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1

Homotopy simulation of non-Newtonian Spriggs fluid flow over a flat plate with oscillating motion

Ray A. K., Vasu B., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2019

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Vol. 24, no. 2

359--385

EN

An incompressible flow of a non-Newtonian Spriggs fluid over an unsteady oscillating plate is investigated using the Homotopy Analysis Method (HAM). An analytic solution of sine and cosine oscillations of the plate has been obtained. The similarity transformation is introduced to reduce the governing partial differentia equations into a single non-linear dimensionless partial differential equation. The effects of the power index of Spriggs fluid and convergence control parameter of HAM for the flow are studied extensively. The range of the convergence control parameter for convergence of series solution for different values of the power index of Spriggs fluid is obtained. The solution for a Spriggs fluid is noticeably different from the solution obtained for a Newtonian fluid. The influences of the shear thinning and shear thickening fluid on the velocity profile are shown graphically. The transient flow effect is higher for non-Newtonian Spriggs fluid than that of a Newtonian fluid. It is also observed that the interval to reach the steady state for the cosine case is less than the sine case. The applications of Stokes’ second problem have been widely found in the variety of fields of biomedical, medical, chemical, micro and nanotechnology.

2

Effects of heat source/sink and chemical reaction on MHD Maxwell nanofluid flow over a convectively heated exponentially stretching sheet using homotopy analysis method

Sravanthi C. S., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2018

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Vol. 23, no. 1

137--159

EN

The aim of this paper is to study the effects of chemical reaction and heat source/sink on a steady MHD (magnetohydrodynamic) two-dimensional mixed convective boundary layer flow of a Maxwell nanofluid over a porous exponentially stretching sheet in the presence of suction/blowing. Convective boundary conditions of temperature and nanoparticle concentration are employed in the formulation. Similarity transformations are used to convert the governing partial differential equations into non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique, namely: the homotopy analysis method (HAM). Expressions for velocity, temperature and nanoparticle concentration fields are developed in series form. Convergence of the constructed solution is verified. A comparison is made with the available results in the literature and our results are in very good agreement with the known results. The obtained results are presented through graphs for several sets of values of the parameters and salient features of the solutions are analyzed. Numerical values of the local skin-friction, Nusselt number and nanoparticle Sherwood number are computed and analyzed.

3

Homotopy analysis of a forced nonlinear beam model with quadratic and cubic nonlinearities

Shahlaei-Far S., Nabarrete A., Balthazar J. M.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 4

1219--1230

EN

This study investigates forced nonlinear vibrations of a simply supported Euler-Bernoulli beam on a nonlinear elastic foundation with quadratic and cubic nonlinearities. Applying the homotopy analysis method (HAM) to the spatially discretized governing equation, we derive novel analytical solutions and discuss their convergence to present nonlinear frequency responses with varying contributions of the nonlinearity coefficients. A comparison with numerical solutions is conducted and nonlinear time responses and phase planes are compared to the results from linear beam theory. The study demonstrates that apart from nonlinear problems of free vibrations, HAM is equally capable of solving strongly nonlinear problems of forced vibrations.

4

Stagnation point flow of Eyring Powell fluid in a vertical cylinder with heat transfer

Rehman A., Achakzai S., Nadeem S., Iqbal S.

Journal of Power Technologies

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2016

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Vol. 96, nr 1

57--62

EN

In this paper an analysis is carried out to examine the effects of natural convection heat transfer for steady boundary layer flow of an Eyring Powell fluid flowing through a vertical circular cylinder. The governing partial differential equations along with the boundary conditions are reduced to dimensionless form by using the boundary layer approximation and applying suitable similarity transformations. The resulting nonlinear coupled system of ordinary differential equations subject to the appropriate boundary conditions is solved using the analytic technique homotopy analysis method (HAM). The effects of the physical parameters on the flow and heat transfer characteristics are presented. The behavior of skinfriction coefficient and Nusselt numbers are also studied for different parameters.

5

Influence of convective heat and mass conditions in MHD flow of nanofluid

Shehzad S. A., Hayat T., Alsaedi A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2015

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Vol. 63, nr 2

465--474

EN

This article aims to investigate the two-dimensional magnetohydrodynamic (MHD) boundary layer flow of nanofluid. Convective mass condition is introduced. Analysis has been discussed in the presence of an applied magnetic field. The Brownian motion and thermophoresis effects are incorporated. The arising nonlinear problems are first converted to ordinary differential equations and then series solutions are constructed. Convergence of series solutions is examined through plots and numerical values. Results are plotted and discussed for the temperature and concentration. Numerical computations for skin-friction coefficient, local Nusselt and Sherwood numbers are performed and analyzed. Comparison with the previous limiting case is noted in an excellent agreement.

6

Approximate analytical solution for Bernoulli-Euler beams under different boundary conditions with non-linear Winkler type foundation

Mohammadpour A., Rokni E., Fooladi M., Kimiaeifar A.

Journal of Theoretical and Applied Mechanics

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2012

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Vol. 50 nr 2

339-355

EN

In this study, a powerful analytical method, known as Homotopy Analysis Method (HAM), is used to obtain an analytical solution to nonlinear ordinary deferential equations arising for Bernoulli-Euler beams with a non-linear foundation of the Winkler type. A comparison between the HAM solution and a solution obtained by a numerical method is made to show the accuracy of the method. It is shown that the present solution is valid for the whole domain of the solution and also for high nonlinear terms, where other methods such as the perturbation method fail to converge. The results clearly indicate that the convergence region can be controlled and adjusted by HAM. Finally, after validating the results, the effect of constant parameters on the deflection and slope for different boundary conditions is presented.

PL

W pracy przedstawiono zastosowanie bardzo wszechstronnej metody homotopii (HAM) do uzyskania analitycznego rozwiązania nieliniowych równań różniczkowych opisujących drgania belek Bernoulliego-Eulera spoczywających na nieliniowym podłożu winklerowskim. W celu zaprezentowania dokładności metody, uzyskane wyniki porównano z rezultatami symulacji numerycznych. Wykazano, że tak otrzymane rozwiązanie jest ważne w całej dziedzinie, także przy uwzględnieniu członów nieliniowych wyższego rzędu. Inne metody, m.in. analiza perturbacyjna, przestają być w takich przypadkach zbieżne. Przeprowadzone badania wyraźnie dowodzą, że obszar zbieżności może być monitorowany i dostosowywany w ramach metody HAM. Na zakończenie rozważań, po weryfikacji obliczeń, przedyskutowano wpływ stałych parametrów układu na ugięcie i kąt ugięcia belek przy równych warunkach zamocowania.

7

Integrated heat, air and moisture modeling in a single simulation environment

Schijndel J. van

Fizyka Budowli w Teorii i Praktyce

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2008

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T. 3

99-104

EN

The modeling and simulation of whole building heat air and moisture (HAM) responses in relation to human comfort, energy and durability are relevant. The paper presents the integration of the following lumped parameter models: whole building. HVAC and primary systems and distributed parameter models: indoor airflow. HAM transport in constructions and external airflow/driving rain into a single simulation environment. It is concluded that the presented simulation environment is capable of modeling and efficiently solving a large range of complex integrated HAM problems related with different time scales and lumped/distributed parameters.