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1 – 10 of 38The purpose of this paper is the comparative analysis of Haar Wavelet Method and Optimal Homotopy Asymptotic Method for fractional Fisher type equation. In this paper, two…
Abstract
Purpose
The purpose of this paper is the comparative analysis of Haar Wavelet Method and Optimal Homotopy Asymptotic Method for fractional Fisher type equation. In this paper, two reliable techniques, Haar wavelet method and optimal homotopy asymptotic method (OHAM), have been presented. The Haar wavelet method is an efficient numerical method for the numerical solution of fractional order partial differential equation like the Fisher type. The approximate solutions of the fractional Fisher-type equation are compared with those of OHAM and with the exact solutions. Comparisons between the obtained solutions with the exact solutions exhibit that both the featured methods are effective and efficient in solving nonlinear problems. However, the results indicate that OHAM provides more accurate value than the Haar wavelet method.
Design/methodology/approach
Comparisons between the solutions obtained by the Haar wavelet method and OHAM with the exact solutions exhibit that both featured methods are effective and efficient in solving nonlinear problems.
Findings
The comparative results indicate that OHAM provides a more accurate value than the Haar wavelet method.
Originality/value
In this paper, two reliable techniques, the Haar wavelet method and OHAM, have been proposed for solving nonlinear fractional partial differential equation, i.e. fractional Fisher-type equation. The proposed novel methods are well suited for only nonlinear fractional partial differential equations. It also exhibits that the proposed method is a very efficient and powerful technique in finding the solutions for the nonlinear time fractional differential equations. The main significance of the proposed method is that it requires less amount of computational overhead in comparison to other numerical and analytical approximate methods. The application of the proposed methods for the solutions of time fractional Fisher-type equations satisfactorily justifies its simplicity and efficiency.
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R Mehmood, Dr. Sohail Nadeem and Noreen Akbar
The present critical analysis has been performed to explore the steady stagnation point flow of Jeffery fluid toward a stretching surface, in the presence of convective boundary…
Abstract
Purpose
The present critical analysis has been performed to explore the steady stagnation point flow of Jeffery fluid toward a stretching surface, in the presence of convective boundary conditions. It is assumed that the fluid strikes the wall obliquely. The governing non-linear partial differential equations for the flow field are converted to ordinary differential equations by using suitable similarity transformations. Optimal homotopy analysis method (OHAM) is operated to deal the resulting ordinary differential equations. OHAM is found to be extremely effective analytical technique to obtain convergent series solutions of highly non-linear differential equations. Graphically, non-dimensional velocities and temperature profile are expressed. Numerical values of skin friction coefficients and heat flux are computed. The comparison of results from this paper with the previous existing literature authorizes the precise accuracy of the OHAM for the limited case. The paper aims to discuss these issues.
Design/methodology/approach
The governing non-linear partial differential equations for the flow field are converted to ordinary differential equations by using suitable similarity transformations. OHAM is operated to deal the resulting ordinary differential equations.
Findings
OHAM is found to be extremely effective analytical technique to obtain convergent series solutions of highly non-linear differential equations. Graphically, non-dimensional velocities and temperature profile are expressed. Numerical values of skin friction coefficients and heat flux are computed.
Originality/value
The comparison of results from this paper with the previous existing literature authorizes the precise accuracy of the OHAM for the limited case.
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Jalil Manafian and Cevat Teymuri sindi
This paper aims to discuss the approximate solution of the nonlinear thin film flow problems. A new analytic approximate technique for addressing nonlinear problems, namely, the…
Abstract
Purpose
This paper aims to discuss the approximate solution of the nonlinear thin film flow problems. A new analytic approximate technique for addressing nonlinear problems, namely, the optimal homotopy asymptotic method (OHAM), is proposed and used in an application to the nonlinear thin film flow problems.
Design/methodology/approach
This approach does not depend upon any small/large parameters. This method provides a convenient way to control the convergence of approximation series and to adjust convergence regions when necessary.
Findings
The obtained solutions show that the OHAM is more effective, simpler and easier than other methods. The results reveal that the method is explicit. By applying the method to nonlinear thin film flow problems, it was found to be simpler in applicability, and more convenient to control convergence. Therefore, the method shows its validity and great potential for the solution of nonlinear problems in science and engineering.
Originality/value
The proposed method is tested upon nonlinear thin film flow equation from the literature and the results are compared with the available approximate solutions including Adomian decomposition method (ADM), homotopy perturbation method, modified homotopy perturbation method and HAM. Moreover, the exact solution is compared with the available numerical solutions. The graphical representation of the solution is given by Maple and is physically interpreted.
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The purpose of this study is to analyze magnetohydrodynamic three-dimensional flow of Casson nanofluid over a stretching sheet in presence of thermophoresis and Brownian motion…
Abstract
Purpose
The purpose of this study is to analyze magnetohydrodynamic three-dimensional flow of Casson nanofluid over a stretching sheet in presence of thermophoresis and Brownian motion effects. In contrast, the convective surface boundary conditions with the effects of radiation are applied.
Design/methodology/approach
The governing partial differential equations are transformed into highly nonlinear coupled ordinary differential equations consisting of the momentum, energy and nanoparticle concentration via suitable similarity transformations, which are then solved the using optimal homotopy analysis method (OHAM) a Mathematica Package BVPh2.0.
Findings
The influence of emerging physical flow parameters on fluid velocity component, temperature distribution and nanoparticle concentration are discussed in detail. Also, an OHAM solution demonstrates very good correlation with those obtained in the previously published results. It is noticed that OHAM can overcome the earlier restriction, assumptions and limitation of traditional perturbation method. The main advantage of this method is that OHAM can be applied directly to nonlinear differential equations without using linearization and round-off errors, and therefore, it cannot be affected by error associated to discretization.
Originality/value
Here the approximate solutions are compared with the numerical results published in earlier work.
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Hamza Berrehal, G. Sowmya and Oluwole Daniel Makinde
In heat transfer, fluids and nanoparticles can provide new innovative technologies with potential to adapt the heat transfer fluid’s thermal properties through control over…
Abstract
Purpose
In heat transfer, fluids and nanoparticles can provide new innovative technologies with potential to adapt the heat transfer fluid’s thermal properties through control over particle size, shape and others. This paper aims to examine the effects of spherical and non-spherical (cylinder, disk, platelets, etc.) shapes of silver (Ag) nanoparticles on heat transfer enhancement and inherent irreversibility in hydromagnetic water base nanoliquid flow over a convectively heated stretching sheet with heat generation/absorption.
Design/methodology/approach
Applying suitable similarity constraints, the model partial differential equations are transformed into a set of nonlinear ordinary differential equations. Solutions are obtained analytically via optimal homotopy asymptotic method (OHAM) and numerically via shooting technique coupled with the Runge-Kutta-Fehlberg (RK-F) method.
Findings
The impact of Ag nanoparticle’s shape along with other germane factors, such as Biot number, magnetic field, solid volume fraction and heat source/sink on velocity and thermal profiles, Nusselt number, skin friction coefficient, heat transfer enhancement, rate of entropy generation and irreversibility ratio, are scrutinized via graphical simulations and discussed. This study revealed that cylindrical shape Ag nanoparticles generate high entropy and fluid friction irreversibility, whereas disk shape Ag nanoparticles exhibit high transfer enhancement rate. Moreover, a boost in magnetic field intensity, volume-fraction parameter and Biot number enhances the thermal boundary layer thickness.
Originality/value
The main objective of this work is to examine the different Ag nanoparticles shape effects on the heat transfer enhancement and inherent irreversibility owing to hydromagnetic nanoliquid flow past a convectively heated stretching sheet with heat source/sink, which has not been yet studied. It is hope that this study will bridge the gap in the present literature and serve as impetus to scholars, engineers and industries for more exploration in this direction. The intrinsic nonlinearity of the model equations precludes its exact solution; hence, OHAM and shooting technique coupled with the RK-F method have been used to numerically tackle the problem. Pertinent results are discussed quantitatively and displayed graphically and in tabular form.
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M. Nawaz, A Zeeshan, R Ellahi, S Abbasbandy and Saman Rashidi
The purpose of this paper is to study the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of genetic…
Abstract
Purpose
The purpose of this paper is to study the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of genetic algorithm (GA). The main emphasis is to find the analytical and numerical solutions for the said mathematical model. The work undertaken is a blend of numerical and analytical studies. Effects of active parameters such as: Hartmann number, Prandtl number, Eckert number, Nusselt number, Skin friction and dimensionless fluids parameters on the flow and heat transfer characteristics have been examined by graphs and tables. Compression is also made with the existing benchmark results.
Design/methodology/approach
Analytical solutions of non-linear coupled equations are developed by optimal homotopy analysis method (OHAM). A very effective and higher order numerical scheme hybrid GA and Nelder-Mead optimization Algorithms are used for numerical investigations.
Findings
An excellent agreement with the existing results in limiting sense is noted. It is observed that the radial velocity is an increasing function of dimensionless material parameters α 1, α 2 and β. Temperature increases by increasing the values of M, Pr, Ec and γ. Non-Newtonian parameter β has similar effects on skin friction coefficient and Nusselt number. The wall heat transfer rate is a decreasing function of A and ß whereas it increases by increasing conjugate parameter γ.
Originality/value
The problem under consideration has been widely studied by many investigators due to its importance and engineering applications. But most of the studies as the authors have documented are for Newtonian or viscous fluids. But no such analysis is available in the literature which can describe the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of GA.
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M. Mudassar Gulzar, Shagufta Jabeen, Muhammad Waqas, Sabir Ali Shehzad, Tasawar Hayat and Ahmed Alsaedi
The purpose of this study is to scrutinize the effects of entropy generation and nonlinear mixed convection on the boundary layer flow of second grade fluid induced by stretching…
Abstract
Purpose
The purpose of this study is to scrutinize the effects of entropy generation and nonlinear mixed convection on the boundary layer flow of second grade fluid induced by stretching sheets. Heat transfer effects are accounted in view of viscous dissipation and nonlinear thermal radiation.
Design/methodology/approach
Optimal homotopic asymptotic method procedure is adopted to obtain the analytical solution of nonlinear ordinary differential equations.
Findings
It has been noticed that Hartmann and Brinkman number has reverse characteristics against entropy generation and Bejan number.
Originality/value
To the best of the authors’ knowledge, no such analysis has been reported to date.
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Sumit Gupta, Devendra Kumar, Jagdev Singh and Sandeep Gupta
The purpose of this paper is to investigate the effect of inclined magnetic field, variable viscosity and Cattaneo–Christov heat and mass flux theories on the steady MHD free…
Abstract
Purpose
The purpose of this paper is to investigate the effect of inclined magnetic field, variable viscosity and Cattaneo–Christov heat and mass flux theories on the steady MHD free convective boundary layer flow of viscous, incompressible and electrically conducting water-driven silver and titanium-oxide nanofluids over a vertical stretching sheet.
Design/methodology/approach
The boundary layer equations of momentum, energy and nanoparticle concentration are partial differential equations in nature, which are reduced to nonlinear ordinary differential equations by means of similarity transformations. The resulting nonlinear equations are solved analytically by means of optimal homotopy analysis method.
Findings
Assessments with numerical results are performed and are found to be in an excellent agreement. Numerical results of the skin friction factor, the local Nusselt number and the local Sherwood number are obtained through tables. The effects of various physical parameters on the velocity, temperature and nanoparticles fraction are incorporated through graphs. The study analyzes the efficiency of heat transfer of nanofluids in cooling plants and rubber sheets.
Originality/value
No research works have been conducted to evaluate the effects of various physical phenomena on the copper and titanium nanofluids flow.
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Muhammad Sohail and Syed Tehseen Abbas
This study aims to analyze the Prandtl fluid flow in the presence of better mass diffusion and heat conduction models. By taking into account a linearly bidirectional stretchable…
Abstract
Purpose
This study aims to analyze the Prandtl fluid flow in the presence of better mass diffusion and heat conduction models. By taking into account a linearly bidirectional stretchable sheet, flow is produced. Heat generation effect, thermal radiation, variable thermal conductivity, variable diffusion coefficient and Cattaneo–Christov double diffusion models are used to evaluate thermal and concentration diffusions.
Design/methodology/approach
The governing partial differential equations (PDEs) have been made simpler using a boundary layer method. Strong nonlinear ordinary differential equations (ODEs) relate to appropriate non-dimensional similarity variables. The optimal homotopy analysis technique is used to develop solution.
Findings
Graphs analyze the impact of many relevant factors on temperature and concentration. The physical parameters, such as mass and heat transfer rates at the wall and surface drag coefficients, are also displayed and explained.
Originality/value
The reported work discusses the contribution of generalized flux models to note their impact on heat and mass transport.
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Memoona Bibi, Muhammad Sohail and Rahila Naz
The purpose of this paper is to perform an analytical approximation for the flow of magnetohydrodynamic Carreau fluid with the association of nanoparticles over a rotating disk…
Abstract
Purpose
The purpose of this paper is to perform an analytical approximation for the flow of magnetohydrodynamic Carreau fluid with the association of nanoparticles over a rotating disk. The disk is moving with a constant uniform speed. Governing equations are obtained by using these assumptions in the form of partial differential equations with boundary conditions. These coupled, highly nonlinear equations are transformed into a coupled system of ordinary differential equations by engaging similarity transformation in the rotating frame of reference.
Design/methodology/approach
An efficient and reliable scheme, namely optimal homotopy asymptotic method, is used to obtain the solutions of the arising physical problem, which is further analyzed graphically. After computing the solutions of the arising problem, plots of velocities, temperature and concentration are discussed briefly.
Findings
It has been observed that dimensionless velocity reduced due to magnetic effect between the boundary layer and escalating values of the magnetic parameter upsurges the temperature and concentration profiles. Contour plots and numerical results are given for local numbers like skin friction coefficient, Nusselt number and Sherwood number.
Originality/value
The work presented in this manuscript is neither published nor submitted anywhere for the consideration/publications. It is a novel work.
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