, the energy produced by the oxidative dehydrogenation method is consumed by the dehydrogenation reaction. The results show that the oxidative dehydrogenation method generated a substantial improvement in the reactor...