Hydrodynamic and hydromagnetic stability

The magnetohydrodynamic thin film nanofluid sprayed on a stretching cylinder with heat transfer is explored. The spray rate is a function of film size. Constant reference temperature is used for the motion past an expanding cylinder. The sundry behavior of the magnetic nano liquid thin film is carefully noticed which results in to bring changes in the flow pattern and heat transfer. Water-based nanofluids like Al 2 O 3 -H 2 O and CuO-H 2 O are investigated under the consideration of thin film. The basic constitutive equations for the motion and transfer of heat of the nanofluid with the boundary conditions have been converted to nonlinear coupled differential equations with physical conditions by employing appropriate similarity transformations. The modeled equations have been computed by using HAM (Homotopy Analysis Method) and lead to detailed expressions for the velocity profile and temperature distribution. The pressure distribution and spray rate are also calculated. The comparison of HAM solution predicts the close agreement with the numerical method solution. The residual errors show the authentication of the present work. The CuO-H 2 O nanofluid results from this study are compared with the experimental results reported in the literature showing high accuracy especially, in investigating skin friction coefficient and Nusselt number. The present work discusses the salient features of all the indispensable parameters of spray rate, velocity profile, temperature and pressure distributions which have been displayed graphically and illustrated.

https://www.mdpi.com/2076-3417/7/3/271/pdf

Magnetohydrodynamic Nanoliquid Thin Film Sprayed on a Stretching Cylinder with Heat Transfer

A brief introduction to the development of the homotopy perturbation method is given, and the main milestones are elucidated with more than 90 references. This paper further improves the method by ...

https://journals.sagepub.com/doi/pdf/10.1177/1461348418811028

Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators

Mixed convection in gravity-driven non-Newtonian nanofluid films (Casson and Williamson) flow containing both nanoparticles and gyrotactic microorganisms along a convectively heated vertical surface is investigated. The actively controlled nanofluid model boundary conditions are used to explore the liquid films flow. The study exhibits an analytical approach for the non-Newtonian thin film nanofluids bioconvection based on physical mechanisms responsible for the nanoparticles and the base fluid, such as Brownian motion and thermophoresis. Both the fluids have almost the same behaviors for the effects of all the pertinent parameters except the effect of Schmidt number on the microorganism density function where the effect is opposite. Ordinary differential equations together with the boundary conditions are obtained through similarity variables from the governing equations of the problem, which are solved by HAM (Homotopy Analysis Method). The solution is expressed through graphs and illustrated which show the influences of all the parameters. The study is relevant to novel microbial fuel cell technologies combining the nanofluid with bioconvection phenomena.

Mixed convection in gravity-driven thin film non-Newtonian nanofluids flow with gyrotactic microorganisms

Buongiorno’s nanofluid model is followed to study the bioconvection in two stretchable rotating disks with entropy generation. Similarity transformations are used to handle the problem equations for non-dimensionality. For the simulation of the modeled equations, Homotopy Analysis Method is applied. The biothermal system is explored for all the embedded parameters whose effects are shown through different graphs. There exists interesting results due to the effects of different parameters on different profiles. Radial velocity decreases with increasing stretching and magnetic field parameters. Temperature increases with Brownian motion and thermophoresis parameters. Nanoparticles concentration decreases on increasing Lewis number and thermophoresis parameter while motile gyrotactic microorganisms profile increases with increasing Lewis and Peclet numbers. Convergence of the solution is found and good agreement is obtained when the results are compared with published work.

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Entropy generation in bioconvection nanofluid flow between two stretchable rotating disks.

This article inquires into the steady boundary layer flow and heat transfer properties of a thin film second-grade fluid through a porous medium past a stretching sheet concerning the effect of viscous dissipation. The aim of the study is to discuss the impacts of film thickness and porosity in the presence of constant reference temperature which completely affect the flow pattern and bring changes in the cooling/heating. The basic governing equations of the problem have been modeled in terms of suitable similarity transformations which result in nonlinear ordinary differential equations with physical conditions. Solution has been obtained by using HAM (Homotopy Analysis Method) which is frequently used for solving nonlinear differential equations encountered in various applied sciences and is found quite useful. Favorable comparison with previously published research papers is performed to show the correlations for the present work. Skin friction coefficient and Nusselt number are presented through tables which describe the verification for the achieved results showing that the thin liquid film results from this study are in close agreement with the results reported in the literature. The physical influences of all the emerging parameters on velocity and temperature fields have been studied graphically and illustrated clearly. The authentication of the present work has been achieved by evaluating the comparison of HAM solution with the numerical method solution. Results achieved by HAM and residual errors are also discussed numerically and graphically.

Thin film flow of a second grade fluid in a porous medium past a stretching sheet with heat transfer

In this research work a new version of Optimal Homotopy Asymptotic Method is applied to solve nonlinear boundary value problems (BVPs) in finite and infinite intervals. It comprises of initial guess, auxiliary functions (containing unknown convergence controlling parameters) and a homotopy. The said method is applied to solve nonlinear Riccati equations and nonlinear BVP of order two for thin film flow of a third grade fluid on a moving belt. It is also used to solve nonlinear BVP of order three achieved by Mostafa et al. for Hydro-magnetic boundary layer and micro-polar fluid flow over a stretching surface embedded in a non-Darcian porous medium with radiation. The obtained results are compared with the existing results of Runge-Kutta (RK-4) and Optimal Homotopy Asymptotic Method (OHAM-1). The outcomes achieved by this method are in excellent concurrence with the exact solution and hence it is proved that this method is easy and effective.

New version of Optimal Homotopy Asymptotic Method for the solution of nonlinear boundary value problems in finite and infinite intervals

A new analytical approach for the research of thin-film flow of magneto hydrodynamic fluid in the presence of thermal conductivity and variable viscosity

This research focuses on the solution of higher order boundary value problems by our proposed method Modified Optimal Homotopy Per- turbation Method (MOHPM). A homotopy with an embedding param- eter and Daftardar-Jafari polynomials are used. To control the conver- gence of solution, some auxiliary functions which depend upon variables and some constants are used. The proposed method is simple, rapid, ef- fective and accurate. The accuracy has been proved by comparing our results with the solutions of optimal homotopy perturbation method (OHPM), optimal homotopy asymptotic method (OHAM), variational iterative method (VIM),variational iteration method using He's poly- nomials (VIMHP), homotopy perturbation method (HPM), Adoman decomposition method (ADM) and Quintic B-Spline Galerkin's scheme.

/pdf/application-of-modified-optimal-homotopy-perturbation-method-s9ukl6agbk.pdf

Liaqat Ali

Papers

Thin film flow of a second grade fluid in a porous medium past a stretching sheet with heat transfer

New version of Optimal Homotopy Asymptotic Method for the solution of nonlinear boundary value problems in finite and infinite intervals

A new analytical approach for the research of thin-film flow of magneto hydrodynamic fluid in the presence of thermal conductivity and variable viscosity

Application of modified optimal homotopy perturbation method to higher order boundary value problems in a finite domain

A novel algorithm for the computation of systems containing different types of integral and integro‐differential equations