Showing papers on "Homotopy analysis method published in 2018"

On the analysis of fractional diabetes model with exponential law

Abstract: In this work, we study the diabetes model and its complications with the Caputo–Fabrizio fractional derivative. A deterministic mathematical model pertaining to the fractional derivative of the diabetes mellitus is discussed. The analytical solution of the diabetes model is derived by exerting the homotopy analysis method, the Laplace transform and the Pade approximation. Moreover, existence and uniqueness of the solution are examined by making use of fixed point theory and the Picard–Lindelof approach. Ultimately, for illustrating the obtained results some numerical simulations are performed.

European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

Abstract: Recently, fractional differential equations (FDEs) have attracted much more attention in modeling real-life problems. Since most FDEs do not have exact solutions, numerical solution methods are used commonly. Therefore, in this study, we have demonstrated a novel approximate-analytical solution method, which is called the Laplace homotopy analysis method (LHAM) using the Caputo–Fabrizio (CF) fractional derivative operator. The recommended method is obtained by combining Laplace transform (LT) and the homotopy analysis method (HAM). We have used the fractional operator suggested by Caputo and Fabrizio in 2015 based on the exponential kernel. We have considered the LHAM with this derivative in order to obtain the solutions of the fractional Black–Scholes equations (FBSEs) with the initial conditions. In addition to this, the convergence and stability analysis of the model have been constructed. According to the results of this study, it can be concluded that the LHAM in the sense of the CF fractional derivative is an effective and accurate method, which is computable in the series easily in a short time.

Modeling and analyzing flow of third grade nanofluid due to rotating stretchable disk with chemical reaction and heat source

Abstract: This article addresses flow of third grade nanofluid due to stretchable rotating disk. Mass and heat transports are analyzed through thermophoresis and Brownian movement effects. Further the effects of heat generation and chemical reaction are also accounted. The obtained ODE's are tackled computationally by means of homotopy analysis method. Graphical outcomes are analyzed for the effects of different variables. The obtained results show that velocity reduces through Reynolds number and material parameters. Temperature and concentration increase with Brownian motion and these decrease by Reynolds number.

Slip flow of Eyring-Powell nanoliquid film containing graphene nanoparticles

Abstract: The purpose of the present study is to discuss the effects of graphene nanoparticles on two dimensional magnetohydrodynamic unsteady flow and heat transfer in a thin film Eyring Powell nanofluid past a stretching sheet using velocity slip condition. The contents of graphene nanoparticles increase simultaneously the thermal conductivity and stability when incorporated into the dispersion of water based liquid network. The basic governing equations for velocity and temperature of the Eyring Powell nanofluid film with the boundary conditions easily and simply provide the transformed nonlinear coupled differential equations by employing appropriate similarity transformations. The modeled equations have been evaluated by using an efficient approach through homotopy analysis method which lead to detailed expressions for the velocity profile and temperature distribution. The present work discusses the salient features of all the indispensable parameters of velocity and temperature profiles which have been displayed graphically and illustrated. Skin friction and Nusselt number show an excellent agreement with the published work. The results are useful in the analysis, design of coating and cooling/heating processes.

Analytical Solutions of Fractional Order Diffusion Equations by Natural Transform Method

Abstract: In this article, we develop an analytical method for solving fractional order partial differential equations Our method is the generalizations of homotopy perturbations Laplace transform method and homotopy perturbations Sumudu transform method The solutions obtained using the proposed method implies that the method is highly accurate and easy to implement The proposed method can be easily applied to a large variety of problems, which are modeled in terms of fractional order partial differential equations Some test problems are solved to show the accuracy of the proposed method Some results are shown graphically also

Entropy generation in hydromagnetic nanofluid flow over a non-linear stretching sheet with Navier’s velocity slip and convective heat transfer

Abstract: The intention behind carrying out this research work is to investigate the unsteady hydromagnetic boundary layer flow of a thermally radiating nanofluid past a non-linear stretching sheet embedded in a porous medium in the presence of an externally applied magnetic field along with Navier’s velocity slip. The governing partial differential equations, defining the flow regime, are transformed into a system of ordinary differential equations by employing suitable similarity transformation. Optimal Homotopy Analysis Method has been incorporated in order to solve the converted non-linear coupled equations. The impact of several regulatory flow parameters on the temperature, velocity, and nanoparticle concentration are explained via graphs, while the variation of some useful engineering quantities such as the Nusselt number, skin friction co-efficient, and Sherwood number are interpreted through tabular values. An analysis regarding entropy generation of the system is also presented. Furthermore, on the numeric data of the skin friction coefficient and Nusselt number, a linear and quadratic multiple linear regression analysis has also been performed. The findings of the present analysis reveal that the velocity slip, unsteadiness and the nonlinearity of the stretching velocity lead to a fall in the velocity profile of the nanofluid.

Soret and Dufour effects on three dimensional Oldroyd-B fluid

Abstract: In this article, a realistic three dimensional magnetohydrodynamic flow of an Oldroyd-B fluid is studied after developing a convergent analytic scheme. Soret and Dufour effects with mixed convection are taken into account. The governing highly non-linear partial differential equations are transformed into the system of ordinary differential equations using similarity transformations. The resulting problems are computed by homotopy analysis method (HAM). Profiles of dimensionless velocities, temperature and concentration are plotted and discussed for various emerging physical parameters. Numerical values of physical quantities of interest such as local Nusselt number and local Sherwood number are tabulated. A comparative study with existing literature are found in an excellent agreement.

The experimental study to examine the stable dispersion of the graphene nanoparticles and to look at the GO–H 2 O nanofluid flow between two rotating disks

Abstract: The nanofluid analysis has been carried out as a function of temperature and this idea is utilized to study the graphene oxide (GO) water-based nanofluid from both experimental and numerical perspectives. Various spectral investigations were used to endorse the successful synthesis of graphene oxide. The obtained GO exhibits large size platelet morphology with stable dispersion in water. The experimental procedure of the preparation of nanofluid and its outputs has been analyzed with numerical data. The obtained results from the Chebyshev spectral scheme were transformed into a mathematical model considering the 3D flow of the dispersed GO nanofluid between two parallel rotating disks using the governing Navier–Stokes equations and energy equation with the utilization of Von Karman similarity transformations. The obtained nonlinear differential equations have been examined through a recently fashionable analytic approximation method called the Optimal Homotopy Analysis Method (OHAM). Opposite and same direction rotational effects have been conferred on the flow characteristics. To analyze how the velocities, pressure and temperature fields are affected by various parameters, plots have been displayed. Convergence of the obtained results has been authenticated with residual errors physically and numerically. Moreover, the physical parameters impact, such as local Nusselt number and skin friction coefficients are obtained through numerical data and inspect.

Flow and heat transfer in water based liquid film fluids dispensed with graphene nanoparticles

Abstract: The unsteady flow and heat transfer characteristics of electrically conducting water based thin liquid film non-Newtonian (Casson and Williamson) nanofluids dispensed with graphene nanoparticles past a stretching sheet are considered in the presence of transverse magnetic field and non-uniform heat source/sink. Embedding the graphene nanoparticles effectively amplifies the thermal conductivity of Casson and Williamson nanofluids. Ordinary differential equations together with the boundary conditions are obtained through similarity variables from the governing equations of the problem, which are solved by the HAM (Homotopy Analysis Method). The solution is expressed through graphs and illustrated which show the influences of all the parameters. The convergence of the HAM solution for the linear operators is obtained. Favorable comparison with previously published research paper is performed to show the correlation for the present work. Skin friction coefficient and Nusselt number are presented through Tables and graphs which show the validation for the achieved results demonstrating that the thin liquid films results from this study are in close agreement with the results reported in the literature. Results achieved by HAM and residual errors are evaluated numerically, given in Tables and also depicted graphically which show the accuracy of the present work.

Entropy Generation on Nanofluid Thin Film Flow of Eyring–Powell Fluid with Thermal Radiation and MHD Effect on an Unsteady Porous Stretching Sheet

Abstract: This research paper investigates entropy generation analysis on two-dimensional nanofluid film flow of Eyring-Powell fluid with heat amd mass transmission over an unsteady porous stretching sheet in the existence of uniform magnetic field (MHD). The flow of liquid films are taken under the impact of thermal radiation. The basic time dependent equations of heat transfer, momentum and mass transfer are modeled and converted to a system of differential equations by employing appropriate similarity transformation with unsteady dimensionless parameters. Entropy analysis is the main focus in this work and the impact of physical parameters on the entropy profile are discussed in detail. The influence of thermophoresis and Brownian motion has been taken in the nanofluids model. An optima approach has been applied to acquire the solution of modeled problem. The convergence of the HAM (Homotopy Analysis Method) has been presented numerically. The disparity of the Nusslet number, Skin friction, Sherwood number and their influence on the velocity, heat and concentration fields has been scrutinized. Moreover, for comprehension, the physical presentation of the embedded parameters are explored analytically for entropy generation and discussed.

Analytical investigation of third grade nanofluidic flow over a riga plate using Cattaneo-Christov model

Abstract: This article addresses third grade nanofluidic flow instigated by riga plate and Cattaneo-Christov theory is adopted to investigate thermal and mass diffusions with the incorporation of newly eminent zero nanoparticles mass flux condition. The governing system of equations is nondimensionalized through relevant similarity transformations and significatory findings are attained by using optimal homotopy analysis method. The behaviors of affecting parameters for velocity, temperature and concentration profiles are depicted graphically and also verified through three dimensional patterns for some parameters. Values of skin friction coefficient and Nusselt number with the apposite discussion have been recorded. The current results reveal that temperature and concentration profiles experience decline when thermal and concentration relaxation parameters are augmented respectively.

Three-dimensional flow of Prandtl fluid with Cattaneo-Christov double diffusion

Abstract: This research paper intends to investigate the 3D flow of Prandtl liquid in the existence of improved heat conduction and mass diffusion models. Flow is created by considering linearly bidirectional stretchable sheet. Thermal and concentration diffusions are considered by employing Cattaneo-Christov double diffusion models. Boundary layer approach has been used to simplify the governing PDEs. Suitable nondimensional similarity variables correspond to strong nonlinear ODEs. Optimal homotopy analysis method (OHAM) is employed for solutions development. The role of various pertinent variables on temperature and concentration are analyzed through graphs. The physical quantities such as surface drag coefficients and heat and mass transfer rates at the wall are also plotted and discussed. Our results indicate that the temperature and concentration are decreasing functions of thermal and concentration relaxation parameters respectively.

Hydromagnetic mixed convective flow over a wall with variable thickness and Cattaneo-Christov heat flux model: OHAM analysis

Abstract: The effect of Cattaneo-Christov heat flux model for the hydro-magnetic mixed convective flow of a non-Newtonian fluid is presented. The flow over a wall having variable thickness is anticipated under the influence of transverse magnetic field and internal heat generation/absorption effects. Mathematical formulation has been performed by making use of the suitable transformations. Convergence analysis has been performed and the optimal values are computed by employing optimal homotopy analysis method. The effects of physical parameters are elaborated in depth via graphical and numerical illustrations.

Entropy Generation in MHD Eyring–Powell Fluid Flow over an Unsteady Oscillatory Porous Stretching Surface under the Impact of Thermal Radiation and Heat Source/Sink

Abstract: In this article, we have briefly examined the entropy generation in magnetohydrodynamic (MHD) Eyring–Powell fluid over an unsteady oscillating porous stretching sheet. The impact of thermal radiation and heat source/sink are taken in this investigation. The impact of embedded parameters on velocity function, temperature function, entropy generation rate, and Bejan number are deliberated through graphs, and discussed as well. By studying the entropy generation in magnetohydrodynamic Eyring–Powell fluid over an unsteady oscillating porous stretching sheet, the entropy generation rate is reduced with escalation in porosity, thermal radiation, and magnetic parameters, while increased with the escalation in Reynolds number. Also, the Bejan number is increased with the escalation in porosity and magnetic parameter, while increased with the escalation in thermal radiation parameter. The impact of skin fraction coefficient and local Nusselt number are discussed through tables. The partial differential equations are converted to ordinary differential equation with the help of similarity variables. The homotopy analysis method (HAM) is used for the solution of the problem. The results of this investigation agree, satisfactorily, with past studies.

Reissner stationary variational principle for nonlocal strain gradient theory of elasticity

Abstract: The general form of Reissner stationary variational principle is established in the framework of the nonlocal strain gradient theory of elasticity. Including two size-dependent characteristic parameters, the nonlocal strain gradient elasticity theory can demonstrate the significance of the strain gradient as well as the nonlocal elastic stress field. Based on the Reissner functional, the governing differential and boundary conditions of dynamic equilibrium and differential constitutive equations of the classical and first-order nonlocal stress tensor are derived in the most general form. Additionally, the boundary congruence conditions are formulated and discussed for the nonlocal strain gradient theory. To exhibit the application value of Reissner variational principle, it is employed to examine the nonlinear vibrations of size-dependent Bernoulli-Euler and Timoshenko beams. In the case of immovable boundary conditions, employing the weighted residual Galerkin method, the homotopy analysis method is also utilized to determine the closed form analytical solutions of the geometrically nonlinear vibration equations. Consequently, the analytical expressions for the nonlinear natural frequencies of Bernoulli-Euler and Timoshenko nonlocal strain gradient beams are derived.

Double stratification effects in chemically reactive squeezed Sutterby fluid flow with thermal radiation and mixed convection

Abstract: A current analysis is carried out to study theoretically the mixed convection characteristics in squeezing flow of Sutterby fluid in squeezed channel. The constitutive equation of Sutterby model is utilized to characterize the rheology of squeezing phenomenon. Flow characteristics are explored with dual stratification. In flowing fluid which contains heat and mass transport, the first order chemical reaction and radiative heat flux affect the transport phenomenon. The systems of non-linear governing equations have been modulating which then solved by mean of convergent approach (Homotopy Analysis Method). The graphs are reported and illustrated for emerging parameters. Through graphical explanations, drag force, rate of heat and mass transport are conversed for different pertinent parameters. It is found that heat and mass transport rate decays with dominant double stratified parameters and chemical reaction parameter. The present two-dimensional examination is applicable in some of the engineering processes and industrial fluid mechanics.

Modelling Study on Internal Energy Loss Due to Entropy Generation for Non-Darcy Poiseuille Flow of Silver-Water Nanofluid: An Application of Purification

Abstract: In this paper, an analytical study of internal energy losses for the non-Darcy Poiseuille flow of silver-water nanofluid due to entropy generation in porous media is investigated. Spherical-shaped silver (Ag) nanosize particles with volume fraction 0.3%, 0.6%, and 0.9% are utilized. Four illustrative models are considered: (i) heat transfer irreversibility (HTI), (ii) fluid friction irreversibility (FFI), (iii) Joule dissipation irreversibility (JDI), and (iv) non-Darcy porous media irreversibility (NDI). The governing equations of continuity, momentum, energy, and entropy generation are simplified by taking long wavelength approximations on the channel walls. The results represent highly nonlinear coupled ordinary differential equations that are solved analytically with the help of the homotopy analysis method. It is shown that for minimum and maximum averaged entropy generation, 0.3% by vol and 0.9% by vol of nanoparticles, respectively, are observed. Also, a rise in entropy is evident due to an increase in pressure gradient. The current analysis provides an adequate theoretical estimate for low-cost purification of drinking water by silver nanoparticles in an industrial process.

Three dimensional radiative flow of magnetite-nanofluid with homogeneous-heterogeneous reactions

Abstract: Present communication deals with the effects of homogeneous-heterogeneous reactions in flow of nanofluid by non-linear stretching sheet. Water based nanofluid containing magnetite nanoparticles is considered. Non-linear radiation and non-uniform heat sink/source effects are examined. Non-linear differential systems are computed by Optimal homotopy analysis method (OHAM). Convergent solutions of nonlinear systems are established. The optimal data of auxiliary variables is obtained. Impact of several non-dimensional parameters for velocity components, temperature and concentration fields are examined. Graphs are plotted for analysis of surface drag force and heat transfer rate.

Study of two-dimensional boundary layer thin film fluid flow with variable thermo-physical properties in three dimensions space

Abstract: The conversion of study in two dimensional (x, y) medium into three dimensions space (x, y, z) of a magnetohydrodynamic mixed convective heat and mass transfer boundary layer flow of a thin film second-grade fluid with temperature dependent viscosity and thermal conductivity in the presence of thermal radiation and viscous dissipation past a stretching sheet is analyzed. The occurrence of Hall current in two dimensional (x, y) medium produces a force in z-direction which generates a cross flow in that direction and so the motion is made in three dimensions space (x, y, z). Similarity transformations are used and the transformed system of equations of the problem has been solved by utilizing homotopy analysis method. The salient impacts of the emerging parameters on velocities, temperature and concentration fields have been displayed graphically and illustrated.

Non-Newtonian nanoliquids thin-film flow through a porous medium with magnetotactic microorganisms

Abstract: Gravity-driven non-Newtonian nanoliquids (Casson and Williamson) thin-film flow through a porous medium containing both nanoparticles and magnetotactic microorganisms is analyzed using passively controlled nanofluid model boundary conditions. Buongiorn’s nanofluid model is used. The thin bio-nanoliquid films contain the copper nanoparticles and magnetotactic microorganisms simulating the forced/free bioconvection in buoyancy-driven flow. The comparison between the role of both the thin nanoliquid films has carefully noticed and discussed the differences in behaviors in detail. The governing equations accompanying the boundary conditions of the problem are reduced to non-linear differential equations by applying particular transformations. These equations along with the boundary conditions are solved analytically by employing homotopy analysis method. The solution consists of the expressions of four different profiles, and with the help of different curves, these profiles are shown graphically and discussed for the impacts of each parameter.

Melting heat transfer and induced magnetic field effects on flow of water based nanofluid over a rotating disk with variable thickness

Abstract: The present article examines the effect of induced magnetic field in stagnation point flow of nanofluid by a rotating disk with variable thickness. Nanofluid comprises water and aluminium oxide. Mathematical modeling is presented in presence of melting heat transfer and heat generation/absorption aspects. The governing equations are transformed into system of ordinary differential equations by similarity transformations. Nonlinear systems are solved by Homotopy Analysis Method (HAM). Convergence of derived solutions is ensured explicitly. Velocity components, induced magnetic field, temperature, skin friction coefficient and local Nusselt number are examined for influential parameter in this consideration. It is found that axial velocity and axial induced magnetic field are decreasing function of thickness coefficient of disk. Magnitude of volume fraction of silver nanoparticles reduces for radial and azimuthal velocities while increases for temperature. Induced magnetic profile decreases for reciprocal of magnetic Prandtl number. Magnitude of local Nusselt number reduces for melting heat transfer.

On MHD radiative Jeffery nanofluid flow with convective heat and mass boundary conditions

Abstract: The prime objective of present exploration is to study effects of magnetohydrodynamic, Joule heating and thermal radiation on an incompressible Jeffrey nanofluid flow over a linearly stretched surface. Simultaneous effects of convective heat and mass boundary conditions are also considered. Obtained system of boundary layer equations is converted into ordinary differential equations with high linearity using appropriate transformations. Analytical solutions via homotopy analysis method are obtained and deliberated accordingly. Discussion of graphs pertaining different prominent parameters is also added. Numerical values of skin friction coefficient, local Nusselt and Sherwood numbers are also given and well deliberated. It is noted that higher values of thermophoretic parameter boost temperature and concentration distributions. Moreover, temperature field is an increasing function of radiation parameter.

Exponentially varying viscosity of magnetohydrodynamic mixed convection Eyring-Powell nanofluid flow over an inclined surface

Abstract: This paper explores the theoretical study of the steady incompressible two dimensional MHD boundary layer flow of Eyring-Powell nanofluid over an inclined surface. The fluid is considered to be electrically conducting and the viscosity of the fluid is assumed to be varying exponentially. The governing partial differential equations (PDE’s) are reduced into ordinary differential equations (ODE’s) by applying similarity approach. The resulting ordinary differential equations are solved successfully by using Homotopy analysis method. The impact of pertinent parameters on velocity, concentration and temperature profiles are examined through graphs and tables. Also coefficient of skin friction, Sherwood and Nusselt numbers are illustrated in tabular and graphical form.

Effects of heat and mass transfer on unsteady boundary layer flow of a chemical reacting Casson fluid

Abstract: In this study, an endeavor is to observe the unsteady two-dimensional boundary layer flow with heat and mass transfer behavior of Casson fluid past a stretching sheet in presence of wall mass transfer by ignoring the effects of viscous dissipation. Chemical reaction of linear order is also invoked here. Similarity transformation have been applied to reduce the governing equations of momentum, energy and mass into non-linear ordinary differential equations; then Homotopy analysis method (HAM) is applied to solve these equations. Numerical work is done carefully with a well-known software MATHEMATICA for the examination of non-dimensional velocity, temperature, and concentration profiles, and then results are presented graphically. The skin friction (viscous drag), local Nusselt number (rate of heat transfer) and Sherwood number (rate of mass transfer) are discussed and presented in tabular form for several factors which are monitoring the flow model.

Impact of Thermal Radiation and Heat Source/Sink on Eyring–Powell Fluid Flow over an Unsteady Oscillatory Porous Stretching Surface

Abstract: The main intention of this article is to examine the heat transmission of the flow of Eyring–Powell fluid over an unstable oscillatory porous stretching surface. The effect of thermal radiation on the fluid flow is investigated, where the flow is actuated by the unbounded flexible surface which is extended occasionally to and fro in its plane. The rudimentary leading equations are changed to differential equations through the use of applicable similarity variables. An optimal and numerical approach has been used to find the solution of the modeled problems. The convergence of the homotopy analysis method has been shown numerically. The homotopy analysis method predictions of the structures formed are in close agreement with the obtained results from the numerical method. Comparisons between HAM and numerical methods are shown graphically as well as numerically. The convergence of this method has been shown numerically. The impacts of the skin friction and heat flux are shown through a table. The influences of the porosity, oscillation, thermal radiation, and heat absorption/generation are the main focus of this work. The consequences of emerging parameters are demonstrated through graphs.