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1

Nonlinear solution to a non-Fourier heat conduction problem in a slab heated by laser source

Noroozi M. J., Saedodin S., Ganji D. D.

Archive of Mechanical Engineering

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2016

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Vol. LXIII, nr 1

129--144

EN

The effect of laser, as a heat source, on a one-dimensional finite body was studied in this paper. The Cattaneo-Vernotte non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The obtained equations were solved using the approximate-analytical Adomian Decomposition Method (ADM). It was concluded that the non-linear analysis is important in non-Fourier heat conduction problems. Significant differences were observed between the Fourier and non-Fourier solutions which stresses the importance of non-Fourier solutions in the similar problems.

PL

W artykule badano działanie laserowego źródła ciepła na ciało jednowymiarowe o skończonych wymiarach. Do analizy rozkładu temperatury zastosowano niefourierowski model przewodnictwa ciepła Cattaneo-Vernotte. Założono, że przewodność cieplna jest zależna od temperatury, w wyniku czego otrzymano równania nieliniowe. Do rozwiązania równań zastosowano przybliżoną analityczną metodę dekompozycji Adomiana (ADM). Stwierdzono, że analiza nieliniowa ma istotne znaczenie w problemach przewodnictwa ciepła typu niefourierowskiego. Zaobserwowano istotne różnice między rozwiązaniami fourierowskimi i niefourierowskimi, co podkreśla celowość stosowania tych ostatnich w podobnych problemach.

2

Thermal performance of porous fins with temperature-dependent heat generation via the homotopy perturbation method and collocation method

Hoshyar H. A., Rahimipetroudi I., Ganji D. D., Majidian A. R.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 4

53--65

EN

An analysis has been performed to study the problem of the thermal performance of a nonlinear problem of the porous fin with temperature-dependent internal heat generation. Highly accurate semi-analytical methods called the collocation method (CM) and the homotopy perturbation method (HPM) are introduced and then are used to obtain a nonlinear temperature distribution equation in a longitudinal porous fin. This study is performed using passage velocity from the Darcy’s model to formulate the heat transfer equation through porous media. The heat generation is assumed to be a function of temperature. The effects of the natural convection parameter Nc, internal heat generation εg, porosity Sh and generation number G parameter on the dimensionless temperature distribution are discussed. Also, numerical calculations called the fourth order Runge-Kutta method were carried out for the various parameters entering into the problem for validation. Results reveal that analytical approaches are very effective and convenient. Also it is found that these methods can achieve more suitable results compared to numerical methods.

3

The comprehensive finite element model for stenting: the influence of stent design on the outcome after coronary stent placement

Imani M., Goudarzi A. M., Ganji D. D., Aghili A. L.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 3

639--648

EN

Stenting is one of the most important methods to treat atherosclerosis. Due to its simplicity and efficiency, the use of coronary stents in interventional procedures has rapidly increased, and different stent designs have been introduced in the market. In order to select the most appropriate stent design, it is necessary to analyze and compare the mechanical behavior of different types of stents. In this paper, the finite element method is used for analyzing the behavior of stents. The aim of this work is to investigate the expansion characteristics of a stent as it is deployed and implanted in an artery containing a plaque and propose a model as close to real conditions of stent implantation as possible. Furthermore, two commercially available stents (the Palmaz-Schatz and Multi-Link stents) are modeled and their behavior during the deployment is compared in terms of stress distribution, radial gain, outer diameter changes and dogboning. Moreover, the effect of stent design on the restenosis rate is investigated by comparing the stress distribution in the arteries. The results show the importance of considering the plaque in finite element simulation of mechanical behavior of the coronary stent. According to the findings, the possibility of restenosis is nonsignificantly lower for the Multi-Link stent in comparison with the Palmaz-Schatz stent, which is in good agreement with clinical results.

4

Analytical solutions of electro-kinetic flow in nano-fluidic components by using He’s homotopy perturbation method

Khaki M., Taeibi-Rahni M., Ganji D. D.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 2

265--274

EN

This paper aims to examine the electro-kinetic flow through nano-channels. The equations governing the fluid flow in a one dimensional channel are derived from the Poisson-Nernst-Planck theory. The boundary conditions for the governing equations are obtained from the electrochemical equilibrium requirements. The coupled equations are transformed into a single differential equation. The transformed equation is solved by He’s homotopy perturbation method and an exact solution is achieved. The validity of results is verified by comparing with existing numerical results. The results are presented for velocity profiles, electrical potential distributions, mole fraction of cation and anion distributions and other physical properties. The results demonstrate reasonable agreement with those provided by other numerical methods and good accuracy of the obtained analytical solutions.

PL

Celem pracy jest przedstawienie wyników badań nad elektrokinetycznym przepływem cieczy przez nano-kanały. Równania opisujące przepływ w jednowymiarowym kanale wyprowadzono na podstawie teorii Poissona-Nernsta-Plancka. Warunki brzegowe uzyskano po spełnieniu wymogów równowagi elektrochemicznej układu. Sprzężone równania przepływu przekształcono do postaci pojedynczego równania różniczkowego. Następnie rozwiązano go za pomocą perturbacyjnej metody homotopii He’go, otrzymując wyrażenie analityczne i dokładne. Poprawność rezultatów sprawdzono, porównując je z istniejącymi wynikami symulacji numerycznych. Zaprezentowano profile prędkości przepływu, rozkłady potencjału elektrycznego, molowe udziały frakcji anionów i kationów oraz inne parametry fizyczne układu. Wszystkie wyniki wykazały dobrą zgodność z obliczeniami opartymi na innych metodach badawczych, co potwierdziło dokładność otrzymanych rozwiązań analitycznych.

5

Analytical solution for magnetohydrodynamic stagnation point flow and heat transfer over a permeable stretching sheet with chemical reaction

Rasekh A., Farzaneh-Gord M., Varedi S. R., Ganji D. D.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 3

675--686

EN

This work deals with the problem of steady two-dimensional magnetohydrodynamic (MHD) stagnation point flow towards a permeable stretching sheet with chemical reaction. The fundamental equations of the boundary layer are transformed into ordinary differential equations, which are then solved analytically using the Optimal Homotopy Asymptotic Method (OHAM). Comparisons are made between the results of the proposed method and the numerical method (fourth-order Runge-Kutta) in solving this problem, and excellent agrement has been observed. Subsequently, effects of different involved parameters on the temperature profiles, concentration profiles, local Nusselt number, local Sherwood number and skin-friction coefficient are presented and discussed in detail.