Comparison of the Adomian decomposition method and the variational iteration method in solving the moving boundary problem

AbstractIn this paper, a comparison between two methods: the Adomian decomposition method and the variational iteration method, used for solving the moving boundary problem, is presented. Both of the methods consist in constructing the appropriate iterative or recurrence formulas, on the basis of the equation considered and additional conditions, enabling one to determine the successive elements of a series or sequence approximating the function sought. The precision and speed of convergence of the procedures compared are verified with an example

Collocation Method using Compactly Supported Radial Basis Function for Solving Volterra's Population Model

In this paper, indirect collocation approach based on compactly supported radial basis function is applied for solving Volterras population model. The method reduces the solution of this problem to the solution of a system of algebraic equations. Volterras model is a non-linear integro-differential equation where the integral term represents the effect of toxin. To solve the problem, we use the well-known CSRBF: Wendland3,5. Numerical results and residual norm 2 show good accuracy and rate of convergence.Comment: 8 pages , 1 figure. arXiv admin note: text overlap with arXiv:1008.233

The radiative conductive transfer equation in cylinder geometry : rocket launch exhaust phenomena for the Alcântara Launch Center

In this work we present a solution for the radiative conductive transfer equation in cylinder geometry for a solid cylinder. We discuss a semi-analytical approach to the non-linear N S problem, where the solution is constructed by Laplace transform and a decomposition method. The obtained solution allows then to construct the relevant near field to characterize the source term for dispersion problems when adjusting the model parameters such as albedo, emissivity, radiation conduction and others in comparison to the observation, that are relevant for far field dispersion processes and may be handled independently from the present problem. In addition to the solution method we also report some solutions and numerical simulations

Thermal prediction of convective-radiative porous fin heatsink of functionally graded material using adomian decomposition method

YesIn recent times, the subject of effective cooling have become an interesting research topic for electronic and mechanical engineers due to the increased miniaturization trend in modern electronic systems. However, fins are useful for cooling various low and high power electronic systems. For improved thermal management of electronic systems, porous fins of functionally graded materials (FGM) have been identified as a viable candidate to enhance cooling. The present study presents an analysis of a convective–radiative porous fin of FGM. For theoretical investigations, the thermal property of the functionally graded material is assumed to follow linear and power-law functions. In this study, we investigated the effects of inhomogeneity index of FGM, convective and radiative variables on the thermal performance of the porous heatsink. The results of the present study show that an increase in the inhomogeneity index of FGM, convective and radiative parameter improves fin efficiency. Moreover, the rate of heat transfer in longitudinal FGM fin increases as b increases. The temperature prediction using the Adomian decomposition method is in excellent agreement with other analytical and method

Effect of nanoparticles on solid-liquid phase change heat transfer rate

Phase change materials (PCMs) have many engineering applications, such as thermal insulation, thermal management, and storing thermal energy. With a high latent heat of fusion, many organic PCMs such as paraffin are ideal for thermal energy storage, but their relatively low thermal conductivity makes the melting and solidification process lengthy. One way to improve this problem is the dispersion of highly conductive nanoparticles to the base PCM, making a mixture of so-called Nano-enhanced Phase Change Materials (NePCMs). However, adding nanoparticles changes many other properties of the mixture, such as viscosity, which may affect the total heat transfer rate in a complicated way. The literature on this topic shows some contradicting findings, with some studies reporting enhanced phase change heat transfer with nanoparticles, but some reporting reduced heat transfer rate. It is critically important to conduct a systematic study for a better understanding of the effects of nanoparticles on the solid-liquid phase change heat transfer rate. This thesis aims to conduct such a study. It starts with a review of the analytical models for the phase change problems, the significant parameters on the phase change rate through scaling analysis, and reported effects of nanoparticles on the phase change rate. Then, a melting problem with Rayleigh-Benard convection is investigated in a rectangular enclosure both numerically and experimentally. It is found that the effect of nanoparticles on the total heat transfer rate during this melting process is highly dependent on the level of domination of natural convection (as compared to conduction) during the phase change process. Based on the scaling analysis and the experimental results, predictive correlations are developed for the viscosity and melting rate of the NePCMs. The effects of nanoparticles on the heat transfer and phase change rate are also numerically analyzed in shell-and-tube thermal energy storage units with and without fins. The different behaviours of nanoparticles are investigated in terms of the significance and domination of natural convection in the melted regions. With a numerical and statistical approach, predictive correlations are developed for each case, and the potential interactions between the parameters in affecting the total heat transfer rate are identified. Most previous researches came up with a critical concentration of nanoparticles for higher phase change rate in a particular energy storage case. The results are often not applicable to other cases. This research systematically analyzes the effects of nanoparticles on the phase change heat transfer rate, leading to better and more general understandings of these effects. It identified the key parameters (e.g., Rayleigh number) in the heat transfer process and developed predictive correlations for phase change rate. The new findings would be useful for designers of latent thermal energy storage systems as to whether and how nanoparticles could be potentially used in the design of latent thermal energy storage units

Numerical study of nano-biofilm stagnation flow from a nonlinear stretching/shrinking surface with variable nanofluid and bioconvection transport properties

A mathematical model is developed for stagnation point flow toward a stretching or shrinking sheet of liquid nano-biofilm containing spherical nano-particles and bioconvecting gyrotactic micro-organisms. Variable transport properties of the liquid (viscosity, thermal conductivity, nano-particle species diffusivity) and micro-organisms (species diffusivity) are considered. Buongiorno’s two-component nanoscale model is deployed and spherical nanoparticles in a dilute nanofluid considered. Using a similarity transformation, the nonlinear systems of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a central space finite difference method in the CodeBlocks Fortran platform. Graphical plots for the distribution of reduced skin friction coefficient, reduced Nusselt number, reduced Sherwood number and the reduced local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms are presented for the influence of wall velocity power-law index (m), viscosity parameter (c2), thermal conductivity parameter (c4), nano-particle mass diffusivity (c6), micro-organism species diffusivity (c8), thermophoresis parameter (Nt), Brownian motion parameter (Nb), Lewis number (Le), bioconvection Schmidt number (Sc), bioconvection constant (σ) and bioconvection Péclet number (Pe). Validation of the solutions via comparison related to previous simpler models is included. Further verification of the general model is conducted with the Adomian decomposition method (ADM). Extensive interpretation of the physics is included. Skin friction is elevated with viscosity parameter (c2) whereas it is suppressed with greater Lewis number and thermophoresis parameter. Temperatures are elevated with increasing thermal conductivity parameter (c4) whereas Nusselt numbers are reduced. Nano-particle volume fraction (concentration) is enhanced with increasing nano-particle mass diffusivity parameter (c6) whereas it is markedly reduced with greater Lewis number (Le) and Brownian motion parameter (Nb). With increasing stretching/shrinking velocity power-law exponent (m), skin friction is decreased whereas Nusselt number and Sherwood number are both elevated. Motile microorganism density is boosted strongly with increasing micro-organism diffusivity parameter (c8) and Brownian motion parameter (Nb) but reduced considerably with greater bioconvection Schmidt number (Sc) and bioconvection Péclet number (Pe). The simulations find applications in deposition processes in nano-bio-coating manufacturing processes