Search results for: Degenerate Differential Equations

Authors: Ramandeep Behl, S. S. Motsa

Abstract:

The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: Basins of attraction, nonlinear equations, simple roots, Super-Halley.

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Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

Abstract:

This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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Authors: Z. El Felsoufi, L. Azrar

Abstract:

This paper studies a mathematical model based on the integral equations for dynamic analyzes numerical investigations of a non-uniform or multi-material composite beam. The beam is subjected to a sub-tangential follower force and elastic foundation. The boundary conditions are represented by generalized parameterized fixations by the linear and rotary springs. A mathematical formula based on Euler-Bernoulli beam theory is presented for beams with variable cross-sections. The non-uniform section introduces non-uniformity in the rigidity and inertia of beams and consequently, more complicated equilibrium who governs the equation. Using the boundary element method and radial basis functions, the equation of motion is reduced to an algebro-differential system related to internal and boundary unknowns. A generalized formula for the deflection, the slope, the moment and the shear force are presented. The free vibration of non-uniform loaded beams is formulated in a compact matrix form and all needed matrices are explicitly given. The dynamic stability analysis of slender beam is illustrated numerically based on the coalescence criterion. A realistic case related to an industrial chimney is investigated.

Keywords: Chimney, BEM and integral equation formulation, non uniform cross section, vibration and Flutter.

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Authors: YaoAn Lu, QingZhen Bi, BaoRui Du, ShuLin Chen, LiMin Zhu, Kai Huang

Abstract:

Taking the design tolerance into account, this paper presents a novel efficient approach to generate iso-scallop tool path for five-axis strip machining with a barrel cutter. The cutter location is first determined on the scallop surface instead of the design surface, and then the cutter is adjusted to locate the optimal tool position based on the differential rotation of the tool axis and satisfies the design tolerance simultaneously. The machining strip width and error are calculated with the aid of the grazing curve of the cutter. Based on the proposed tool positioning algorithm, the tool paths are generated by keeping the scallop height formed by adjacent tool paths constant. An example is conducted to confirm the validity of the proposed method.

Keywords: Strip machining, barrel cutter, iso-scallop tool path, sculptured surfaces, differential motion.

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Authors: Ioan Popa, Cristiana Tudor, Radu Lupu

Abstract:

The interdependences among stock market indices were studied for a long while by academics in the entire world. The current financial crisis opened the door to a wide range of opinions concerning the understanding and measurement of the connections considered to provide the controversial phenomenon of market integration. Using data on the log-returns of 17 stock market indices that include most of the CEE markets, from 2005 until 2009, our paper studies the problem of these dependences using a new methodological tool that takes into account both the volatility clustering effect and the stochastic properties of these linkages through a Dynamic Conditional System of Simultaneous Equations. We find that the crisis is well captured by our model as it provides evidence for the high volatility – high dependence effect.

Keywords: Stock market interdependences, Dynamic System ofSimultaneous Equations, financial crisis

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Authors: Aurora Cerri, Niko Pullojani

Abstract:

Long-term differential settlement between the bridge structure and the bridge embankment typically results in an abrupt grade change, causing driver discomfort, impairing driver safety, and exerting a potentially excessive impact traffic loading on the abutment. This paper has analysed a case of study showing the effect of an approaching slab realized in a bridge constructed at Tirane-Elbasan Motorway. The layer thickness under the slab is modeled as homogenous, the slab is a reinforced concrete structure and over that the asphaltic layers take place. Analysis indicates that reinforced concrete approaching slab distributes the stresses quite uniformly into the road fill layers and settlements varies in a range less than 2.50 cm in the total slab length of 6.00 m with a maximum slope of 1/240. Results taken from analytical analysis are compared with topographic measurements done on field and they carry great similarities.

Keywords: Approach slab, bridge, road pavement, differential settlement.

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Authors: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz

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In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.

Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma.

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Authors: Hnin Hnin Kyi, Khaing Khaing Aye

Abstract:

Acoustic function plays an important role in aerodynamic mechanical engineering. It can classify the kind of air-vehicle such as subsonic or supersonic. Acoustic velocity relates with velocity and Mach number. Mach number relates again acoustic stability or instability condition. Mach number plays an important role in growth or decay in energy system. Acoustic is a function of temperature and temperature is directly proportional to pressure. If we control the pressure, we can control acoustic function. To get pressure stability condition, we apply Navier-Stokes equations.

Keywords: Acoustic velocity, Irrotational, Mach number, Rotational.

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Authors: Tusharkanta Das, Tumbanath Samantara, Sukanta Kumar Sahoo

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Unsteady effects of MHD free convection flow past in an infinite vertical plate with heat source in presence of radiation with reference to all critical parameters that appear in field equations are studied in this paper. The governing equations are developed by usual Boussinesq’s approximation. The problem is solved by using perturbation technique. The results are obtained for velocity, temperature, Nusselt number and skin-friction. The effects of magnetic parameter, prandtl number, Grashof number, permeability parameter, heat source/sink parameter and radiation parameter are discussed on flow characteristics and shown by means of graphs and tables.

Keywords: Heat transfer, radiation, MHD, free convection, porous medium, suction.

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Authors: E. Keramaris, V. Kanakoudis

Abstract:

In this study the water flow in an open channel over a sharp-crested weir is investigated experimentally. For this reason a series of laboratory experiments were performed in an open channel with a sharp-crested weir. The maximum head expected over the weir, the total upstream water height and the downstream water height of the impact in the constant bed of the open channel were measured. The discharge was measured using a tank put right after the open channel. In addition, the discharge and the upstream velocity were also calculated using already known equations. The main finding is that the relative error percentage for the majority of the experimental measurements is ± 4%, meaning that the calculation of the discharge with a sharp-crested weir gives very good results compared to the numerical results from known equations.

Keywords: Sharp-crested weir, weir height, flow measurement, open channel flow.

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Authors: Balgaisha Mukanova, Tolkyn Mirgalikyzy

Abstract:

Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.

Keywords: Ground surface relief, method of integral equations, numerical method.

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Authors: Muhammad Haitham Albahnassi, Adnan Malki, Shokri Almekdad

Abstract:

In this paper, a method for reconfiguring bandwidth in a circular dual-mode resonator is presented. The method concerns the optimized geometry of a structure that may be used to host the tuning elements, which are typically RF (Radio Frequency) switches. The tuning elements themselves, and their performance during tuning, are not the focus of this paper. The designed resonator is able to reconfigure its fractional bandwidth by adjusting the inter-coupling level between the degenerate modes, while at the same time improving its response by adjusting the external-coupling level and keeping the center frequency fixed. The inter-coupling level has been adjusted by changing the dimensions of the perturbation element, while the external-coupling level has been adjusted by changing one of the feeder dimensions. The design was arrived at via optimization. Agreeing simulation and measurement results of the designed and implemented filters showed good improvements in return loss values and the stability of the center frequency.

Keywords: Dual-mode resonators, perturbation element, perturbation theory, reconfigurable filters, software defined radio (SDR), cognitine radio.

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Authors: Mostafa Raki, Mahdi Hamzehei

Abstract:

Equilibrium and stability equations of a thin rectangular plate with length a, width b, and thickness h(x)=C1x+C2, made of functionally graded materials under thermal loads are derived based on the first order shear deformation theory. It is assumed that the material properties vary as a power form of thickness coordinate variable z. The derived equilibrium and buckling equations are then solved analytically for a plate with simply supported boundary conditions. One type of thermal loading, uniform temperature rise and gradient through the thickness are considered, and the buckling temperatures are derived. The influences of the plate aspect ratio, the relative thickness, the gradient index and the transverse shear on buckling temperature difference are all discussed.

Keywords: Stability of plate, thermal buckling, rectangularplate, functionally graded material, first order shear deformationtheory.

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Authors: Dmitry V. Fomichev, Vladimir I. Solonin

Abstract:

This paper presents the findings from a numerical simulation of the flow in 37-rod fuel assembly models spaced by a double-wire trapezoidal wrapping as applied to the BREST-OD-300 experimental nuclear reactor. Data on a high static pressure distribution within the models, and equations for determining the fuel bundle flow friction factors have been obtained. Recommendations are provided on using the closing turbulence models available in the ANSYS Fluent. A comparative analysis has been performed against the existing empirical equations for determining the flow friction factors. The calculated and experimental data fit has been shown.

An analysis into the experimental data and results of the numerical simulation of the BREST-OD-300 fuel rod assembly hydrodynamic performance are presented.

Keywords: BREST-OD-300, ware-spaces, fuel assembly, computation fluid dynamics.

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Authors: Kaltima Phichai, Pornchanoke Pragrobpondee, Thaweesak Khumpart, Samorn Hirunpraditkoon

Abstract:

The paper provides biomasses characteristics by proximate analysis (volatile matter, fixed carbon and ash) and ultimate analysis (carbon, hydrogen, nitrogen and oxygen) for the prediction of the heating value equations. The heating value estimation of various biomasses can be used as an energy evaluation. Thirteen types of biomass were studied. Proximate analysis was investigated by mass loss method and infrared moisture analyzer. Ultimate analysis was analyzed by CHNO analyzer. The heating values varied from 15 to 22.4MJ kg-1. Correlations of the calculated heating value with proximate and ultimate analyses were undertaken using multiple regression analysis and summarized into three and two equations, respectively. Correlations based on proximate analysis illustrated that deviation of calculated heating values from experimental heating values was higher than the correlations based on ultimate analysis.

Keywords: Heating value equation, Proximate analysis, Ultimate analysis.

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Authors: S. Sendilkumar, B. L. Mathur, Joseph Henry

Abstract:

A new approach for protection of power transformer is presented using a time-frequency transform known as Wavelet transform. Different operating conditions such as inrush, Normal, load, External fault and internal fault current are sampled and processed to obtain wavelet coefficients. Different Operating conditions provide variation in wavelet coefficients. Features like energy and Standard deviation are calculated using Parsevals theorem. These features are used as inputs to PNN (Probabilistic neural network) for fault classification. The proposed algorithm provides more accurate results even in the presence of noise inputs and accurately identifies inrush and fault currents. Overall classification accuracy of the proposed method is found to be 96.45%. Simulation of the fault (with and without noise) was done using MATLAB AND SIMULINK software taking 2 cycles of data window (40 m sec) containing 800 samples. The algorithm was evaluated by using 10 % Gaussian white noise.

Keywords: Power Transformer, differential Protection, internalfault, inrush current, Wavelet Energy, Db9.

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Authors: Kokiat Aodsup, Thanatchai Kulworawanichpong

Abstract:

This paper describes a finite-difference time-domainFDTD) method to analyze lightning surge propagation in electric transmission lines. Numerical computation of solving the Telegraphist-s equations is determined and investigated its effectiveness. A source of lightning surge wave on power transmission lines is modeled by using Heidler-s surge model. The proposed method was tested against medium-voltage power transmission lines in comparison with the solution obtained by using lattice diagram. As a result, the calculation showed that the method is one of accurate methods to analyze transient lightning wave in power transmission lines.

Keywords: Traveling wave, Lightning surge, Bewley lattice diagram, Telegraphist's equations, Finite-difference time-domain (FDTD) method,

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Authors: Raphael Zanella, Todd A. Oliver, Karl W. Schulz

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This work deals with the finite element approximation of axisymmetric compressible flows with swirl velocity. We are interested in problems where the flow, while weakly dependent on the azimuthal coordinate, may have a strong azimuthal velocity component. We describe the approximation of the compressible Navier-Stokes equations with H1-conformal spaces of axisymmetric functions. The weak formulation is implemented in a C++ solver with explicit time marching. The code is first verified with a convergence test on a manufactured solution. The verification is completed by comparing the numerical and analytical solutions in a Poiseuille flow case and a Taylor-Couette flow case. The code is finally applied to the problem of a swirling subsonic air flow in a plasma torch geometry.

Keywords: Axisymmetric problem, compressible Navier- Stokes equations, continuous finite elements, swirling flow.

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Authors: Xin Luo, Jin Huang, Pan Cheng

Abstract:

By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, which implies that the accuracy of the approximations by MQMs possesses high accuracy order O (h3). Finally, the numerical examples show the efficiency of our methods.

Keywords: Stokes problem, boundary integral equation, mechanical quadrature methods, asymptotic expansions.

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Authors: F.Saadi, A.Aboudi Asl

Abstract:

In this paper, the dynamic analysis of fuel storage tanks has been studied and some equations are presented for the created fluid waves due to storage tank motions. Also, the equations for finite elements of fluid and structure interactions, and boundary conditions dominant on structure and fluid, were researched. In this paper, a numerical simulation is performed for the dynamic analysis of a storage tank contained a fluid. This simulation has carried out by ANSYS software, using FSI solver (Fluid and Structure Interaction solver), and by considering the simulated fluid dynamic motions due to earthquake loading, based on velocities and movements of structure and fluid according to all boundary conditions dominant on structure and fluid.

Keywords: fluid and structure interactions, finite elementmethod, ANSYS – FSI

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Authors: Abdulatif Abdusalam, Mohamed Shaban

Abstract:

In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We then discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.

Keywords: Bragg grating, Nonuniform fiber, Nonlinear pulse.

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Authors: M. Najafi, S. Bab, F. Rahimi Dehgolan

Abstract:

The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations.

Keywords: Axially moving beam, Galerkin method, non-linear vibration, super harmonic resonances.

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Authors: Dilavar Khan, Z. Ahmad

Abstract:

Riprap is mostly used to prevent erosion by flows down the steep slopes in river engineering. A total of 53 stability tests performed on angular riprap with a median stone size ranging from 15 to 278 mm and slope ranging from 1 to 40% are used in this study. The existing equations for the prediction of medium size of angular stones are checked for their accuracy using the available data. Predictions of median size using these equations are not satisfactory and results show deviation by more than ±20% from the observed values. A multivariable power regression analysis is performed to propose a new equation relating the median size with unit discharge, bed slope, riprap thickness and coefficient of uniformity. The proposed relationship satisfactorily predicts the median angular stone size with ±20% error. Further, the required size of the rounded stone is more than the angular stone for the same unit discharge and the ratio increases with unit discharge and also with embankment slope of the riprap.

Keywords: Angularity, Gradation, Riprap, Stabilization

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Authors: J. Hey, D. A. Howey, R. Martinez-Botas, M. Lamperth

Abstract:

This paper presents the development of a hybrid thermal model for the EVO Electric AFM 140 Axial Flux Permanent Magnet (AFPM) machine as used in hybrid and electric vehicles. The adopted approach is based on a hybrid lumped parameter and finite difference method. The proposed method divides each motor component into regular elements which are connected together in a thermal resistance network representing all the physical connections in all three dimensions. The element shape and size are chosen according to the component geometry to ensure consistency. The fluid domain is lumped into one region with averaged heat transfer parameters connecting it to the solid domain. Some model parameters are obtained from Computation Fluid Dynamic (CFD) simulation and empirical data. The hybrid thermal model is described by a set of coupled linear first order differential equations which is discretised and solved iteratively to obtain the temperature profile. The computation involved is low and thus the model is suitable for transient temperature predictions. The maximum error in temperature prediction is 3.4% and the mean error is consistently lower than the mean error due to uncertainty in measurements. The details of the model development, temperature predictions and suggestions for design improvements are presented in this paper.

Keywords: Electric vehicle, hybrid thermal model, transient temperature prediction, Axial Flux Permanent Magnet machine.

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Authors: N. Basanta Singh, Sanjoy Deb, G. P Mishra, Subir Kumar Sarkar

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Carrier mobility has become the most important characteristic of high speed low dimensional devices. Due to development of very fast switching semiconductor devices, speed of computer and communication equipment has been increasing day by day and will continue to do so in future. As the response of any device depends on the carrier motion within the devices, extensive studies of carrier mobility in the devices has been established essential for the growth in the field of low dimensional devices. Small-signal ac transport of degenerate two-dimensional hot electrons in GaAs quantum wells is studied here incorporating deformation potential acoustic, polar optic and ionized impurity scattering in the framework of heated drifted Fermi-Dirac carrier distribution. Delta doping is considered in the calculations to investigate the effects of double delta doping on millimeter and submillimeter wave response of two dimensional hot electrons in GaAs nanostructures. The inclusion of delta doping is found to enhance considerably the two dimensional electron density which in turn improves the carrier mobility (both ac and dc) values in the GaAs quantum wells thereby providing scope of getting higher speed devices in future.

Keywords: Carrier mobility, Delta doping, Hot carriers, Quantum wells.

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Authors: H.R.Goshayeshi, M.Fahim inia, M.M.Naserian

Abstract:

In this research, the laminar heat transfer of natural convection on vertical surfaces has been investigated. Most of the studies on natural convection have been considered constantly whereas velocity and temperature domain, do not change with time, transient one are used a lot. Governing equations are solved using a finite volume approach. The convective terms are discretized using the power-law scheme, whereas for diffusive terms the central difference is employed. Coupling between the velocity and pressure is made with SIMPLE algorithm. The resultant system of discretized linear algebraic equations is solved with an alternating direction implicit scheme. Then a configuration of rectangular fins is put in different ways on the surface and heat transfer of natural convection on these surfaces without sliding is studied and finally optimization is done.

Keywords: Natural convection, vertical surfaces, SIMPLE algorithm, Rectangular fins.

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Authors: Ding Guo-hao, Li Hua, Wang Wen-long

Abstract:

A parallel computational fluid dynamics code has been developed for the study of aerodynamic heating problem in hypersonic flows. The code employs the 3D Navier-Stokes equations as the basic governing equations to simulate the laminar hypersonic flow. The cell centered finite volume method based on structured grid is applied for spatial discretization. The AUSMPW+ scheme is used for the inviscid fluxes, and the MUSCL approach is used for higher order spatial accuracy. The implicit LU-SGS scheme is applied for time integration to accelerate the convergence of computations in steady flows. A parallel programming method based on MPI is employed to shorten the computing time. The validity of the code is demonstrated by comparing the numerical calculation result with the experimental data of a hypersonic flow field around a blunt body.

Keywords: Aerodynamic Heating, AUSMPW+, MPI, ParallelComputation

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Authors: Azza A. Al-Ghamdi, Abir S. Abdel-Naby

Abstract:

Cellulose acetate (CA) is a natural biodegradable polymer. It forms transparent films by the casting technique. CA suffers from high degree of water permeability as well as the low thermal stability at high temperatures. To adjust the CA polymeric films to the manufacture of food packaging, its thermal and mechanical properties should be improved. The modification of CA by grafting it with N-Amino phenyl maleimide (N-APhM) led to the construction of hydrophobic branches throughout the polymeric matrix which reduced its wettability as compared to the parent CA. The branches built onto the polymeric chains had been characterized by UV/Vis, ¹³C-NMR and ESEM. The improvement of the thermal properties was investigated and compared to the parent CA using thermal gravimetric analysis (TGA), differential scanning calorimetry (DSC), differential thermal analysis (DTA), contact angle and mechanical testing measurements. The results revealed that the water-uptake was reduced by increasing the graft percentage. The thermal and mechanical properties were also improved.

Keywords: Cellulose acetate, food packaging, graft copolymerization.

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Authors: A. B. Adehor, P. R. Burrell

Abstract:

The Integrated Management of Child illnesses (IMCI) and the surveillance Health Information Systems (HIS) are related strategies that are designed to manage child illnesses and community practices of diseases. However, both strategies do not function well together because of classification incompatibilities and, as such, are difficult to use by health care personnel in rural areas where a majority of people lack the basic knowledge of interpreting disease classification from these methods. This paper discusses a single approach on how a stand-alone expert system can be used as a prompt diagnostic tool for all cases of illnesses presented. The system combines the action-oriented IMCI and the disease-oriented HIS approaches to diagnose malaria and typhoid fever in the rural areas of the Niger-delta region.

Keywords: Differential diagnosis, Health Information System(HIS), Integrated Management of Child Illnesses (IMCI), Malaria andTyphoid fever.

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Authors: Ayesha Sohail, Khadija Maqbool, Anila Asif, Haroon Ahmad

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These days, the field of tissue engineering is getting serious attention due to its usefulness. Bone tissue engineering helps to address and sort-out the critical sized and non-healing orthopedic problems by the creation of manmade bone tissue. We will design and validate an efficient numerical model, which will simulate the effective diffusivity in bone tissue engineering. Our numerical model will be based on the finite element analysis of the diffusion-reaction equations. It will have the ability to optimize the diffusivity, even at multi-scale, with the variation of time. It will also have a special feature “parametric sweep”, with which we will be able to predict the oxygen, glucose and cell density dynamics, more accurately. We will fix these problems by modifying the governing equations, by selecting appropriate spatio-temporal finite element schemes and by transient analysis.

Keywords: Bone tissue engineering, Transient Analysis, Scaffolds, fabrication techniques.

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