Implicit Finite Difference Method Research Articles

A novel model of non-linear radiative Williamson nanofluid flow along a vertical wavy cone in the presence of gyrotactic microorganisms

ABSTRACT A novel mathematical technique for an unsteady bioconvective flow of Williamson nanofluids over a vertical wavy cone in the presence of non-linear radiation and viscous dissipation impacts is investigated. The cone surface is described by a sinusoidal function while the components of the extra stress tensor are presented in terms of the dynamic viscosity. The irregular wavy surface is referred to the convective boundary conditions and nanoparticle passively controls conditions. The governing equations are presented in general forms then the condition and suitable transformations are used to map the wavy cone to regular domain. A fully implicit finite differences method (FDM) is applied to solve the converted system and wide ranges of independent variables are assumed. . The major outcomes disclosed that the increase in the Williamson number causes a reduction the nanofluid flow while the skin friction coefficient is rising. Further, there is an enhancement in the values of the Nusselt number up to 75% is obtained as Biot number is altered from 0.1 to 0.4. Also, the convective boundary conditions in presence of the non-linear radiations are recommended to enhance the velocity, temperature and rate of the heat transfer.

A Method for Solving Time-Fractional Initial Boundary Value Problems of Variable Order

Various scholars have lately employed a wide range of strategies to resolve specific types of symmetrical fractional differential equations. This paper introduces a new implicit finite difference method with variable-order time-fractional Caputo derivative to solve semi-linear initial boundary value problems. Despite its extensive use in other areas, fractional calculus has only recently been applied to physics. This paper aims to find a solution for the fractional diffusion equation using an implicit finite difference scheme, and the results are displayed graphically using MATLAB and the Fourier technique to assess stability. The findings show the unconditional stability of the implicit time-fractional finite difference method. This method employs a variable-order fractional derivative of time, enabling greater flexibility and the ability to tackle more complicated problems.

Effects of Suction/Injection on Free Convective Radiative Flow In A Vertical Porous Channel With Mass Transfer And Chemical Reaction

This paper presents an analysis of the effect of suction/injection on free convective flow past a vertical porous plate under the action of thermal radiation and chemical reaction when heat is supplied to the plate at constant rate. The governing equations are solved using implicit finite difference method. The results are obtained for the velocity, temperature, concentration, skin-friction, Nusselt number, and Sherwood number. The effects of various parameters on flow variables are illustrated physically, and the physical aspects of the problem are discussed. During the course of numerical computation, it was found that the velocity and temperature profiles increase with an increase in suction/injection parameter. Also, the skin-friction and rate of heat transfer increase with increase in radiation parameter and it shows reverse effect in the case of Sherwood number.

Influences of Physical Parameters of a Solar Concentrator Cooker

This work focuses on the modelling and simulation of a solar concentrator cooker. The equations governing the heat transfers of the solar cooker are discretised by an implicit finite difference method and solved via the Gaussian algorithm, coupled with an iterative procedure.
 The FORTRAN numerical code that simulates the operation of the solar cooker, using meteorological data from the city of Bangui, was developed. In this simulation, the influence of physical parameters as well as of the different components of the cooker is analysed, notably: the nature of the materials used, the dimensions of the cooker. The results show that a solar flux of 900W/m² allows the determination of the different optimal parameters of the cooker.
 The dimensions of the parallelepipedic cooker [60 cm*50 cm*50 cm], made it possible to obtain a thermal efficiency varying from 42% to 45%. The influence of these physical parameters shows that copper is a good conductor and the thermal conductivity is higher the thinner the wall thickness (3 mm) of the pot.

Influence of multiple slips and magnetic effects on the quadratic convective flow over a vertical wedge

AbstractThis paper investigates the quadratic convective flow of Williamson nanoliquid with the impacts of velocity, thermal and concentration slips over a vertical wedge. Further, the magnetic effects and the Buongiorno two‐phase nanoparticle model are considered. The study of this type of flows over a vertical wedge appears in various engineering applications such as thermal insulation, engine parts of vehicles, aerospace, crude oil extraction and heat exchangers. The physical problem is formulated as a set of quadratic coupled partial differential equations (PDEs), which are dimensional. Further, the dimensionless PDEs obtained by the non‐similar transformations are solved with the aid of the implicit finite difference method and the Quasilinearization technique. The effects of slip parameters, streamwise coordinate, fluid material parameters and magnetic field on various gradients and profiles are explored through graphs. The greater values of concentration slip and thermal slip parameters improve the concentration and temperature profiles, but the fluid's velocity is reduced with the velocity slip parameter. The streamwise coordinate significantly influences the fluid's velocity more than the concentration and temperature profiles. The velocity and skin friction coefficient are pronounced more for a higher wedge angle. Also, the numerical results of this investigation compared to similar works that have been published before show that they are very consistent.

Simulation of one-dimensional dam-break flood routing based on HEC-RAS

Dam-break is a serious disaster resulting in severe damage to downstream communities. Therefore, analyzing the affected range and the evolution process of dam-break floods in advance is valuable. However, the difficulties and challenges lie in the complexity of the breaking process of earth-rock dams, the uncertainty in the evolution of dam-break floods, and the geographical variability. Given this, the objective of this study is to analyze the characteristics of the dam-break flood evolution. The study chooses Chengbi River Reservoir as the research object, HEC-RAS as the simulation software, unsteady flow differential equations and one-dimensional Saint-Venant equations as the control equations, and it uses four-point implicit finite difference method for discrete solution. In this paper, the dam-break flood evolution is simulated under three boundary conditions (full breach, 1/2 breach, 1/3 breach), and the main results are as follows. From the dam site section to the Tianzhou hy-drological station section, the peak discharge decay rates of the three schemes are 78%, 77%, and 67%, respectively. The water level decay rates of the three schemes are 47%, 36%, and 30%, respectively. A 1 m increase in the bursting water level elevation increases the peak flow by ap-proximately 7%, and the highest water level in front of the dam by 1 m, and delays the peak time by 1.5 h on average. In addition, the preliminary inundation extent for the Baise City is obtained. The analysis results can provide a fundamental basis for flood control as well as a reference for flood disaster management.

New Trends in the Modeling of Diseases Through Computational Techniques

The computational techniques are a set of novel problem-solving methodologies that have attracted wider attention for their excellent performance. The handling strategies of real-world problems are artificial neural networks (ANN), evolutionary computing (EC), and many more. An estimated fifty thousand to ninety thousand new leishmaniasis cases occur annually, with only 25% to 45% reported to the World Health Organization (WHO). It remains one of the top parasitic diseases with outbreak and mortality potential. In 2020, more than ninety percent of new cases reported to World Health Organization (WHO) occurred in ten countries: Brazil, China, Ethiopia, Eritrea, India, Kenya, Somalia, South Sudan, Sudan, and Yemen. The transmission of visceral leishmaniasis is studied dynamically and numerically. The study included positivity, boundedness, equilibria, reproduction number, and local stability of the model in the dynamical analysis. Some detailed methods like Runge Kutta and Euler depend on time steps and violate the physical relevance of the disease. They produce negative and unbounded results, so in disease dynamics, such developments have no biological significance; in other words, these results are meaningless. But the implicit nonstandard finite difference method does not depend on time step, positive, bounded, dynamic and consistent. All the computational techniques and their results were compared using computer simulations.

Numerical Study of Natural Solutal Convection in an Isoscele Trapezoidal Cavity

A numerical study of the natural heat and mass transfer in a cavity with a straight isoscele cross-section containing air is made in this paper. The two inclined side walls are kept in natural convection with the surrounding environment. The upper horizontal wall is subjected to a heat flux of constant density, while the lower one is adiabatic. Under the Boussinesq assumption, the thermodynamic conditions are numerically studied using the unsteady convection equations formulated as a secondary variable of vorticity and a stream function, energy and moisture. The system of equations discretised by the implicit finite difference method is solved by the Thomas algorithm. The results show a flow structure, isotherms and isohumidities dependent on the study parameters. Thus, on one hand, an increase in the inclination angle of the walls is accompanied by an increase in the velocity of the fluid. On the other hand, an increase in the aspect ratio or Lewis number leads to a decrease in the fluid’s velocity. The average Nusselt number, which is independent of the Rayleigh number, increases slightly as the inclination angle of the walls decreases. The increase of the Lewis number results in the decrease of the flow velocity components values. It is observed that the maxima values of velocity components were reached for Rayleigh number equal to 7.103.

An IFDM analysis of low Reynolds number flow generated in a complex wavy curved passage formed by artificial beating cilia

Mother nature utilizes an assembly of beating cilia to transport liquid in various circumstances. The arrays of these hair-like cellular appendages also aid in propelling microorganisms like spermatozoa and paramecium. In our implicit finite difference analysis, we present a pumping performance of a curved channel comprising mucus flow induced via active cilium. The non-Newtonian mucus is modelled as Carreau fluid model. The undulating cilia attached with curved walls are assumed to be complex wavy. The tips of these cilia form a complex wavy peristaltic curved passage with porous medium effects. Well-known continuity and momentum equations (in curvilinear coordinates) are utilized to model the flow problem. Cilia-driven flow is creeping which is based on low Reynolds number assumption. Moreover, long wavelength assumption is also employed in this analysis. The reduced fourth-order BVP is solved via implicit finite difference method (IFDM). The computed results are plotted by using MATLAB (2021a). The mucus velocity is plotted at three different cross-sections and flow rates. Moreover, velocity of mucus, pressure gradient, pressure rise, and level curves are also expounded for various rheological, porous and cilia-based parameters. A special case of straight passage is also presented in the graphical result section.

The mixed convection flow of a Williamson nanoliquid over a rotating sphere with the aspects of activation energy

ABSTRACT The nonlinear mixed convective flow of a Williamson nanofluid over a rotating sphere with liquid hydrogen diffusion is examined in this paper. In addition, the activation energy and magnetic effects are taken into account in the analysis. This study is novel because it investigates the effects of nanoparticles, sphere rotation, and nonlinear convection on flow and heat transfer. The Boussinesq approximation is used to transform the problem into a system of nonlinear coupled partial differential equations (PDEs). The implicit finite difference method and the quasilinearization technique are used for mathematical computations. The heat transfer rate is about 9% more in the presence of nonlinear convection than in the absence of nonlinear convection. The mass transfer rate is increased by about 19% when the value of the Brownian motion parameter rises from 0.1 to 0.3. The streamwise velocity is more pronounced for the nanofluid than for the Williamson nanofluid. The higher activation energy values decrease the concentration of the chemical species.

Numerical analysis of spatial moment for colloid-facilitated contaminant transport through porous media

ABSTRACT Transport of contaminants in the presence of colloids is a three-phase problem in the groundwater porous media and colloids can also enhance the transport of contaminants by reducing the retardation factor. In this study, the numerical solution of the equilibrium model is obtained using a fully implicit Crank-Nicolson finite-difference method and validated with ten experimental results. Sensitivity and spatial moment analysis have been performed to investigate the mobility and spreading behavior of contaminants in the presence of colloids. Results suggest that enhancement of contaminant transport in the presence of colloids depends on the colloid concentration and the physical and chemical interaction of contaminants with the stationary solid matrix and suspended colloids. As the colloidal concentration increases, the mobility of contaminants augments, resulting in the early arrival of contaminants at the column outlet. The affinity of contaminants toward the stationary solid matrix of porous media can lead to the reduced transport of contaminants even under the presence of a significant amount of colloid concentration. In contrast, enhanced transport of contaminants is observed if the affinity of contaminants is more toward the suspended colloids.

A numerical investigation into the influence of the surfactant injection technique on the foam flow in heterogeneous porous media

We propose a sequential algorithm to investigate the influence of surfactant injection on foam-induced mobility reduction in two-phase liquid–gas flows in highly heterogeneous porous media. A foam model in local equilibrium is adopted in this context, assuming non-Newtonian foam behavior. A fractional flow formulation based on global pressure that includes the surfactant in the liquid phase is adopted, resulting in a system that couples elliptic and hyperbolic equations. These equations are split into two sub-systems that group equations of the same kind and are solved employing a sequential numerical algorithm that combines a locally conservative hybrid finite element method to approximate the hydrodynamics of the system with a central-upwind finite volume method for the transport equations. The resulting spatial discretized system is approximated in time by applying a multi-step, implicit finite difference method. The hydrodynamics and hyperbolic problems are solved using a staggered algorithm in different time scales. Through comparison with experimental data and classical numerical methods, we validated the proposed methodology and demonstrated its ability to produce stable approximations with reduced numerical dissipation and computational cost. Then, we apply the sequential algorithm to compare the co-injection of the water–gas–surfactant with the Surfactant Alternating Gas (SAG) technique in two-dimensional flows in highly heterogeneous media. The numerical results suggest a better sweep efficiency using the SAG injection technique when compared with the co-injection approach for the equivalent amount of injected surfactant.

Analytical – numerical estimation of temperature distribution in living tissue by the DPL bio-heat model

Here, we used mathematical modeling to predict and simulate the behavior and effect of temperature on human skin, together with studying the effects of the blood perfusion parameters, the time of tissue exposure to the laser, and the effect of the delay times on temperature distribution on living tissue. The model that has been used is a dual-phase lag DPL bioheat transfer model. The solution of the model has been obtained by using the analytical scheme represented by Laplace transforms, as well as the numerical scheme represented by the implicit finite difference method. The paper involves comparing analytical and numerical solutions, a comparison between the temperature distribution according to various bio-heat models and the resulting thermal damage. The results of the DPL bioheat model have been compared with the previous study and it showed. A favorable convergence results have been presented graphically and discussed in detail.

Efficient ADI schemes and preconditioning for a class of high-dimensional spatial fractional diffusion equations with variable diffusion coefficients

In this paper, alternating direction implicit (ADI) finite difference method and preconditioned Krylov subspace method are combined to solve a class of high-dimensional spatial fractional diffusion equations with variable diffusion coefficients. We prove the unconditional stability and convergence rate of the ADI finite difference method provided that the diffusion coefficients satisfy the given conditions. For the linear system in each spatial direction, we establish a circulant approximate inverse preconditioner to accelerate the Krylov subspace method. In addition, we also use matrix-free algorithms and fast Fourier transforms (FFT) to speed up the solution of linear systems. Numerical experiments show the utility of the ADI method and the preconditioner.

Numerical solution of the three-dimensional Burger’s equation by using the DQ-FD combined method in the determination of the 3D velocity of the flow

In this paper, the differential quadrature and the finite difference combined method (DQ-FDM) was applied to solve the three-dimensional Burger’s equation in the determination of the 3D velocity of the flow; so that spatial terms were discretized by the differential quadrature method, and the temporal term was discretized by the finite difference method, and the resulting nonlinear equations were solved using the Newton–Raphson method. All variables were considered as dimensionless in this equation. The solution results were compared with solution results of the two-dimensional equation in the two other numerical methods available in the literature which provided an acceptable accuracy. Also, the results of the mentioned numerical method were compared with those of the fully implicit finite difference method that was solved for larger than or equal viscosities of 0.1. The results showed that by increasing time and viscosity, the longitudinal, depth and transverse velocities were decreased. The occurrence of the upward flow was observed especially in the upsilon = 0.05 in the close of the bed, end of the length and width that in the presence of very fine particles of the clay and silt shows suspension of these particles in some spaces. The position of the longitudinal, depth and transverse velocities in the plan for the passing plates through the section depth for different viscosities and times showed that by increasing viscosity and time, the position of the maximum velocities became closer to the middle of the section width. Also, stream lines were plotted in all of sections and then analyzed.

The effect of single and hybrid nanofluids in the performance of Solar Water Heating System

In the present study, the feasibility of using single particle Cu and hybrid Cu/Al2O3 nanofluids as heat transfer fluids in a coupled solar parabolic trough collector-heat water storage tank for domestic absorption cooling systems. A computer program based on one dimensional implicit finite difference method and energy balance approach has been developed to investigate the behavior of the studied system under the real climate conditions of a typical summer day in Adrar city, Algeria. The simulation findings reveal that solar parabolic trough collector with small area of 6m² and storage tank of 0.3m3 can ensure higher storage tank temperature able to drive an absorption cooling machine. Solar system with hybrid nanofluid shows superior performance compared to single nanofluid and pure water. Furthermore, the effect of nanoparticle's volume fraction is evaluated. The heat storage tank temperature can attain starting operating chiller temperature more rapidly with small volume fraction equal to 0.2% in the case of Cu-Al2O3/Water hybrid nanofluid.

Effect of Ohmic heating on magnetohydrodynamic flow with variable pressure gradient: a computational approach

ABSTRACT Ohmic heating, which significantly affects magnetohydrodynamic flow, is one of the exciting effects to be experienced. This study looks at the significance of Ohmic heating on two-dimensional flow and dissipative heat transfer of a viscous fluid over a flat surface. The mainstream flow is subjected to a pressure gradient and externally oriented inclined magnetic field. An implicit finite difference method has been used to obtain the convergent solutions and the graphical results have been obtained using MATLAB software. A positive correlation is found between temperature and viscous dissipation parameter. Further, the flow encountered higher resistance due to the magnetic field, which is more prominent when the magnetic field is normal to the flow direction .

Computer Simulations of Silicide-Tetrahedrite Thermoelectric Generators.

With global warming and rising energy demands, it is important now than ever to transit to renewable energy systems. Thermoelectric (TE) devices can present a feasible alternative to generate clean energy from waste heat. However, to become attractive for large-scale applications, such devices must be cheap, efficient, and based on ecofriendly materials. In this study, the potential of novel silicide-tetrahedrite modules for energy generation was examined. Computer simulations based on the finite element method (FEM) and implicit finite difference method (IFDM) were performed. The developed computational models were validated against data measured on a customized system working with commercial TE devices. The models were capable of predicting the TEGs' behavior with low deviations (≤10%). IFDM was used to study the power produced by the silicide-tetrahedrite TEGs for different ΔT between the sinks, whereas FEM was used to study the temperature distributions across the testing system in detail. To complement these results, the influence of the electrical and thermal contact resistances was evaluated. High thermal resistances were found to affect the devices ΔT up to ~15%, whereas high electrical contact resistances reduced the power output of the silicide-tetrahedrite TEGs by more than ~85%.

Dissipated-radiative compressible flow of nanofluids over unsmoothed inclined surfaces with variable properties

This study aims to examine the impacts of the variable nanofluid properties on the compressible flow over an inclined irregular surface. The density, dynamic viscosity and thermal conductivity of the nano liquid are assumed to be dependent on the temperature, and the viscous dissipation in this case is introduced. Sinusoidal formulations for the unsmoothed surface together with the governing system in case of are presented. The temperature on the edge is, also, variable and depending on the discerption function of the surface. The nonlinear radiation is taken into account, and the two-phase model for the nanofluid is applied. A fully implicit finite difference method (FDM) is used to solve the governing system. The major outcomes revealed that the skin friction coefficient and Nusselt number are rising as the compressibility parameter is altered. Also, the maximization of the thermal conductivity-variation is better for the velocity and temperature behaviors.

Eavesdropping and Anti-Eavesdropping Game in UAV Wiretap System: A Differential Game Approach

Despite its advantages of flexility and low-cost networking, unmanned aerial vehicle (UAV) communications face various attacks such as eavesdropping. Existing studies on secure UAV communications assume fixed-location eavesdroppers and rarely consider interactions between legitimate nodes and eavesdroppers. In this paper, we investigate eavesdropping and anti-eavesdropping interaction between a UAV-enabled eavesdropper (UAV-E) and a UAV-enabled base station (UAV-BS) in a downlink wiretap system. The UAV-E aims to wiretap downlink signals by adaptively adjusting its trajectory while the UAV-BS aims to maximize secrecy-sum-rate with minimum power consumption by jointly optimizing user scheduling, power control, and trajectory. Dynamic differential equations are formulated to characterize motions of UAVs, following which a zero-sum differential game is formulated to model the “pursuit-evasion” interaction between the UAV-BS and the UAV-E. Definition and existence of Nash equilibrium (NE) are provided. To obtain the NE, Pontryagins minimum principle is leveraged to solve the trajectory design problem. Further, Gauss-Seidel-like implicit finite-difference method is leveraged to obtain saddle-point strategies at NE. Finally, numerical results are provided to verify the effectiveness of the proposed game model. It is revealed that the differential game can well-characterize the strategy interactions between UAVs. Moreover, results show that the initial positions and weights of UAVs, the energy consumption factor, and the user scheduling have key impacts on motion interactions between the UAV-BS and the UAV-E and further on UAV-BS’s power control.